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Today's topics:
* Queuing theory... - 4 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/853742404d1ba2a6?hl=en
* Threadpool with priorities version 1.54 - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/3a765b03ab36c1b3?hl=en
* Concurrent FIFO Queue 1.01 - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/73de55ea89ca5de7?hl=en
* An M/M/n queuing model simulation - 3 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/a4d462b8599c98e1?hl=en
* About Locks... - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/7d83cd7d9303f972?hl=en
* Formatting text to xml - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/420a40ecbde861df?hl=en
* Haswell AVX2 for Simple Integer Bitwise Operations - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/6238df8d2ec4f8bd?hl=en
* SOLUTIONS MANUAL: An Introduction to Economic Dynamics by Ronald Shone - 1
messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/0dc89b64f208cf3d?hl=en
* NatSys Lock-free Queue vs LMAX Disruptor vs boost::lockfree::queue - 2
messages, 2 authors
http://groups.google.com/group/comp.programming.threads/t/7d8862a3ca3cfbe0?hl=en
* Scalable RWLock and FIFO fairness - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/a2868b50b829fb53?hl=en
* Again my scalable RWLock and FIFO fairness - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/1474a413ea8fa68f?hl=en
* I have to be smart and scalable RWLOCK - 1 messages, 1 author
http://groups.google.com/group/comp.programming.threads/t/9b91bbd7fc319c85?hl=en
* Intelligence... - 8 messages, 3 authors
http://groups.google.com/group/comp.programming.threads/t/eb2b878ee4caef93?hl=en
==============================================================================
TOPIC: Queuing theory...
http://groups.google.com/group/comp.programming.threads/t/853742404d1ba2a6?hl=en
==============================================================================
== 1 of 4 ==
Date: Tues, Dec 17 2013 1:48 pm
From: aminer
Hello,
I want to talk about the mathematical modeling of
queuing networks , if you have noticed in a webserver
that uses a distributed database , the database
have to be modeled as a queuing system with an
hyperexponential service, but this will complicate the
mathematical modeling of the webserver since the
database have to be modeled as an M/G/1 queuing system,
so we have to simplify the mathematical modeling , so if
for exemple the database's write transactions takes in average
much more time than a database's read transaction so we have
to choose the worst case scenario , that means we have to choose
the rate of the database's write transactions as the rate
of the arrival to the queuing system of the database so
that the database can be modeled as an M/M/1 queuing system
(M: means markovian), so that the webserver can finally be
modeled as two M/M/1 queuing system in series, one for
the database and one for the internet network.
But there is still a problem, if we want to also resolve the
worst case scenario when for exemple thousands of custumers
arrive at the same time to the webserver.. so the webserver
have to be modeled taking into acount this worst case scenario...
Here is the matematical modeling of an M/M/1 queuing system:
We already know that to satisfy a Poisson process we must
have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
that means the counting increments must be independant.
We have the following relation between the Poisson law
and Exponential law:
the expected value E(X exponential) = 1 / E(X poisson)
so f the arrival is poissonian then the interarrivals are
exponential..
Now i will calculate the expected mean waiting time and
mean number of custumers in the queuing system:
The Little law says that the waiting time in the queuing system:
Ws = Ls/lambda
And the waiting time in the queue of the queuing system is:
Wq = Ws - 1/Mu
= Ls/lambda - 1/Mu
And the Little law gives us the expected mean number of custumers in the
queue:
Lq = Wq*lambda = Ls - Phi et Phi = lamda/Mu
That implies:
Ls - Lq = Phi
When the system is in a stationary state , the balance equations gives:
State rate in = rate out
state 0: Mu * P1 = lambda*P0
state 1: lambda*P0 + Mu*P2 = lambda*P1 + Mu*P1
state 2: lambda*P1 + Mu*P3 = lambda*P2 + Mu*P2
...
state n: lambda*Pn-1 + Mu*Pn+1 = lambda*Pn + Mu*Pn
And that gives us the following balance equations:
lambda * P0 = Mu*P1 <=> P1 = (lambda/Mu)*P0
lambda * P1 = Mu*P2 <=> P1 = (lambda/Mu)^2*P0
lambda * P2 = Mu*P3 <=> P1 = (lambda/Mu)^3*P0
...
lambda * Pn-1 = Mu*Pn <=> P_n = (lambda/Mu)^k*P0 [1]
Note: P0 means the probality of having zero custumer in the queuing system.
and ^ means power.
And we have also that:
Sum(n=0 -> infini) (Pn) = 1 that means the sum of probabilities equal 1
And [1] gives us:
Sum(n=0 -> infini) (Phi^n*P0) =1
And by resolving the sum if a geometric series that gives us:
P0 * 1/(1-Phi) = 1 => P0 = 1 - Phi and Phi < 1
And [1] gives us:
Pn = (1-Phi) Phi^n
And we have that means the mean expected number iof custumer in the
queing system is:
Ls = Sum(n=0 -> infini) (n*Pn)
That implies:
Ls = Sum(n=0 -> infini) (n*(1-Phi)*Phi^n) = Phi/1-Phi et Phi<1
and we have the mean expected number of custumer in the queue of the
queing system is :
Lq = Ls -Phi = Phi^2/ (1-Phi) et Phi<1
Little law gives us the mean waiting time in the system and in the queue:
Ws = 1/lambda * Phi/(1-Phi) and Phi<1
et
Wq= 1/lambda * Phi^2/(1-Phi) and Phi<1
I have just read the following page, look at the the USL
(Universal Law of Computational Scalability) of Dr. Gunther,
he wrote this: (See: http://en.wikipedia.org/wiki/Neil_J._Gunther )
--------------
The relative capacity C(N) of a computational platform is given by:
C(N) = N
------------------------------------------
1 + α (N - 1) + ß N (N - 1)
where N represents either the number of physical processors
in the hardware configuration or the number of users driving the
software application. The parameters α and ß represent respectively
the levels of contention (e.g., queueing for shared resources) and
coherency delay (i.e., latency for data to become consistent) in the
system. The ß parameter also quantifies the retrograde throughput
seen in many stress tests but not accounted for in either Amdahl's law
or event-based simulations.
----------
His website: http://www.perfdynamics.com/
If you read carefully , you will see that Dr. Gunther is using this
model to predict scalability after he simulates a relatively small
number of vusers in LoadRunner ( because of licensing costs, it's
cost-effective) and after that he finds the coefficients of the
2nd-degree polynomial (quadratic equation) and then transform
those coefficients back to the USL parameters using the α = b - a
and ß = a.
And then he is extrapolating with the USL model to higher loads
to predict scalability.
He is also applying the model to webservers with heterogeneous
workloads. like in the following page:
http://perfdynamics.blogspot.com/2009/04/assessing-usl-scalability-wi...
Now my question follows:
Suppose we have obtained a small number of measured load-points
with Loadrunner or others tools, and we calculated the USL equation
to predict scalability of a webserver , how the USL model can predict
if the scalability/performance is limited by the network bandwidth
and not the server ? I think USL can not predict this.
When we are modeling webservers , we have to include
the network node in our network queuig model (that includes
the computer server queue) , and since the service in the
computer server is comprised of multiple services (when we
are using htmls , databases etc.) the network queue will not
be markovian in its service , and we have to model the network
queue as an M/G/1 and this will complicate the mathematical
analytical modeling...
So, i think the best way is to use a webserver stress tool
like http://fwptt.sourceforge.net/
You can even test the webserver with an heterogeneous
workloads by starting multiple fwtpp processes, and
you should increase the number of threads to 5 and after
that to 10 threads, 15 ... and so on until the webserver
applications stops responding propperly(and this will inform
on the maximum number of users that you can have in the same time...)
and as you are stress testing you can even see (by testing/measuring
it) if the network bandwidth is not the bottleneck... and this can
not be done by the USL model.
We already know that to satisfy a Poisson process we must
have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
that means the counting increments must be independant.
We have the following relation between the Poisson law
and Exponential law:
the expected value E(X exponential) = 1 / E(X poisson)
and if the arrival is poissonian then the interarrivals are
exponential..
Now what about a webserver ?
I have read the following paper:
http://docs.google.com/viewer?a=v&q=cache:JFYCp_dSPP4J:citeseerx.ist....
And it says that a simple model with M/M/1/k with FCFS discipline
can predict webserver performance quite well..
Hence, i think we can model our webserver over internet
with 3 queues connected as a Jackson Network like this
A -> M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: is the arrival rate
and we have the following:
Ni: number of jobs in each queue
Ui: utilization of each queue
Ni = Ui / (1-Ui)
Adding all the Ni in each individual queue will give the
average number of jobs in the entire queuing network.
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
And after that from the mathematical analytical equation
we can simulate the jackson queuing network that model our
webservers...
Now there is still an important question that i have:
Our analytical jackson network model can give us insight
on the webservers behavivior.. but the difficulty that i find in
practice is that: suppose we have found the right parametters
that we want to choose, like for example the service rate of
the M/M/1 Server Queue , how , from this service rate, can
we buy the right computer that satisfies the service rate
that we want ?
We say in OR that:
"Understanding the behavior of a system is what Queueing Theory
and Little's Law is all about. But, managing a Queue requires not
just understanding the behavior of a system, but also in-depth
knowledge of how to improve a system - improving both aspects
of Queueing will mean a better, more efficient and cost-effective
system and, more importantly, a much better customer experience."
I wrote before that:
---
"It says that a simple model with M/M/1/k with FCFS discipline
can predict webserver performance quite well..
Hence, i think we can model our webserver over internet
with 3 queues connected as a Jackson Network like this
A -> M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: the arrival rate
and we have the following:
Ni: number of jobs in each queue
Ui: utilization of each queue
Ni = Ui / (1-Ui)
Adding all the Ni in each individual queue will give the
average number of jobs in the entire queuing network.
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
And after that from the mathematical analytical equation
we can simulate the jackson queuing"
--
As you have noticed , this mathematical model of
this jackson network does in fact take into account
the M/M/1 Network queue node , the USL model can not
do this... and with this performance data from the mathematical
analytical model simulation we can for example validate
the performance data of the fwptt stress webserver simulation..
But you have to take into account worst cases and the
peak traffic loads...
Let for example we have a a webserver hosting html pages
and it is receiving 1000000 HTTP operations
per day with an average file size of 10 KB.
What would be the network bandwidth required for this website
considering peak traffic if the peak traffic load from past
observations was four times greater than average loads?
Required bandwidth is solved by the following equation:
HTTP op/sec x average file size or
1000000 HTTP ops per day =1000000/24 = 41,667 op/hour =
41,667/3600= 11.6 HTTP ops/sec
The needed bandwidth is
11.6 HTTP ops/sec X 10 KB/HTTP op = 116 KB/sec = 928 Kbps.
If we assume a protocol overhead of 20% then the actual throughput
required is 928 Kbps X 1.2 = 1,114 Kbps.
However if peak loads, as i said before, is as much as
4 times greater, the bandwidth required to handle spikes
would be 4 X 1,114 Kbps = 4.456 Mbps.
So you have to think also about the cost of this line...
I will add the following:
As you have noticed i said that:
"As you have noticed , this mathematical model of
this jackson network does in fact take into account
the M/M/1 Network queue node , the USL model can not
do this... and with this performance data from the mathematical
analytical model simulation we can for example validate
the performance data of the fwptt stress webserver simulation.."
and i said that:
"Hence, i think we can model our webserver over internet
with 3 queues connected as a Jackson Network like this
An M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client queue"
And of course on Capacity Planning for Enterprise Datacenters
and Websites , you can mirror many computer servers and load
balance between them with a software... to make the system much
FASTER, and this will be modeled as a jackson network like this:
A -> M/M/n Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: the arrival rate to the system
But there is still an important thing , as i have showed before
on my calculations:
"However if peak loads, as i said before, is as much as
4 times greater, the bandwidth required to handle spikes
it would be 4 X 1,114 Kbps = 4.456 Mbps.
So you have to think also about the cost of this line..."
I think that you have also to take into account the knee utilisation
of your M/M/n Servers Queues, if for example the number of computer
servers is 8 and the Knee is 74% that means that in our previous
example the bandwidth must equal to:
74% X 4.456 Mbps = 3.297 Mbps.
Cause as you know, above this Knee of 74% for 8 servers
the curve of the waiting time does grow quickly ..
And we have to take into account the cost of the line ...
Let us take another example:
In the network node of the Jackson network, there is three
main parameters that are responsable for its performance:
latency, bandwidth and utilization.
Now, if for example you take a look at my provider
http://www.videotron.com/service/internet-services/internet-access/hi...
My upload network speed is clearly 820 Kbs => 102.5 Kbytes/sec
Hence, if the average file size on my web site is for
example 25 Kbyte and the protocol overhead is 20%, that
means that the file size will be in average:
25 * 120% = 30 Kbyte
And if the Knee of the M/M/1 queuing node in our Jackson network
is 50%, then the bandwidth available will be reduced to
102.5 Kbytes/sec * 50% = 51.25 Kbytes/sec
If the download speed of the client is for example 7.5 Mbps,
that means that the file can be retrieved in no more than
30 / 51.25 = 0.585 second = 585 milliseconds.
But if we assume for example that a typical web visitor
to my web site is spending 585 milliseconds retrieving the
page and 60 seconds reading the HTML page THEN each client
on average only requires:
0.585 / (0.585 + 60) = 9.6% of the bandwidth that is allocated to
it..
but in practice i think we have to consider the worst case
scenarios..
So, since we can support a constraint of no more than 5 seconds
in the T (average response time), that means:
585 ms * X = 5000 milliseconds => X = 8.54
Hence, in worst case , my network node can not support more
than 8.54 users in the same time...
So, on *average* my network node can support:
(8.54 * 86400) / 5 = 147571 users per day
I wrote before that:
--
And of course on Capacity Planning for Enterprise Datacenters
and Websites , you can mirror many computer servers and load
balance between them with a software... to make the system much
FASTER, and this will be modeled as a Jackson network like this:
(1)
A -> M/M/n Server Queue -> M/M/1 Network queue ->
-> M/M/1 Client queue -> A
A: the arrival rate to the system"
--
We know also from an operational law of queuing theory that:
(2) the rate of job leaving any stable node must equal
its arrival rate.
(2) is from the Equivalence property.
Equivalence property: Assume that a service facility with
s servers and infinite queue has a Poisson input with
parameter lambda and the same exponential service-time
distribution with parameter Mu for each server (the M/M/s model),
where s * Mu > lambda. Then the steady-state output of
this service facility is also poisson process with parameter
lambda.
We know for an M/M/c queue that:
Note: try to add servers with almost the same hardware
configuration...
C(c, U) = Erlang formula = P(c) / (1 - Utilization)
note: c the number of servers..
P(c): means the probability that all the servers are busy
P(0): means the probability that there is no waiting time in the
queue, that means also: AT LEAST one server among the C servers
are not busy...
The average waiting time in the 'queue' =
C(c,U) / (service rate x c x (1 - Utilization)) (3)
It's approximatly equal to:
Utilization^C/(service rate x (1 - Utilization^C)
Note: ^ means power
This approximation is exact for the M/M/1 and M/M/2 models,
but 'slightly' lower than the result in (3) if c > 2
and
Utilization = Density of circulation / C (number of servers)
Note: ^ means power()
and C means the number of servers
Response time = The average waiting time in the 'queue' +
(1 / service rate)
average numbers of users in the system = service rate x response time
average number of users in queue = service rate x average waiting
time
in the 'queue'
Now as i said before:
--
So the equation for
Ni: number of jobs in each queue
Ui: utilization of each queue
Ni = Ui / (1-Ui)
Adding all the Ni in each individual queue will give the
average number of jobs in the entire queuing network.
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
And after that from the mathematical analytical equation
we can simulate the jackson queuing network that model our
webservers...
---
If we try to calculate the Ni = Ui / (1-Ui) in
the Jackson network, and from the operational law (2) above
this will give us:
Ns for the M/M/n Server queue is:
(DC / n) / (1 - (DC/n))
and DC = Ss / A => Ns = ((Ss/A)/n) / (1 -((Ss/A)/n))
Ss: service rate at the queuing server.
A: Arrival rate to the jackson network
DC: is the Density of circulation
n: number of servers
And Nn for the M/M/1 Network queue is:
and Utilization in the M/M/1 network queue = Sn / A
this imply that => Nn = (Sn/A) / (1 -(Sn/A))
Nn: number of jobs in the M/M/1 network queue node
Un: Utilization in the network queue node
Sn: service rate at the queuiNg server.
A: Arrival rate to the jackson network
And Nc for the M/M/1 Client queue node is:
and Uc= Sc / (F/5)
this imply that => Nc = (Sc/(F/5)) / (1 -(Sc/(F/5)))
Note: F/5, if for example the rate is one file every 5 seconds.
Nc: number of jobs in the M/M/1 client queue node
Uc: Utilization in the M/M/1 client queue node
Sc: service rate at the queuiNg server.
A: Arrival rate to the Jackson network
F: Average file size
Adding all the Ni in each individual queue will
give the average number of jobs in the entire
queuing network that is equal to:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
this imply that the T(the average response time in the Jackson
network)
is:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
Now finally we have our mathematical analytic equation
and we can begin to simulate our Enteprise webserver
and also validate the performance data with the fwptt stress
webserver simulation tool...
And don't forget what i have said about USL:
"Suppose we have obtained a small number of measured
load-points with Loadrunner or others tools, and we
calculated the USL equation to predict scalability of
a webserver , how the USL model can predict if the
scalability/performance is limited by the network bandwidth
and not the server ? I think USL can not predict this."
Also i wrote about USL that:
"As you have noticed , this mathematical model of
this jackson network does in fact take into account
the M/M/1 Network queue node , the USL model can not
do this... and with this performance data from the mathematical
analytical model simulation we can for example validate
the performance data of the fwptt stress webserver simulation.."
If you have noticed i have tried to show also that one
of the principal objectives is to control and manage
the *Quality* of the system or process, i wrote in my
post the following:
---
this imply that the T(the average response time in the Jackson
network)
is:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
Now finally we have our mathematical analytic equation
and we can begin to simulate our Enteprise webserver
and also validate the performance data with the fwptt stress
webserver simulation tool...
---
So, as you have noticed you can simulate our enterprise
webserver with this mathematical analytical equation and
validate the data collected by fwptt stress webserrer tool
and try to keep T( the average response time of your HTTP requests)
bellow or equal to 5 seconds, and see also if your webserver
is scaling, and we call this also Quality control using OR
(operational research).
In quality management, quality can also be maintained and
improved through the detection and reduction of process
variation. Where statistical techniques as ANOVA and others
can be used..
The ANOVA method , for example, analyses the variation in
the data set to discover the amount of variation that can
be attributed to each factor.. etc.
There is still an important thing..
As you have noticed, i have finally arrived to the following
mathematical model of our Jackson network that model an Enterprise
website:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
T: is the average response time..
So read it carefully an you will notice that this mathematical
model also can simulate and predict an intranet website behavior
or an internet website..
First look at the first factor (((Ss/A)/n) / (1 -((Ss/A)/n))
in our mathematical model, as you have noticed as
n (number of servers) grows this will make the denominator
grow rapidly and this will make (((Ss/A)/n) / (1 -((Ss/A)/n))
smaller, that's good for the response time...
Now let's look at the other factors in this mathematical
model:
IF the system is an Intranet, and for example the local
area network Sn is faster than the multiserver, that means:
We have Sn >> Ss, and that means => Ss /A >> Ss /A => that the
Knee in the server side can be reached more quickly than the
Knee in the network node of our Jackson network, so that
the bottleneck becomes the server node.
In the other hand if:
Ss >> Sn => Ss /A >> Sn / A => the Knee in the M/M/1 network
node can be reached more quickly, so that the network node in
the Jackson network becomes the bottleneck.
Availability:
The demand for high availability and reliability of computer and
software systems has led to a formal verification of such systems.
There are two principal approaches to formal verification:
model checking and theorem proving.
And i wrote about Petri Nets and how to model parallel
programs and how to exploit verification tools as Tina to verify
the properties such as liveleness of the system.
Please take a look at my other article about Petri Nets:
http://pages.videotron.com/aminer/PetriNet/formal.htm
And by using Petri Net and Tina you can make your system
more reliable , and if it's more reliable then the system
will have higher availability.
There are important factors to take into consideration when
building systems, factors such us availability and
efficiency(scalability etc....).
System availability is also calculated by modeling the system
as an interconnection of parts in series and parallel.
The availability A of a system is calculated like this
A = MTBF / (MTBF + MTTR)
MTBF: Mean time between failure
MTTR :Mean time to repair
and the MTTR is composed of:
time to respond to the failure + time to find
the problem + time to correct the problem + time
to verify that the system is working corretly.
Now if the interconnected parts are parallel , the equation
that we use to calculate the availability is:
A = 1- (U1 * U2 * U3 * ... * Un) (1)
Ui: is the non-availability of the component part of the system...
The availability of a system composed of interconnected parts in
series is:
A = A1 * A2 * ... * An (2)
Now as you have noticed i have modeled an enterprise website
as a Jackson network, and i have said before that:
--
And of course on Capacity Planning for Enterprise Datacenters
and Websites , you can mirror many computer servers and load
balance between them with a software... to make the system much
FASTER, and this will be modeled as a jackson network like this:
A -> M/M/n Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: the arrival rate to the system
--
As you have noticed i wrote "FASTER" but i didn't spook
about the AVAILABILITY, you will notice that you can not just
make your system more EFFICIENT and FASTER , but also
you can higher the AVAILABILITY of your system by mirroring
many servers...
I have also wrote before that:
---
"If you have noticed i have tried to show also that one
of the principal objectives is to control and manage
the *Quality* of the system or process, i wrote in my
previous post the following:
this imply that the T(the average response time in the Jackson
network)
is:
T = Ni /A = (Nn + Ns + Nc) /A
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/A) / (1 -(Sn/A))) / A
Now finally we have our mathematical analytic equation
and we can begin to simulate our Enteprise webserver
and also validate the performance data with the fwptt stress
webserver simulation tool...
So, as you have noticed you can simulate our enterprise
webserver with this mathematical analytical equation and
validate the data collected by fwptt stress webserrer tool
and try to keep T( the average response time of your HTTP requests)
bellow or equal to 5 seconds, and see also if your webserver
is scaling, and we call this also Quality control using OR
(operational research).
In quality management, quality can also be maintained and
improved through the detection and reduction of process
variation. Where statistical techniques as ANOVA and others
can be used.. "
---
We have many mathematical tools that we can use in Quality control,
example: Correlation, Regression , ANOVA etc.
ANOVA is a powerfull and important mathematic tool in
Quality control , by calculating the p-value in Excel or other
statistical tools , this will give us an important information like
if one or more variables have a significant effect on other
variables. If for example the p-value <= 0.05 (or if F > critical F value)
this imply that the null hypothesis is rejected , and the factor (or
factors)
has in fact an effect..
Regards,
Amine Moulay Ramdane.
== 2 of 4 ==
Date: Tues, Dec 17 2013 2:08 pm
From: aminer
I correct: infini in french means infinity..
On 12/17/2013 4:48 PM, aminer wrote:
>
> Hello,
>
> I want to talk about the mathematical modeling of
> queuing networks , if you have noticed in a webserver
> that uses a distributed database , the database
> have to be modeled as a queuing system with an
> hyperexponential service, but this will complicate the
> mathematical modeling of the webserver since the
> database have to be modeled as an M/G/1 queuing system,
> so we have to simplify the mathematical modeling , so if
> for exemple the database's write transactions takes in average
> much more time than a database's read transaction so we have
> to choose the worst case scenario , that means we have to choose
> the rate of the database's write transactions as the rate
> of the arrival to the queuing system of the database so
> that the database can be modeled as an M/M/1 queuing system
> (M: means markovian), so that the webserver can finally be
> modeled as two M/M/1 queuing system in series, one for
> the database and one for the internet network.
>
> But there is still a problem, if we want to also resolve the
> worst case scenario when for exemple thousands of custumers
> arrive at the same time to the webserver.. so the webserver
> have to be modeled taking into acount this worst case scenario...
>
> Here is the matematical modeling of an M/M/1 queuing system:
>
> We already know that to satisfy a Poisson process we must
> have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
> that means the counting increments must be independant.
>
> We have the following relation between the Poisson law
> and Exponential law:
>
> the expected value E(X exponential) = 1 / E(X poisson)
>
> so f the arrival is poissonian then the interarrivals are
> exponential..
>
> Now i will calculate the expected mean waiting time and
> mean number of custumers in the queuing system:
>
> The Little law says that the waiting time in the queuing system:
>
> Ws = Ls/lambda
>
> And the waiting time in the queue of the queuing system is:
>
> Wq = Ws - 1/Mu
> = Ls/lambda - 1/Mu
>
> And the Little law gives us the expected mean number of custumers in the
> queue:
>
> Lq = Wq*lambda = Ls - Phi et Phi = lamda/Mu
>
> That implies:
>
> Ls - Lq = Phi
>
>
> When the system is in a stationary state , the balance equations gives:
>
> State rate in = rate out
>
> state 0: Mu * P1 = lambda*P0
> state 1: lambda*P0 + Mu*P2 = lambda*P1 + Mu*P1
> state 2: lambda*P1 + Mu*P3 = lambda*P2 + Mu*P2
> ...
> state n: lambda*Pn-1 + Mu*Pn+1 = lambda*Pn + Mu*Pn
>
>
> And that gives us the following balance equations:
>
> lambda * P0 = Mu*P1 <=> P1 = (lambda/Mu)*P0
>
> lambda * P1 = Mu*P2 <=> P1 = (lambda/Mu)^2*P0
>
> lambda * P2 = Mu*P3 <=> P1 = (lambda/Mu)^3*P0
>
> ...
>
> lambda * Pn-1 = Mu*Pn <=> P_n = (lambda/Mu)^k*P0 [1]
>
>
>
> Note: P0 means the probality of having zero custumer in the queuing system.
> and ^ means power.
>
>
> And we have also that:
>
> Sum(n=0 -> infini) (Pn) = 1 that means the sum of probabilities equal 1
>
> And [1] gives us:
>
> Sum(n=0 -> infini) (Phi^n*P0) =1
>
> And by resolving the sum if a geometric series that gives us:
>
> P0 * 1/(1-Phi) = 1 => P0 = 1 - Phi and Phi < 1
>
> And [1] gives us:
>
> Pn = (1-Phi) Phi^n
>
> And we have that means the mean expected number iof custumer in the
> queing system is:
>
> Ls = Sum(n=0 -> infini) (n*Pn)
>
> That implies:
>
> Ls = Sum(n=0 -> infini) (n*(1-Phi)*Phi^n) = Phi/1-Phi et Phi<1
>
> and we have the mean expected number of custumer in the queue of the
> queing system is :
>
> Lq = Ls -Phi = Phi^2/ (1-Phi) et Phi<1
>
>
> Little law gives us the mean waiting time in the system and in the queue:
>
> Ws = 1/lambda * Phi/(1-Phi) and Phi<1
>
> et
>
> Wq= 1/lambda * Phi^2/(1-Phi) and Phi<1
>
>
> I have just read the following page, look at the the USL
>
> (Universal Law of Computational Scalability) of Dr. Gunther,
> he wrote this: (See: http://en.wikipedia.org/wiki/Neil_J._Gunther )
>
> --------------
>
> The relative capacity C(N) of a computational platform is given by:
>
> C(N) = N
> ------------------------------------------
> 1 + α (N - 1) + ß N (N - 1)
>
> where N represents either the number of physical processors
> in the hardware configuration or the number of users driving the
> software application. The parameters α and ß represent respectively
> the levels of contention (e.g., queueing for shared resources) and
> coherency delay (i.e., latency for data to become consistent) in the
> system. The ß parameter also quantifies the retrograde throughput
> seen in many stress tests but not accounted for in either Amdahl's law
> or event-based simulations.
>
> ----------
>
> His website: http://www.perfdynamics.com/
>
> If you read carefully , you will see that Dr. Gunther is using this
> model to predict scalability after he simulates a relatively small
> number of vusers in LoadRunner ( because of licensing costs, it's
> cost-effective) and after that he finds the coefficients of the
> 2nd-degree polynomial (quadratic equation) and then transform
> those coefficients back to the USL parameters using the α = b - a
> and ß = a.
>
> And then he is extrapolating with the USL model to higher loads
> to predict scalability.
>
> He is also applying the model to webservers with heterogeneous
> workloads. like in the following page:
>
> http://perfdynamics.blogspot.com/2009/04/assessing-usl-scalability-wi...
>
> Now my question follows:
>
> Suppose we have obtained a small number of measured load-points
> with Loadrunner or others tools, and we calculated the USL equation
> to predict scalability of a webserver , how the USL model can predict
> if the scalability/performance is limited by the network bandwidth
> and not the server ? I think USL can not predict this.
>
> When we are modeling webservers , we have to include
> the network node in our network queuig model (that includes
> the computer server queue) , and since the service in the
> computer server is comprised of multiple services (when we
> are using htmls , databases etc.) the network queue will not
> be markovian in its service , and we have to model the network
> queue as an M/G/1 and this will complicate the mathematical
> analytical modeling...
>
> So, i think the best way is to use a webserver stress tool
> like http://fwptt.sourceforge.net/
>
> You can even test the webserver with an heterogeneous
> workloads by starting multiple fwtpp processes, and
> you should increase the number of threads to 5 and after
> that to 10 threads, 15 ... and so on until the webserver
> applications stops responding propperly(and this will inform
> on the maximum number of users that you can have in the same time...)
> and as you are stress testing you can even see (by testing/measuring
> it) if the network bandwidth is not the bottleneck... and this can
> not be done by the USL model.
>
> We already know that to satisfy a Poisson process we must
> have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
> that means the counting increments must be independant.
>
> We have the following relation between the Poisson law
> and Exponential law:
>
> the expected value E(X exponential) = 1 / E(X poisson)
>
> and if the arrival is poissonian then the interarrivals are
> exponential..
>
> Now what about a webserver ?
>
> I have read the following paper:
>
> http://docs.google.com/viewer?a=v&q=cache:JFYCp_dSPP4J:citeseerx.ist....
>
> And it says that a simple model with M/M/1/k with FCFS discipline
> can predict webserver performance quite well..
>
> Hence, i think we can model our webserver over internet
> with 3 queues connected as a Jackson Network like this
>
> A -> M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
>
> A: is the arrival rate
>
> and we have the following:
>
> Ni: number of jobs in each queue
> Ui: utilization of each queue
>
> Ni = Ui / (1-Ui)
>
> Adding all the Ni in each individual queue will give the
> average number of jobs in the entire queuing network.
>
> After that we apply the Little formula:
>
> A: network arrival rate
> T: average response time
>
> N = A*T => T = N / A
>
> And after that from the mathematical analytical equation
> we can simulate the jackson queuing network that model our
> webservers...
>
> Now there is still an important question that i have:
>
> Our analytical jackson network model can give us insight
> on the webservers behavivior.. but the difficulty that i find in
> practice is that: suppose we have found the right parametters
> that we want to choose, like for example the service rate of
> the M/M/1 Server Queue , how , from this service rate, can
> we buy the right computer that satisfies the service rate
> that we want ?
>
> We say in OR that:
>
> "Understanding the behavior of a system is what Queueing Theory
> and Little's Law is all about. But, managing a Queue requires not
> just understanding the behavior of a system, but also in-depth
> knowledge of how to improve a system - improving both aspects
> of Queueing will mean a better, more efficient and cost-effective
> system and, more importantly, a much better customer experience."
>
> I wrote before that:
>
> ---
>
> "It says that a simple model with M/M/1/k with FCFS discipline
> can predict webserver performance quite well..
> Hence, i think we can model our webserver over internet
> with 3 queues connected as a Jackson Network like this
> A -> M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
>
> A: the arrival rate
> and we have the following:
> Ni: number of jobs in each queue
> Ui: utilization of each queue
>
> Ni = Ui / (1-Ui)
>
> Adding all the Ni in each individual queue will give the
> average number of jobs in the entire queuing network.
> After that we apply the Little formula:
>
> A: network arrival rate
> T: average response time
>
> N = A*T => T = N / A
>
> And after that from the mathematical analytical equation
> we can simulate the jackson queuing"
>
== 3 of 4 ==
Date: Tues, Dec 17 2013 2:18 pm
From: aminer
Hello,
I will correct the following part cause i have just
translate it myself from french and it contains
some mistakes...
Here is the matematical modeling of an M/M/1 queuing system:
We already know that to satisfy a Poisson process we must
have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
that means the counting increments must be independant.
We have the following relation between the Poisson law
and Exponential law:
the expected value E(X exponential) = 1 / E(X poisson)
so if the arrival is poissonian then the interarrivals are
exponential..
Now i will calculate the expected mean waiting time and
mean number of custumers in the queuing system:
The Little law says that the waiting time in the queuing system:
Ws = Ls/lambda
And the waiting time in the queue of the queuing system is:
Wq = Ws - 1/Mu
= Ls/lambda - 1/Mu
And the Little law gives us the expected mean number of custumers in the
queue:
Lq = Wq*lambda = Ls - Phi and Phi = lambda/Mu
That implies:
Ls - Lq = Phi
When the system is in a stationary state , the balance equations gives:
State rate in = rate out
state 0: Mu * P1 = lambda*P0
state 1: lambda*P0 + Mu*P2 = lambda*P1 + Mu*P1
state 2: lambda*P1 + Mu*P3 = lambda*P2 + Mu*P2
...
state n: lambda*Pn-1 + Mu*Pn+1 = lambda*Pn + Mu*Pn
And that gives us the following balance equations:
lambda * P0 = Mu*P1 <=> P1 = (lambda/Mu)*P0
lambda * P1 = Mu*P2 <=> P1 = (lambda/Mu)^2*P0
lambda * P2 = Mu*P3 <=> P1 = (lambda/Mu)^3*P0
...
lambda * Pn-1 = Mu*Pn <=> P_n = (lambda/Mu)^k*P0 [1]
Note: P0 means the probability of having zero custumer in the queuing
system and ^ means power.
And we have also that:
Sum(n=0 -> infinity) (Pn) = 1 that means the sum of probabilities equal 1
And [1] gives us:
Sum(n=0 -> infinity) (Phi^n*P0) =1
And by resolving the sum if a geometric series that gives us:
P0 * 1/(1-Phi) = 1 => P0 = 1 - Phi and Phi < 1
And [1] gives us:
Pn = (1-Phi) Phi^n
And we have that means the mean expected number iof custumer in the
queing system is:
Ls = Sum(n=0 -> infinity) (n*Pn)
That implies:
Ls = Sum(n=0 -> infinity) (n*(1-Phi)*Phi^n) = Phi/1-Phi et Phi<1
and we have the mean expected number of custumer in the queue of the
queing system is :
Lq = Ls -Phi = Phi^2/ (1-Phi) et Phi<1
Little law gives us the mean waiting time in the system and in the queue:
Ws = 1/lambda * Phi/(1-Phi) and Phi<1
et
Wq= 1/lambda * Phi^2/(1-Phi) and Phi<1
Thank you,
Amine Moulay Ramdane.
== 4 of 4 ==
Date: Tues, Dec 17 2013 2:31 pm
From: aminer
J'ai ecrit:
"We have the following relation between the Poisson law
and Exponential law:
the expected value E(X exponential) = 1 / E(X poisson)
so if the arrival is poissonian then the interarrivals are
exponential.. "
Alors c'est plus facile de faire une simulation d'une file d'attente
M/M/1 ou M/M/n puisque les services et les arrivées devraient etre
exponentiallement distribués et vous allez trouver ma simulation
dans mon site web:
http://pages.videotron.com/aminer/
Merci,
Amine Moulay Ramdane.
==============================================================================
TOPIC: Threadpool with priorities version 1.54
http://groups.google.com/group/comp.programming.threads/t/3a765b03ab36c1b3?hl=en
==============================================================================
== 1 of 1 ==
Date: Sat, Dec 21 2013 9:16 am
From: aminer
Hello,
Threadpool with priorities was updated to version 1.54 (stable version),
and threadpool was updated to version 1.55, i have changed something
inside the scalable Anderson lock so that the exemples works correcly,
now Threadpool with priorities is very stable.
Author: Amine Moulay Ramdane
Language: FPC Pascal v2.2.0+ / Delphi 5+: http://www.freepascal.org/
Operating Systems: Win , Linux and Mac (x86).
Description:
Thread Pool Engine.
The following have been added:
- You can give the following priorities to jobs:
LOW_PRIORITY
NORMAL_PRIORITY
HIGH_PRIORITY
- Uses a FIFO queue that satisfies many requirements: it is FIFO fair,
it minimizes efficiently the cache-coherence traffic and it is energy
efficient on the pop(): when there is no items in the queue it will not
spin-wait , but it will wait on a portable manual event object..
- Enters in a wait state when there is no job in the queue - for more
efficiency -
- You can distribute your jobs to the workers threads and call any
method with the threadpool's execute() method.
- Uses O(1) complexity on enqueue and O(3) worst case complexity on
dequeue.
Look into defines.inc there is many options:
CPU32: for 32 bits architecture
CPU64: for 64 bits architecture
Please read an article that i wrote about my Threadpool engine: article.
Look at test1.pas demo inside the zip file...
You can dowload Threadpool with priorities 1.54 from:
http://pages.videotron.com/aminer/
Required FPC switches: -O3 -Sd -dFPC -dWin32 -dFreePascal
-Sd for delphi mode....
Required Delphi switches: -DMSWINDOWS -$H+
For Delphi 5,6,7 use -DDelphi
For Delphi 2005,2006,2007,2009,2010+ use the switch -DDELPHI2005+
{$DEFINE CPU32} and {$DEFINE Win32} for 32 bit systems
{$DEFINE CPU64} and {$DEFINE Win64} for 64 bit systems
Note: testpool.pas is a parallel program of a Matrix multiply by a
vector that uses SSE+ and it requires Delphi 5+. test.pas and
test_thread.pas works with both FreePascal and Delphi.
Thank you,
Amine Moulay Ramdane.
==============================================================================
TOPIC: Concurrent FIFO Queue 1.01
http://groups.google.com/group/comp.programming.threads/t/73de55ea89ca5de7?hl=en
==============================================================================
== 1 of 1 ==
Date: Sat, Dec 21 2013 9:36 am
From: aminer
Hello,
Concurrent FIFO Queue was updated to version 1.01, i have added the
Ticket Spinlock with a proportional backoff so that
it becomes FIFO fair and so that it reduces the cache-coherence traffic
, my
concurrent FIFO queue is also energy efficient on the pop(): when there
is no items in the queue it will not spin-wait , but it will wait on a
portable manual event object, and now using the Ticket Spinlock with a
proportional backoff it gives 3 millions push transactions per second
much better than the scalable Anderson lock and that's excellent, you
can use also the scalable Anderson lock but it gives less throughput than
the TicketSpinlock with a proportional backoff.
If you want to use the TicketSpinlock
use "Ticket" inside the defines.inc and
if you want to use the scalable Anderson lock use "ALOCK" inside the
defines.inc.
Authors: Amine Moulay Ramdane.
Description:
A concurrent FIFO queue that satisfies many requirements: it is FIFO
fair, it minimizes efficiently the cache-coherence traffic and it is
energy efficient on the pop(): when there is no items in the queue it
will not spin-wait , but it will wait on a portable manual event object.
Please take a look a the test.pas Object Pascal demo inside the zipfile,
compile and run it...
You can download Concurrent FIFO Queue 1.01 from:
http://pages.videotron.com/aminer/
Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/
Operating Systems: Windows, Mac OSX , Linux , Unix...
Required FPC switches: -O3 -Sd -dFPC -dFreePascal
-Sd for delphi mode....
{$DEFINE CPU32} and {$DEFINE Windows32} for 32 bit systems
{$DEFINE CPU64} and {$DEFINE Windows64} for 64 bit systems
Thank you,
Amine Moulay Ramdane.
==============================================================================
TOPIC: An M/M/n queuing model simulation
http://groups.google.com/group/comp.programming.threads/t/a4d462b8599c98e1?hl=en
==============================================================================
== 1 of 3 ==
Date: Sat, Dec 21 2013 10:07 am
From: aminer
Hello,
An M/M/n queuing model simulation with Object Pascal and my Thread Pool
Engine - version 1.02
You can download it from:
http://pages.videotron.com/aminer/
Author: Amine Moulay Ramdane
Description:
It's harder and sometimes impossible to get analytical results about
waiting times and queue length for general interarrival and service
distributions; so, it's important to be able to estimate these
quantities by observing the results of simulation.
It's very easy in Object Pascal to simulate a sequence of arrival times
with a given interarrival distribution.
Look at the examples MM1.pas( M/M/1 queuing model) and MMn.pas(M/M/n -
n: number of servers -) inside the zip file:
---------------------------
InterArrivals:=TExponentialDistribution.Create(420623,1.0/3.0);
ServiceTimes:=TExponentialDistribution.Create(220623,1.0/4.0);
currtime:=0.0;
for i:=1 to simnumber
do
begin
obj:=TJob.create;
obj.simnumber:=simnumber;
obj.number:=i;
currtime:=currtime+InterArrivals.Sample;
obj.ArrivalTime:=currtime;
obj.Servicetime:= ServiceTimes.sample;
TP.execute(myobj.myproc1,pointer(obj),NORMAL_PRIORITY);
end;
-------------------------------------------
Here we have the InterArrivals object and ServiceTimes object and we are
calling InterArrivals.Sample to get our samples from the Exponential
Distribution.
After that we are calling myobj.myproc1 to simulate our M/M/1 queuing
model...
If you look at MM1.pas , you will see that the arrival rate is: 3 and
the service rate is 4 , so, this will give us a theoretical value of
1/(4-3) = 1 for one server, and the Object Pascal simulation gave me
1.02 for one server.
Now i want to talk about themathematical modeling of
queuing networks , if you have noticed in a webserver
that uses a distributed database , the database
have to be modeled as a queuing system with an
hyperexponential service, but this will complicate the
mathematical modeling of the webserver since the
database have to be modeled as an M/G/1 queuing system,
so we have to simplify the mathematical modeling , so if
for exemple the database's write transactions takes in average
much more time than a database's read transaction so we have
to choose the worst case scenario , that means we have to choose
the rate of the database's write transactions as the rate
of the arrival to the queuing system of the database so
that the database can be modeled as an M/M/1 queuing system
(M: means markovian), so that the webserver can finally be
modeled as two M/M/1 queuing system in series, one for
the database and one for the internet network.
But there is still a problem, if we want to also resolve the
worst case scenario when for exemple thousands of custumers
arrive at the same time to the webserver.. so the webserver
have to be modeled taking into acount this worst case scenario...
Here is the matematical modeling of an M/M/1 queuing system:
We already know that to satisfy a Poisson process we must
have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
that means the counting increments must be independant.
We have the following relation between the Poisson law
and Exponential law:
the expected value E(X exponential) = 1 / E(X poisson)
so if the arrival is poissonian then the interarrivals are
exponential..
Now i will calculate the expected mean waiting time and
mean number of custumers in the queuing system:
The Little law says that the waiting time in the queuing system:
Ws = Ls/lambda
And the waiting time in the queue of the queuing system is:
Wq = Ws - 1/Mu
= Ls/lambda - 1/Mu
And the Little law gives us the expected mean number of custumers in the
queue:
Lq = Wq*lambda = Ls - Phi et Phi = lamda/Mu
That implies:
Ls - Lq = Phi
When the system is in a stationary state , the balance equations gives:
State rate in = rate out
state 0: Mu * P1 = lambda*P0
state 1: lambda*P0 + Mu*P2 = lambda*P1 + Mu*P1
state 2: lambda*P1 + Mu*P3 = lambda*P2 + Mu*P2
...
state n: lambda*Pn-1 + Mu*Pn+1 = lambda*Pn + Mu*Pn
And that gives us the following balance equations:
lambda * P0 = Mu*P1 <=> P1 = (lambda/Mu)*P0
lambda * P1 = Mu*P2 <=> P1 = (lambda/Mu)^2*P0
lambda * P2 = Mu*P3 <=> P1 = (lambda/Mu)^3*P0
...
lambda * Pn-1 = Mu*Pn <=> P_n = (lambda/Mu)^k*P0 [1]
Note: P0 means the probality of having zero custumer in the queuing system.
and ^ means power.
And we have also that:
Sum(n=0 -> infini) (Pn) = 1 , that means the sum of probabilities equal 1
And [1] gives us:
Sum(n=0 -> infinite) (Phi^n*P0) =1
And by resolving the sum of a geometric series that gives us:
P0 * 1/(1-Phi) = 1 => P0 = 1 - Phi and Phi < 1
And [1] gives us:
Pn = (1-Phi) * Phi^n
And we have the mean expected number iof custumer in the queuing system is:
Ls = Sum(n=0 -> infinite) (n*Pn)
That implies:
Ls = Sum(n=0 -> infinite) (n*(1-Phi)*Phi^n) = Phi/1-Phi and Phi<1
and we have the mean expected number of custumers in the queue of the
queing system is :
Lq = Ls -Phi = Phi^2/ (1-Phi) et Phi<1
Little law gives us the mean waiting time in the system and in the queue:
Ws = 1/lambda * Phi/(1-Phi) and Phi<1
et
Wq= 1/lambda * Phi^2/(1-Phi) and Phi<1
I have just read the following page, look at the the USL
(Universal Law of Computational Scalability) of Dr. Gunther,
he wrote this: (See: http://en.wikipedia.org/wiki/Neil_J._Gunther )
--------------
The relative capacity C(N) of a computational platform is given by:
C(N) = N
------------------------------------------
1 + α (N - 1) + ß N (N - 1)
where N represents either the number of physical processors
in the hardware configuration or the number of users driving the
software application. The parameters α and ß represent respectively
the levels of contention (e.g., queueing for shared resources) and
coherency delay (i.e., latency for data to become consistent) in the
system. The ß parameter also quantifies the retrograde throughput
seen in many stress tests but not accounted for in either Amdahl's law
or event-based simulations.
----------
His website: http://www.perfdynamics.com/
If you read carefully , you will see that Dr. Gunther is using this
model to predict scalability after he simulates a relatively small
number of vusers in LoadRunner ( because of licensing costs, it's
cost-effective) and after that he finds the coefficients of the
2nd-degree polynomial (quadratic equation) and then transform
those coefficients back to the USL parameters using the α = b - a
and ß = a.
And then he is extrapolating with the USL model to higher loads
to predict scalability.
He is also applying the model to webservers with heterogeneous
workloads. like in the following page:
http://perfdynamics.blogspot.com/2009/04/assessing-usl-scalability-wi...
Now my question follows:
Suppose we have obtained a small number of measured load-points
with Loadrunner or others tools, and we calculated the USL equation
to predict scalability of a webserver , how the USL model can predict
if the scalability/performance is limited by the network bandwidth
and not the server ? I think USL can not predict this.
When we are modeling webservers , we have to include
the network node in our network queuig model (that includes
the computer server queue) , and since the service in the
computer server is comprised of multiple services (when we
are using htmls , databases etc.) the network queue will not
be markovian in its service , and we have to model the network
queue as an M/G/1 and this will complicate the mathematical
analytical modeling...
So, i think the best way is to use a webserver stress tool
like http://fwptt.sourceforge.net/
You can even test the webserver with an heterogeneous
workloads by starting multiple fwtpp processes, and
you should increase the number of threads to 5 and after
that to 10 threads, 15 ... and so on until the webserver
applications stops responding propperly(and this will inform
on the maximum number of users that you can have in the same time...)
and as you are stress testing you can even see (by testing/measuring
it) if the network bandwidth is not the bottleneck... and this can
not be done by the USL model.
We already know that to satisfy a Poisson process we must
have that N(t1)- N(t0), N(t2)- N(t1) etc. must be independant
that means the counting increments must be independant.
We have the following relation between the Poisson law
and Exponential law:
the expected value E(X exponential) = 1 / E(X poisson)
and if the arrival is poissonian then the interarrivals are
exponential..
Now what about a webserver ?
I have read the following paper:
http://docs.google.com/viewer?a=v&q=cache:JFYCp_dSPP4J:citeseerx.ist....
And it says that a simple model with M/M/1/k with FCFS discipline
can predict webserver performance quite well..
Hence, i think we can model our webserver over internet
with 3 queues connected as a Jackson Network like this
A -> M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: is the arrival rate
and we have the following:
Ni: number of jobs in each queue
Ui: utilization of each queue
Ni = Ui / (1-Ui)
Adding all the Ni in each individual queue will give the
average number of jobs in the entire queuing network.
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
And after that from the mathematical analytical equation
we can simulate the jackson queuing network that model our
webservers...
Now there is still an important question that i have:
Our analytical jackson network model can give us insight
on the webservers behavivior.. but the difficulty that i find in
practice is that: suppose we have found the right parametters
that we want to choose, like for example the service rate of
the M/M/1 Server Queue , how , from this service rate, can
we buy the right computer that satisfies the service rate
that we want ?
We say in OR that:
"Understanding the behavior of a system is what Queueing Theory
and Little's Law is all about. But, managing a Queue requires not
just understanding the behavior of a system, but also in-depth
knowledge of how to improve a system - improving both aspects
of Queueing will mean a better, more efficient and cost-effective
system and, more importantly, a much better customer experience."
I wrote before that:
---
"It says that a simple model with M/M/1/k with FCFS discipline
can predict webserver performance quite well..
Hence, i think we can model our webserver over internet
with 3 queues connected as a Jackson Network like this
A -> M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: the arrival rate
and we have the following:
Ni: number of jobs in each queue
Ui: utilization of each queue
Ni = Ui / (1-Ui)
Adding all the Ni in each individual queue will give the
average number of jobs in the entire queuing network.
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
And after that from the mathematical analytical equation
we can simulate the jackson queuing"
--
As you have noticed , this mathematical model of
this jackson network does in fact take into account
the M/M/1 Network queue node , the USL model can not
do this... and with this performance data from the mathematical
analytical model simulation we can for example validate
the performance data of the fwptt stress webserver simulation..
But you have to take into account worst cases and the
peak traffic loads...
Let for example we have a a webserver hosting html pages
and it is receiving 1000000 HTTP operations
per day with an average file size of 10 KB.
What would be the network bandwidth required for this website
considering peak traffic if the peak traffic load from past
observations was four times greater than average loads?
Required bandwidth is solved by the following equation:
HTTP op/sec x average file size or
1000000 HTTP ops per day =1000000/24 = 41,667 op/hour =
41,667/3600= 11.6 HTTP ops/sec
The needed bandwidth is
11.6 HTTP ops/sec X 10 KB/HTTP op = 116 KB/sec = 928 Kbps.
If we assume a protocol overhead of 20% then the actual throughput
required is 928 Kbps X 1.2 = 1,114 Kbps.
However if peak loads, as i said before, is as much as
4 times greater, the bandwidth required to handle spikes
would be 4 X 1,114 Kbps = 4.456 Mbps.
So you have to think also about the cost of this line...
I will add the following:
As you have noticed i said that:
"As you have noticed , this mathematical model of
this jackson network does in fact take into account
the M/M/1 Network queue node , the USL model can not
do this... and with this performance data from the mathematical
analytical model simulation we can for example validate
the performance data of the fwptt stress webserver simulation.."
and i said that:
"Hence, i think we can model our webserver over internet
with 3 queues connected as a Jackson Network like this
An M/M/1 Server Queue -> M/M/1 Network queue -> M/M/1 Client queue"
And of course on Capacity Planning for Enterprise Datacenters
and Websites , you can mirror many computer servers and load
balance between them with a software... to make the system much
FASTER, and this will be modeled as a jackson network like this:
A -> M/M/n Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: the arrival rate to the system
But there is still an important thing , as i have showed before
on my calculations:
"However if peak loads, as i said before, is as much as
4 times greater, the bandwidth required to handle spikes
it would be 4 X 1,114 Kbps = 4.456 Mbps.
So you have to think also about the cost of this line..."
I think that you have also to take into account the knee utilisation
of your M/M/n Servers Queues, if for example the number of computer
servers is 8 and the Knee is 74% that means that in our previous
example the bandwidth must equal to:
74% X 4.456 Mbps = 3.297 Mbps.
Cause as you know, above this Knee of 74% for 8 servers
the curve of the waiting time does grow quickly ..
And we have to take into account the cost of the line ...
Let us take another example:
In the network node of the Jackson network, there is three
main parameters that are responsable for its performance:
latency, bandwidth and utilization.
Now, if for example you take a look at my provider
http://www.videotron.com/service/internet-services/internet-access/hi...
My upload network speed is clearly 820 Kbs => 102.5 Kbytes/sec
Hence, if the average file size on my web site is for
example 25 Kbyte and the protocol overhead is 20%, that
means that the file size will be in average:
25 * 120% = 30 Kbyte
And if the Knee of the M/M/1 queuing node in our Jackson network
is 50%, then the bandwidth available will be reduced to
102.5 Kbytes/sec * 50% = 51.25 Kbytes/sec
If the download speed of the client is for example 7.5 Mbps,
that means that the file can be retrieved in no more than
30 / 51.25 = 0.585 second = 585 milliseconds.
But if we assume for example that a typical web visitor
to my web site is spending 585 milliseconds retrieving the
page and 60 seconds reading the HTML page THEN each client
on average only requires:
0.585 / (0.585 + 60) = 9.6% of the bandwidth that is allocated to
it..
but in practice i think we have to consider the worst case
scenarios..
So, since we can support a constraint of no more than 5 seconds
in the T (average response time), that means:
585 ms * X = 5000 milliseconds => X = 8.54
Hence, in worst case , my network node can not support more
than 8.54 users in the same time...
So, on *average* my network node can support:
(8.54 * 86400) / 5 = 147571 users per day
I wrote before that:
--
And of course on Capacity Planning for Enterprise Datacenters
and Websites , you can mirror many computer servers and load
balance between them with a software... to make the system much
FASTER, and this will be modeled as a Jackson network like this:
(1)
A -> M/M/n Server Queue -> M/M/1 Network queue ->
-> M/M/1 Client queue -> A
A: the arrival rate to the system"
--
We know also from an operational law of queuing theory that:
(2) the rate of job leaving any stable node must equal
its arrival rate.
(2) is from the Equivalence property.
Equivalence property: Assume that a service facility with
s servers and infinite queue has a Poisson input with
parameter lambda and the same exponential service-time
distribution with parameter Mu for each server (the M/M/s model),
where s * Mu > lambda. Then the steady-state output of
this service facility is also poisson process with parameter
lambda.
We know for an M/M/c queue that:
Note: try to add servers with almost the same hardware
configuration...
C(c, U) = Erlang formula = P(c) / (1 - Utilization)
note: c the number of servers..
P(c): means the probability that all the servers are busy
P(0): means the probability that there is no waiting time in the
queue, that means also: AT LEAST one server among the C servers
are not busy...
The average waiting time in the 'queue' =
C(c,U) / (service rate x c x (1 - Utilization)) (3)
It's approximatly equal to:
Utilization^C/(service rate x (1 - Utilization^C)
Note: ^ means power
This approximation is exact for the M/M/1 and M/M/2 models,
but 'slightly' lower than the result in (3) if c > 2
and
Utilization = Density of circulation / C (number of servers)
Note: ^ means power()
and C means the number of servers
Response time = The average waiting time in the 'queue' +
(1 / service rate)
average numbers of users in the system = service rate x response time
average number of users in queue = service rate x average waiting
time
in the 'queue'
Now as i said before:
--
So the equation for
Ni: number of jobs in each queue
Ui: utilization of each queue
Ni = Ui / (1-Ui)
Adding all the Ni in each individual queue will give the
average number of jobs in the entire queuing network.
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
And after that from the mathematical analytical equation
we can simulate the jackson queuing network that model our
webservers...
---
If we try to calculate the Ni = Ui / (1-Ui) in
the Jackson network, and from the operational law (2) above
this will give us:
Ns for the M/M/n Server queue is:
(DC / n) / (1 - (DC/n))
and DC = Ss / A => Ns = ((Ss/A)/n) / (1 -((Ss/A)/n))
Ss: service rate at the queuing server.
A: Arrival rate to the jackson network
DC: is the Density of circulation
n: number of servers
And Nn for the M/M/1 Network queue is:
and Utilization in the M/M/1 network queue = Sn / A
this imply that => Nn = (Sn/A) / (1 -(Sn/A))
Nn: number of jobs in the M/M/1 network queue node
Un: Utilization in the network queue node
Sn: service rate at the queuiNg server.
A: Arrival rate to the jackson network
And Nc for the M/M/1 Client queue node is:
and Uc= Sc / (F/5)
this imply that => Nc = (Sc/(F/5)) / (1 -(Sc/(F/5)))
Note: F/5, if for example the rate is one file every 5 seconds.
Nc: number of jobs in the M/M/1 client queue node
Uc: Utilization in the M/M/1 client queue node
Sc: service rate at the queuiNg server.
A: Arrival rate to the Jackson network
F: Average file size
Adding all the Ni in each individual queue will
give the average number of jobs in the entire
queuing network that is equal to:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
After that we apply the Little formula:
A: network arrival rate
T: average response time
N = A*T => T = N / A
this imply that the T(the average response time in the Jackson
network)
is:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
Now finally we have our mathematical analytic equation
and we can begin to simulate our Enteprise webserver
and also validate the performance data with the fwptt stress
webserver simulation tool...
And don't forget what i have said about USL:
"Suppose we have obtained a small number of measured
load-points with Loadrunner or others tools, and we
calculated the USL equation to predict scalability of
a webserver , how the USL model can predict if the
scalability/performance is limited by the network bandwidth
and not the server ? I think USL can not predict this."
Also i wrote about USL that:
"As you have noticed , this mathematical model of
this jackson network does in fact take into account
the M/M/1 Network queue node , the USL model can not
do this... and with this performance data from the mathematical
analytical model simulation we can for example validate
the performance data of the fwptt stress webserver simulation.."
If you have noticed i have tried to show also that one
of the principal objectives is to control and manage
the *Quality* of the system or process, i wrote in my
post the following:
---
this imply that the T(the average response time in the Jackson
network)
is:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
Now finally we have our mathematical analytic equation
and we can begin to simulate our Enteprise webserver
and also validate the performance data with the fwptt stress
webserver simulation tool...
---
So, as you have noticed you can simulate our enterprise
webserver with this mathematical analytical equation and
validate the data collected by fwptt stress webserrer tool
and try to keep T( the average response time of your HTTP requests)
bellow or equal to 5 seconds, and see also if your webserver
is scaling, and we call this also Quality control using OR
(operational research).
In quality management, quality can also be maintained and
improved through the detection and reduction of process
variation. Where statistical techniques as ANOVA and others
can be used..
The ANOVA method , for example, analyses the variation in
the data set to discover the amount of variation that can
be attributed to each factor.. etc.
There is still an important thing..
As you have noticed, i have finally arrived to the following
mathematical model of our Jackson network that model an Enterprise
website:
Ni = Nn + Ns + Nc
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/(F/5)) / (1 -(Sc/(F/5)))
T: is the average response time..
So read it carefully an you will notice that this mathematical
model also can simulate and predict an intranet website behavior
or an internet website..
First look at the first factor (((Ss/A)/n) / (1 -((Ss/A)/n))
in our mathematical model, as you have noticed as
n (number of servers) grows this will make the denominator
grow rapidly and this will make (((Ss/A)/n) / (1 -((Ss/A)/n))
smaller, that's good for the response time...
Now let's look at the other factors in this mathematical
model:
IF the system is an Intranet, and for example the local
area network Sn is faster than the multiserver, that means:
We have Sn >> Ss, and that means => Ss /A >> Ss /A => that the
Knee in the server side can be reached more quickly than the
Knee in the network node of our Jackson network, so that
the bottleneck becomes the server node.
In the other hand if:
Ss >> Sn => Ss /A >> Sn / A => the Knee in the M/M/1 network
node can be reached more quickly, so that the network node in
the Jackson network becomes the bottleneck.
Availability:
The demand for high availability and reliability of computer and
software systems has led to a formal verification of such systems.
There are two principal approaches to formal verification:
model checking and theorem proving.
And i wrote about Petri Nets and how to model parallel
programs and how to exploit verification tools as Tina to verify
the properties such as liveleness of the system.
Please take a look at my other article about Petri Nets:
http://pages.videotron.com/aminer/PetriNet/formal.htm
And by using Petri Net and Tina you can make your system
more reliable , and if it's more reliable then the system
will have higher availability.
There are important factors to take into consideration when
building systems, factors such us availability and
efficiency(scalability etc....).
System availability is also calculated by modeling the system
as an interconnection of parts in series and parallel.
The availability A of a system is calculated like this
A = MTBF / (MTBF + MTTR)
MTBF: Mean time between failure
MTTR :Mean time to repair
and the MTTR is composed of:
time to respond to the failure + time to find
the problem + time to correct the problem + time
to verify that the system is working corretly.
Now if the interconnected parts are parallel , the equation
that we use to calculate the availability is:
A = 1- (U1 * U2 * U3 * ... * Un) (1)
Ui: is the non-availability of the component part of the system...
The availability of a system composed of interconnected parts in
series is:
A = A1 * A2 * ... * An (2)
Now as you have noticed i have modeled an enterprise website
as a Jackson network, and i have said before that:
--
And of course on Capacity Planning for Enterprise Datacenters
and Websites , you can mirror many computer servers and load
balance between them with a software... to make the system much
FASTER, and this will be modeled as a jackson network like this:
A -> M/M/n Server Queue -> M/M/1 Network queue -> M/M/1 Client -> A
A: the arrival rate to the system
--
As you have noticed i wrote "FASTER" but i didn't spook
about the AVAILABILITY, you will notice that you can not just
make your system more EFFICIENT and FASTER , but also
you can higher the AVAILABILITY of your system by mirroring
many servers...
I have also wrote before that:
---
"If you have noticed i have tried to show also that one
of the principal objectives is to control and manage
the *Quality* of the system or process, i wrote in my
previous post the following:
this imply that the T(the average response time in the Jackson
network)
is:
T = Ni /A = (Nn + Ns + Nc) /A
= (((Ss/A)/n) / (1 -((Ss/A)/n)) + (Sn/A) / (1 -(Sn/A))
+ (Sc/A) / (1 -(Sn/A))) / A
Now finally we have our mathematical analytic equation
and we can begin to simulate our Enteprise webserver
and also validate the performance data with the fwptt stress
webserver simulation tool...
So, as you have noticed you can simulate our enterprise
webserver with this mathematical analytical equation and
validate the data collected by fwptt stress webserrer tool
and try to keep T( the average response time of your HTTP requests)
bellow or equal to 5 seconds, and see also if your webserver
is scaling, and we call this also Quality control using OR
(operational research).
In quality management, quality can also be maintained and
improved through the detection and reduction of process
variation. Where statistical techniques as ANOVA and others
can be used.. "
---
We have many mathematical tools that we can use in Quality control,
example: Correlation, Regression , ANOVA etc.
ANOVA is a powerfull and important mathematic tool in
Quality control , by calculating the p-value in Excel or other
statistical tools , this will give us an important information like
if one or more variables have a significant effect on other
variables. If for example the p-value <= 0.05 (or if F > critical F value)
this imply that the null hypothesis is rejected , and the factor (or
factors)
has in fact an effect..
Regards,
Amine Moulay Ramdane.
== 2 of 3 ==
Date: Sat, Dec 21 2013 10:49 am
From: aminer
Hello,
Don't forget to read all the text inside my post
about also that i have mathematically modeled using a queuing network,
even a web server with a distributed database...i have corrected some
typos, so please read again...
Thank you,
Amine Moulay Ramdane.
== 3 of 3 ==
Date: Sat, Dec 21 2013 10:52 am
From: aminer
Hello,
Don't forget to read all the text inside my post
about also a web server that i have mathematically modeled using a
queuing network,
even a web server with a distributed database...i have corrected some
typos, so please read again...
Thank you,
Amine Moulay Ramdane.
==============================================================================
TOPIC: About Locks...
http://groups.google.com/group/comp.programming.threads/t/7d83cd7d9303f972?hl=en
==============================================================================
== 1 of 1 ==
Date: Sat, Dec 21 2013 3:45 pm
From: aminer
Hello,
I have tested my Threadpool engine with priorities and i have
noticed that my application hangs from time to time, and i have
debuged my code all this afternoon, and i have found that this
was a problem with the operating system , i am using Windows 2008,
and i have found the follwing solution: to avoid this problem you must
use a sleep(0) at the end of the Leave() method inside my Scalable
Anderson Lock, and this has solved the problem but it has reduced
somewhat the throughput, you have to do the same with my Ticket Spinlock
with an exponential backoff to avoid this problem, but now it is rock
solid and stable, i have updated all my other projects with this update
, please download them again if you need them from:
http://pages.videotron.com/aminer/
Thank you,
Amine Moulay Ramdane,
==============================================================================
TOPIC: Formatting text to xml
http://groups.google.com/group/comp.programming.threads/t/420a40ecbde861df?hl=en
==============================================================================
== 1 of 1 ==
Date: Thurs, Jan 2 2014 1:06 pm
From: andrew@cucumber.demon.co.uk (Andrew Gabriel)
In article <54782458-aaa1-43e7-a80d-b9622ca4f323@googlegroups.com>,
allenjoommen@gmail.com writes:
> My church currently uses a program called VerseView to present Bible verses. The program runs on Adobe Air. Unfortunately, a NIV version of the Bible =
> is not available to use. The bible version databases are run as xml files by the program. Here is a link to one of the .xml versions: http://goo.gl/VxoaXX. Is there anyway I can format the NIV Bible into an .xml version like the one above without going in and having to manually copy and paste each verse? Thank you
comp.text would be the right newsgroup for this question.
--
Andrew Gabriel
[email address is not usable -- followup in the newsgroup]
==============================================================================
TOPIC: Haswell AVX2 for Simple Integer Bitwise Operations
http://groups.google.com/group/comp.programming.threads/t/6238df8d2ec4f8bd?hl=en
==============================================================================
== 1 of 1 ==
Date: Tues, Jan 7 2014 3:11 pm
From: Alexander Krizhanovsky
Hi All!
I've made small benchmark of new Intel Haswell AVX2 instructions in application to simple bitwise operations with integers and compared manual optimizations using vector instructions with -O3 G++-4.7 optimizations. I hope it will be interesting for you.
http://natsys-lab.blogspot.ru/2014/01/haswell-avx2-for-simple-integer-bitwise.html
==============================================================================
TOPIC: SOLUTIONS MANUAL: An Introduction to Economic Dynamics by Ronald Shone
http://groups.google.com/group/comp.programming.threads/t/0dc89b64f208cf3d?hl=en
==============================================================================
== 1 of 1 ==
Date: Fri, Jan 10 2014 7:59 pm
From: macmorino5@gmail.com
I have the instructor's solution manual for these textbooks .. They are all in PDF format .. If you are interested in any one, please send an email to macmorino(at)gmail(dot)com .. Please I CHARGE for sending the PDF files.
Here are the solution manual to some titles..
SOLUTIONS MANUAL: A First Course in the Finite Element Method, 4th Edition logan
SOLUTIONS MANUAL: A Course in Modern Mathematical Physics by Peter Szekeres
SOLUTIONS MANUAL: A Course in Ordinary Differential Equations by Swift, Wirkus
SOLUTIONS MANUAL: A First Course in Abstract Algebra (7th Ed., John B. Fraleigh)
SOLUTIONS MANUAL: A First Course in Differential Equations - The Classic Fifth Edition By Zill, Dennis G
SOLUTIONS MANUAL: A First Course in Differential Equations, 9th Ed by Dennis G. Zill
SOLUTIONS MANUAL: A First Course In Probability 7th Edition by Sheldon M. Ross
SOLUTIONS MANUAL: A First Course in Probability Theory, 6th edition, by S. Ross.
SOLUTIONS MANUAL: A First Course in String Theory, 2004, Barton Zwiebach
SOLUTIONS MANUAL: A Practical Introduction to Data Structures and Algorithm Analysis 2Ed by Shaffer
SOLUTIONS MANUAL: A Quantum Approach to Condensed Matter Physics (Philip L. Taylor & Olle Heinonen)
SOLUTIONS MANUAL: A Short Course in General Relativity 2e by J. Foster and J. D. Nightingale
SOLUTIONS MANUAL: A Short Introduction to Quantum Information and Quantum Computation by Michel Le Bellac
SOLUTIONS MANUAL: A Transition to Advanced Mathematics 5th E by Smith, Eggen, Andre
SOLUTIONS MANUAL: Accounting Principles 8e by Kieso, Kimmel
SOLUTIONS MANUAL: Accounting principles 8th Ed by Weygandt
SOLUTIONS MANUAL: Accounting, 23 Ed by Carl S. Warren, James M. Reeve, Jonathan Duchac
SOLUTIONS MANUAL: Accounting,8th Ed by Horngren,Harrison, Oliver
SOLUTIONS MANUAL: Adaptive Control, 2nd. Ed., by Astrom, Wittenmark
SOLUTIONS MANUAL: Adaptive Filter Theory (4th Ed., Simon Haykin)
SOLUTIONS MANUAL: Advanced Accounting 10E international ED by Beams , Clement, Anthony, Lowensohn
SOLUTIONS MANUAL: Advanced accounting 9th Ed by Hoyle, Schaefer
SOLUTIONS MANUAL: Advanced Calculus Gerald B. Folland
SOLUTIONS MANUAL: Advanced Digital Design with the Verilog HDL by Michael D. Ciletti
SOLUTIONS MANUAL: Advanced Dynamics (Greenwood)
SOLUTIONS MANUAL: Advanced Engineering Electromagnetics by Constantine A. Balanis
SOLUTIONS MANUAL: Advanced Engineering Mathematics 3rd ed zill
SOLUTIONS MANUAL: Advanced Engineering Mathematics 8Ed Erwin Kreyszig
SOLUTIONS MANUAL: Advanced Engineering Mathematics by Erwin Kreyszig, 9th ed
SOLUTIONS MANUAL: Advanced Engineering Mathematics, 6th Edition by Peter V. O'Neil
SOLUTIONS MANUAL: Advanced Engineering Mathematics, 7th Ed by Peter V. O'Neil
SOLUTIONS MANUAL: Advanced Engineering Mathematics,2E, by Zill, Cullen
SOLUTIONS MANUAL: Advanced Engineering Thermodynamics, 3rd Edition by Adrian Bejan
SOLUTIONS MANUAL: Advanced Financial Accounting by Baker
SOLUTIONS MANUAL: Advanced Financial Accounting 5 Ed by Baker
SOLUTIONS MANUAL: Advanced Financial Accounting 8 Ed by Baker
SOLUTIONS MANUAL: Advanced Functions & Introductory Calculus by Kirkpatrick, McLeish, Montesanto
SOLUTIONS MANUAL: Advanced Industrial Economics by Martin
SOLUTIONS MANUAL: Advanced Industrial Economics, 2nd ED Stephen Martin
SOLUTIONS MANUAL: Advanced Macroeconomics 2nd edition by David Romer
SOLUTIONS MANUAL: Advanced Macroeconomics, by David Romer
SOLUTIONS MANUAL: Advanced Mathematical Concepts Precalculus with Applications ( Glencoe )
SOLUTIONS MANUAL: Advanced Mechanics of Materials 6th ed by Boresi, Schmidt
SOLUTIONS MANUAL: Advanced Modern Engineering Mathematics 3rd Ed Glyn James
SOLUTIONS MANUAL: Advanced Modern Engineering Mathematics 4th Ed Glyn James
SOLUTIONS MANUAL: Advanced Modern Engineering Mathematics, 3rd Ed., by G. James
SOLUTIONS MANUAL: Advanced Organic Chemistry Part A- Structure and Mechanisms 5th E by Carey, Sundberg
SOLUTIONS MANUAL: Aircraft Structures for Engineering Students (4th Ed., T.H.G. Megson)
SOLUTIONS MANUAL: Algebra & Trigonometry and Precalculus, 3rd Ed By Beecher, Penna, Bittinger
SOLUTIONS MANUAL: Algebra Baldor
SOLUTIONS MANUAL: Algebra-By Thomas W. Hungerford
SOLUTIONS MANUAL: Algorithm Design (Jon Kleinberg & Éva Tardos)
SOLUTIONS MANUAL: An Interactive Introduction to Mathematical Analysis 2nd E (Jonathan Lewin)
SOLUTIONS MANUAL: An Introduction To Analysis (3rdEd) -by William Wade
SOLUTIONS MANUAL: An Introduction To Analysis 4th Ed by William Wade
SOLUTIONS MANUAL: An Introduction to Database Systems (8th Ed., C.J. Date)
SOLUTIONS MANUAL: An Introduction to Derivatives and Risk Management by chance, brooks
SOLUTIONS MANUAL: An Introduction to Economic Dynamics by Ronald Shone
SOLUTIONS MANUAL: An Introduction To Management Science Quantitative Approaches To Decision Making 12th Ed by Anderson, Sweeney
SOLUTIONS MANUAL: An Introduction to Modern Astrophysics (2nd Ed., Bradley W. Carroll & Dale A. Ostlie)
SOLUTIONS MANUAL: An Introduction to Numerical Analysis By Endre Süli,David F. Mayers
SOLUTIONS MANUAL: An Introduction to Ordinary Differential Equations (James C. Robinson)
SOLUTIONS MANUAL: An Introduction to Signals and Systems by John Stuller
SOLUTIONS MANUAL: An Introduction to Stochastic Modeling 3rd Ed by Taylor, Karlin
SOLUTIONS MANUAL: An Introduction to the Finite Element Method (3rd Ed., J. N. Reddy)
SOLUTIONS MANUAL: An Introduction to Thermal Physics by Schroeder, Daniel V
SOLUTIONS MANUAL: An Introduction to Thermodynamics and Statistical Mechanics (2nd Ed, Keith Stowe)
SOLUTIONS MANUAL: An Introduction to Wavelets through Linear Algebra by Frazier
SOLUTIONS MANUAL: Analog Integrated Circuit Design, by Johns, Martin
SOLUTIONS MANUAL: Analysis and Design of Analog Integrated Circuits (4th Edition) by Gray , Lewis , Meyer
SOLUTIONS MANUAL: Analysis and Design of Analog Integrated Circuits 5th Ed ( vol.1 ) ch1-4 by Gray, Meyer
SOLUTIONS MANUAL: Analysis With an Introduction to Proof 4th Ed By Steven R. Lay
SOLUTIONS MANUAL: Analysis, Synthesis,and Design of Chemical Processes 3rd ED by Turton, Shaeiwitz
SOLUTIONS MANUAL: Analytical Chemistry, Higson
SOLUTIONS MANUAL: Analytical Mechanics 7E by Grant R. Fowles, George L. Cassiday
SOLUTIONS MANUAL: Antenna Theory 2nd edition by Balanis
SOLUTIONS MANUAL: Antenna Theory and Design, 2nd Ed Vol.1 by Stutzman, Thiele
SOLUTIONS MANUAL: Antennas for All Applications (3rd Ed., John Kraus & Ronald Marhefka)
SOLUTIONS MANUAL: Applied Calculus by Hallett,Gleason, Lock, Flath
SOLUTIONS MANUAL: Applied Calculus for the Managerial, Life, and Social Sciences, 7 E, by Soo T. Tan
SOLUTIONS MANUAL: Applied Calculus for the Managerial, Life, and Social Sciences, 8 E, by Soo T. Tan
SOLUTIONS MANUAL: Applied Econometric Time Series, 2nd Edition by Enders
SOLUTIONS MANUAL: Applied Electromagnetism 2nd Ed by Shen, Huang
SOLUTIONS MANUAL: Applied Finite Element Analysis 2ed, by LJ SEGERLIND
SOLUTIONS MANUAL: Applied Fluid Mechanics (6th Ed., Mott)
SOLUTIONS MANUAL: Applied Linear Regression 3rd Ed by Sanford Weisberg
SOLUTIONS MANUAL: Applied Linear Statistical Models 5th Ed by Kutner, Nachtsheim
SOLUTIONS MANUAL: Applied Mathematics, 3rd Ed by J. David Logan
SOLUTIONS MANUAL: Applied Numerical Analysis, 7th Edition, by Gerald, Wheatley
SOLUTIONS MANUAL: Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd E by Chapra
SOLUTIONS MANUAL: Applied Numerical Methods with MATLAB for Engineers and Scientists( Steven C. Chapra)
SOLUTIONS MANUAL: Applied Partial Differential Equations (4th Ed., Haberman)
SOLUTIONS MANUAL: Applied Partial Differential Equations by J. David Logan
SOLUTIONS MANUAL: Applied Quantum Mechanics ( A. F. J. Levi )
SOLUTIONS MANUAL: Applied Statistics and Probability for Engineers ( 2nd Ed., Douglas Montgomery & George Runger )
SOLUTIONS MANUAL: Applied Statistics and Probability for Engineers (3rd Ed., Douglas Montgomery & George Runger)
SOLUTIONS MANUAL: Applied Strength of Materials (4th Ed., Mott)
SOLUTIONS MANUAL: Applied Strength of Materials (5th Ed., Mott)
SOLUTIONS MANUAL: Applying Maths in the Chemical and Biomolecular Sciences, Beddard
SOLUTIONS MANUAL: Artificial Intelligence A Modern Approach 2e by Russell, Norvig
SOLUTIONS MANUAL: Artificial Neural Networks by B. Yegnanarayana and S. Ramesh
SOLUTIONS MANUAL: Assembly Language for Intel-Based Computers ( 3rd Edition ) by Kip R. Irvine
SOLUTIONS MANUAL: Auditing and Assurance Services- An Integrated Approach 12E by Arens
SOLUTIONS MANUAL: Auditing and Assurance Services, 12th edition, Alvin A Arens, Randal J Elder, Mark Beasley
SOLUTIONS MANUAL: Auditing and Assurance Services, 13 ed by Arens, Elder, Beasley
SOLUTIONS MANUAL: Auditing and Assurance Services, 2nd Ed by Louwers
SOLUTIONS MANUAL: Automatic Control Systems 9 Ed by Kuo, Golnaraghi
SOLUTIONS MANUAL: Automatic Control Systems, 8E, by Kuo, Golnaraghi
SOLUTIONS MANUAL: Basic Econometrics 4 ed by Damodar N. Gujarati
SOLUTIONS MANUAL: Basic Electrical Engineering By Nagrath, D P Kothari
SOLUTIONS MANUAL: Basic Electromagnetics with Applications by Nannapaneni Narayana Rao
SOLUTIONS MANUAL: Basic Engineering Circuit Analysis, 7th Ed by David Irwin
SOLUTIONS MANUAL: Basic Engineering Circuit Analysis, 8th Edition by J. David Irwin, R. Mark Nelms
SOLUTIONS MANUAL: Basic Engineering Circuit Analysis, 9th Ed by Irwin, Nelms
SOLUTIONS MANUAL: Basic Engineering Mathematics by Chan, Hung
SOLUTIONS MANUAL: Basic Heat and Mass Transfer by A. F. Mills
SOLUTIONS MANUAL: Basic Principles and Calculations in Chemical Engineering 7th E by Himmelblau, Riggs
SOLUTIONS MANUAL: Basic Probability Theory by Robert B. Ash
SOLUTIONS MANUAL: Bayesian Core by Christian P. Robert and Jean-Michel Marin
SOLUTIONS MANUAL: Bioprocess Engineering Principles (Pauline M. Doran)
SOLUTIONS MANUAL: Business Statistics - Decision Making 7th E by David F. Groebner
SOLUTIONS MANUAL: C++ for Computer Science and Engineering by Vic Broquard
SOLUTIONS MANUAL: C++ How to Program 3rd edition - Deitel
SOLUTIONS MANUAL: C++ How to Program 7th Ed by Deitel
SOLUTIONS MANUAL: CALCULO VECTORIAL 7th Ed. by Louis Leithold
SOLUTIONS MANUAL: Calculus 8th Edition by Varberg, Purcell, Rigdon
SOLUTIONS MANUAL: Calculus - Early Transcendental Functions 3rd ED by Larson, Ron
SOLUTIONS MANUAL: Calculus - Early Transcendentals, 6th E, by Anton, Bivens, Davis
SOLUTIONS MANUAL: Calculus - Early Transcendentals, 7E, by Anton, Bivens, Davis
SOLUTIONS MANUAL: Calculus - Late Transcendentals Single Variable, 8th Ed by Anton, Bivens, Davis
SOLUTIONS MANUAL: Calculus (9th Ed., Dale Varberg, Edwin Purcell & Steve Rigdon)
SOLUTIONS MANUAL: Calculus 2nd edition-M. Spivak
SOLUTIONS MANUAL: Calculus 3rd Ed by Michael Spivak
SOLUTIONS MANUAL: Calculus 6th ed by James Stewart
SOLUTIONS MANUAL: Calculus 8th Ed by Ron Larson, Robert P. Hostetler, Bruce H. Edwards
SOLUTIONS MANUAL: Calculus A Complete Course 6th Edition by by R.A. Adams
SOLUTIONS MANUAL: CALCULUS An Intuitive and Physical Approach 2nd ed by Morris Kline
SOLUTIONS MANUAL: Calculus and its Applications (11th Ed., Larry J Goldstein, Schneider, Lay & Asmar)
SOLUTIONS MANUAL: Calculus by Gilbert Strang
SOLUTIONS MANUAL: Calculus early transcendentals 8th Ed, by Anton Bivens Davis
SOLUTIONS MANUAL: Calculus Early Transcendentals, 5th Edition, JAMES STEWART
SOLUTIONS MANUAL: Calculus George Thomas 10th ed Vol 1
SOLUTIONS MANUAL: Calculus of Variations MA 4311 LECTURE NOTES ( Russak )
SOLUTIONS MANUAL: Calculus On Manifolds by Spivak
SOLUTIONS MANUAL: Calculus One & Several Variables 8e by S Salas
SOLUTIONS MANUAL: Calculus One And Several Variables 10th Edition by S Salas
SOLUTIONS MANUAL: Calculus Vol 2 by Apostol
SOLUTIONS MANUAL: Calculus Volume 1 by J. Marsden, A. Weinstein
SOLUTIONS MANUAL: Calculus With Analytic Geometry 4th ( Henry Edwards & David E. Penney)
SOLUTIONS MANUAL: Calculus with Applications 8 Edition by Lial, Greenwell, Ritchey
SOLUTIONS MANUAL: Calculus, 4th edition stewart
SOLUTIONS MANUAL: Calculus, Early Transcendentals 7 Ed by Edwards & Penny
SOLUTIONS MANUAL: Calculus, Single and Multivariable, 4E.,Vol 1& Vol 2 by Hughes-Hallett,McCallum
SOLUTIONS MANUAL: Calculus, Single Variable, 3E by Hughes-Hallett,McCallum
SOLUTIONS MANUAL: Chemical and Engineering Thermodynamics 3Ed by Stanley I. Sandler
SOLUTIONS MANUAL: Chemical Engineering Design (Coulson & Richardson's Chemical Engineering - Volume 6) - (4th Ed., Sinnott)
SOLUTIONS MANUAL: Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker
SOLUTIONS MANUAL: Chemical Reaction Engineering 3rd ED by Octave Levenspiel
SOLUTIONS MANUAL: Chemical, Biochemical, and Engineering Thermodynamics, 4th Ed by Sandler
SOLUTIONS MANUAL: Chemistry 2nd Edition Vol.1 by Julia Burdge
SOLUTIONS MANUAL: Chemistry, 10th Ed by Chang
SOLUTIONS MANUAL: Chemistry, 7th Edition by Susan A. Zumdahl
SOLUTIONS MANUAL: Chip Design for Submicron VLSI CMOS Layout and Simulation, John P. Uyemura
SOLUTIONS MANUAL: Cisco Technical Solution Series IP Telephony Solution Guide Version 2.0
SOLUTIONS MANUAL: Classical Dynamics of Particles and Systems, 5th Ed, by Marion, Thornton
SOLUTIONS MANUAL: Classical Dynamics, A Contemporary Approach (Jorge V. Jose)
SOLUTIONS MANUAL: Classical Electrodynamics 2nd ED by John David Jackson
SOLUTIONS MANUAL: Classical Electrodynamics by John David Jackson
SOLUTIONS MANUAL: Classical Mechanics (Douglas Gregory)
SOLUTIONS MANUAL: Classical Mechanics 2nd Ed by Goldstein
SOLUTIONS MANUAL: CMOS Analog Circuit Design, 2ed by Phillip E. Allen, Douglas R. Holberg
SOLUTIONS MANUAL: CMOS- Circuit Design, Layout, and Simulation, Revised 2nd Ed by R. Jacob Baker
SOLUTIONS MANUAL: Cmos Digital Integrated Circuits , Sung-Mo Kang,Yusuf Leblebici
SOLUTIONS MANUAL: CMOS Mixed-Signal Circuit Design, 2nd Ed by R. Jacob Baker
SOLUTIONS MANUAL: CMOS VLSI Design Circuit & Design Perspective 3rd Ed by Haris & West
SOLUTIONS MANUAL: College Algebra 8th Ed by Michael Sullivan
SOLUTIONS MANUAL: COLLEGE ALGEBRA AND TRIGONOMETRY 6th E by Aufmann, Barker, Verity
SOLUTIONS MANUAL: College Geometry A Discovery Approach 2nd E by David Kay
SOLUTIONS MANUAL: College Physics 8 ED by Serway, Faughn, Vuille
SOLUTIONS MANUAL: College Physics 9th ED by Serway,Vuille (Teague)
SOLUTIONS MANUAL: Communication Networks, 2e, Alberto Leon-Garcia, Indra Widjaja
SOLUTIONS MANUAL: Communication Systems (4th Ed., Simon Haykin)
SOLUTIONS MANUAL: Communication Systems An Introduction to Signals and Noise in Electrical Communication, 4E, A. Bruce Carlson
SOLUTIONS MANUAL: Communication Systems Engineering (2nd Ed., John G. Proakis & Masoud Salehi)
SOLUTIONS MANUAL: Complex Variables and Applications 7 ed by JW Brown RV Churchill
SOLUTIONS MANUAL: Complex Variables with Applications, 3rd ED by David A. Wunsch
SOLUTIONS MANUAL: COMPUTATIONAL FINANCE A SCIENTIFIC PERSPECTIVE MILEN KASSABOV,CORNELIS A. LOS
SOLUTIONS MANUAL: Computational Techniques for Fluid Dynamics Srinivas, K., Fletcher, C.A.J.
SOLUTIONS MANUAL: Computer Architecture - A Quantitative Approach, 4th Ed by Hennessy, Patterson
SOLUTIONS MANUAL: Computer Architecture Pipelined & Parallel Processor Design by Michael J Flynn
SOLUTIONS MANUAL: Computer Graphics Using OpenGL 3rd E by Francis S Hill, Jr. & Stephen M Kelley
SOLUTIONS MANUAL: Computer Networking A Top-Down Approach Featuring the Internet, 3E Kurose,Ross
SOLUTIONS MANUAL: Computer Networking: A Top-Down Approach (4th Ed., James F. Kurose & Keith W. Ross)
SOLUTIONS MANUAL: Computer Networks - A Systems Approach 3 ed by Peterson Davie
SOLUTIONS MANUAL: Computer Networks - A Systems Approach 4 ed by Peterson Davie
SOLUTIONS MANUAL: Computer Networks A Systems Approach, 2nd Edition, Larry Peterson, Bruce Davie
SOLUTIONS MANUAL: Computer Networks, 4th Ed., by Andrew S. Tanenbaum
SOLUTIONS MANUAL: Computer Organization 3rd Edition by Carl Hamacher , Zvonoko Vranesic ,Safwat Zaky
SOLUTIONS MANUAL: Computer Organization and Architecture: Designing for Performance (7th Ed., William Stallings)
SOLUTIONS MANUAL: Computer Organization and Design The Hardware Software Interface 4 ed by David A Patterson
SOLUTIONS MANUAL: Computer Organization and Design The Hardware Software Interface, 3rd edition by David A Patterson and John L Hennessy
SOLUTIONS MANUAL: Computer Science Illuminated 4th ed by Nell Dale, John Lewis
SOLUTIONS MANUAL: Computer system architecture 3rd Ed Morris Mano
SOLUTIONS MANUAL: Computer Systems- A Programmer's Perspective by Bryant, O'Hallaron
SOLUTIONS MANUAL: Computer Systems Organization and Architecture by John D. Carpinelli
SOLUTIONS MANUAL: Computer Vision A Modern Approach by Forsyth, Ponce
SOLUTIONS MANUAL: Computer-Controlled Systems 3rd ED by Astrom, Wittenmark
SOLUTIONS MANUAL: Concepts and Applications of Finite Element Analysis (4th Ed., Cook, Malkus, Plesha & Witt)
SOLUTIONS MANUAL: Concepts in Thermal Physics 2nd Ed by Blundell
SOLUTIONS MANUAL: Concepts of Modern Physics 6th ED by Arthur Beiser
SOLUTIONS MANUAL: Concepts of Physics (Volume 1 & 2) by H.C. Verma
SOLUTIONS MANUAL: Concepts of Programming Languages 7th ED by Sebesta
SOLUTIONS MANUAL: Construction Surveying and Layout 2ed by Crawford
SOLUTIONS MANUAL: Contemporary Engineering Economics (4th Ed., Chan Park)
SOLUTIONS MANUAL: Contemporary Engineering Economics 5th Ed by Chan S. Park
SOLUTIONS MANUAL: Continuum Electromechanics by James R. Melcher
SOLUTIONS MANUAL: Control Systems Engineering, 4E, by Norman Nise
SOLUTIONS MANUAL: Control Systems Engineering, 6th ED by Norman Nise
SOLUTIONS MANUAL: Control Systems Principles and Design 2e by M. Gopal
SOLUTIONS MANUAL: Convex Analysis and Optimization Dimitri P. Bertsekas
SOLUTIONS MANUAL: Corporate Finance & MyFinanceLab Student Access Code Card, Global 2 Ed by Berk, DeMarzo
SOLUTIONS MANUAL: Corporate Finance 8th edition by Ross
SOLUTIONS MANUAL: Corporate Finance 9th edition by Ross
SOLUTIONS MANUAL: Corporate Finance The Core plus MyFinanceLab Student Access Kit (Jonathan Berk & Peter DeMarzo)
SOLUTIONS MANUAL: Corporate Finance, 7E, by Ross
SOLUTIONS MANUAL: Corporations, Partnerships, Estates and Trusts ( 2011 ) by Hoffman, Maloney
SOLUTIONS MANUAL: COST ACCOUNTING - Creating Value for Management 5th E by MICHAEL MAHER
SOLUTIONS MANUAL: Cost Accounting-A Managerial Emphasis 13th Ed by Charles Horngren
SOLUTIONS MANUAL: Coulson & Richardson's Chemical Engineering (Vol 2 - 5th Ed) & (Vol 3 - 3rd Ed) by BACKHURST, HARKER
SOLUTIONS MANUAL: Cryptography and Network Security (4th Ed., William Stallings)
SOLUTIONS MANUAL: Data & Computer Communication, 7th Ed, by William Stallings
SOLUTIONS MANUAL: Data Communications Networking 4th Ed by Behrouz Forouzan
SOLUTIONS MANUAL: Data Structures and Algorithm Analysis in C 2nd ED by Weiss
SOLUTIONS MANUAL: Data Structures with Java by John R. Hubbard, Anita Huray
SOLUTIONS MANUAL: Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke
SOLUTIONS MANUAL: Database System Concepts 4th ED by Silberschatz , Korth , Sudarshan
SOLUTIONS MANUAL: Database System Concepts 5th ED by Silberschatz, Korth, Sudarshan
SOLUTIONS MANUAL: Derivatives - Principles & Practice by Sundaram , Das
SOLUTIONS MANUAL: Design Analysis in Rock Mechanics by William G. Pariseau
SOLUTIONS MANUAL: Design and Analysis of Experiments, 6E, by Montgomery
SOLUTIONS MANUAL: Design of Analog CMOS Integrated Circuits by Razavi
SOLUTIONS MANUAL: Design of Analog CMOS Integrated Circuits, 2 Edition, by Razavi Douglas C. Montgomery
SOLUTIONS MANUAL: Design of Fluid Thermal Systems, 2nd Edition janna
SOLUTIONS MANUAL: Design of Machinery (3rd Ed., Norton)
SOLUTIONS MANUAL: Design of machinery 4th ed by Norton
SOLUTIONS MANUAL: Design of Reinforced Concrete, 8th Ed by McCormac, Brown
SOLUTIONS MANUAL: Design with Constructal Theory by Adrian Bejan, Lorente
SOLUTIONS MANUAL: Design with Operational Amplifiers and Analog Integrated Circuits (3rd Ed., Sergio Franco)
SOLUTIONS MANUAL: Device Electronics for Integrated Circuits 3rd Edition by muller kamins
SOLUTIONS MANUAL: Differential Equations & Linear Algebra 3rd ed by C. Henry Edwards & David E. Penney
SOLUTIONS MANUAL: Differential Equations and Boundary Value Problems - Computing and Modeling 4th Ed by Edwards, Penney
SOLUTIONS MANUAL: Differential Equations and Linear Algebra ( 2nd Ed., Jerry Farlow, Hall, McDill & West)
SOLUTIONS MANUAL: Differential Equations and Linear Algebra ( C. Henry Edwards & David E. Penney)
SOLUTIONS MANUAL: Differential Equations and Linear Algebra 3e by Stephen W Goode
SOLUTIONS MANUAL: Differential Equations with Boundary Value Problems (2e, John Polking, Al Boggess & Arnold)
SOLUTIONS MANUAL: Digital & Analog Communication Systems (7th Ed., Leon W. Couch)
SOLUTIONS MANUAL: Digital Communication 3rd ED by Barry, Lee, Messerschmitt
SOLUTIONS MANUAL: Digital Communications Fundamentals and Applications 2e Bernard Sklar
SOLUTIONS MANUAL: Digital Communications, 4E, by Proakis
SOLUTIONS MANUAL: Digital Control & State Variable Methods 2nd Ed by Madan Gopal
SOLUTIONS MANUAL: Digital Design (4th Ed., M. Morris Mano & Michael D. Ciletti)
SOLUTIONS MANUAL: Digital Design: Principles and Practices Package (4th Ed., John F. Wakerly)
SOLUTIONS MANUAL: Digital Fundamentals ( 9th Ed., Thomas L. Floyd)
SOLUTIONS MANUAL: Digital Image Processing, 2e, by Gonzalez, Woods
SOLUTIONS MANUAL: Digital Integrated Circuits, 2nd Ed., by Rabaey
SOLUTIONS MANUAL: Digital Logic Design by Mano
SOLUTIONS MANUAL: Digital Signal Processing - A Modern Introduction, by Ashok Ambardar
SOLUTIONS MANUAL: Digital Signal Processing Principles, Algorithms and Applications, 3rd Edition by John G. Proakis
SOLUTIONS MANUAL: Digital Signal Processing 4th Ed by Proakis, Manolakis
SOLUTIONS MANUAL: Digital Signal Processing a computer based approach (2nd Ed.) (Mitra)
SOLUTIONS MANUAL: Digital Signal Processing a computer based approach (Mitra)
SOLUTIONS MANUAL: Digital Signal Processing by Proakis & Manolakis
SOLUTIONS MANUAL: Digital Signal Processing by Thomas J. Cavicchi
SOLUTIONS MANUAL: Digital Systems - Principles and Applications (10th Ed., Ronald Tocci, Neal Widmer, Greg Moss)
SOLUTIONS MANUAL: Discovering Advanced Algebra - An Investigative Approach
SOLUTIONS MANUAL: Discrete and Combinatorial Mathematics 5e by Ralph P. Grimaldi
SOLUTIONS MANUAL: Discrete Mathematics ( 6th Ed., Richard Johnsonbaugh )
SOLUTIONS MANUAL: Discrete Mathematics ( 6th Edition) by Richard Johnsonbaugh
SOLUTIONS MANUAL: Discrete Mathematics 3rd ED by Goodaire, Parmenter
SOLUTIONS MANUAL: Discrete Mathematics with Applications 3rd ED by Susanna S. Epp
SOLUTIONS MANUAL: Discrete Random Signals and Statistical Signal Processing Charles W. Therrien
SOLUTIONS MANUAL: Discrete Time Signal Processing, 2nd Edition, Oppenheim
SOLUTIONS MANUAL: Discrete-Event System Simulation 3rd Ed by banks
SOLUTIONS MANUAL: Discrete-Time Signal Processing 3rd ed by Oppenheim, Schafer
SOLUTIONS MANUAL: DSP First A Multimedia Approach-Mclellan, Schafer & Yoder
SOLUTIONS MANUAL: Dynamic Modeling and Control of Engineering Systems 2 E T. Kulakowski , F. Gardner, Shearer
SOLUTIONS MANUAL: Dynamics of Flight- Stability and Control, 3rd Ed by Etkin, Reid
SOLUTIONS MANUAL: Dynamics of Mechanical Systems by C. T. F. Ross
SOLUTIONS MANUAL: Dynamics of Structures 2nd ED by Clough, Penzien
SOLUTIONS MANUAL: Dynamics of structures 3rd E by Anil K. Chopra
SOLUTIONS MANUAL: Econometric Analysis of Cross Section and Panel Data (2003 ) by Jeffrey M Wooldridge
SOLUTIONS MANUAL: Econometric Analysis, 5E, by Greene
SOLUTIONS MANUAL: Econometric Analysis, 6E, by Greene
SOLUTIONS MANUAL: Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira
SOLUTIONS MANUAL: Econometrics, 2nd edition by Badi H. Baltagi
SOLUTIONS MANUAL: Econometrics: A Modern Introduction (Michael P. Murray)
SOLUTIONS MANUAL: Elasticity - Theory, Applications and Numerics 2nd ED by Martin H. Sadd
SOLUTIONS MANUAL: Electric Circuits (7th Ed., James W Nilsson & Susan Riedel)
SOLUTIONS MANUAL: Electric Circuits (8th Ed., James W Nilsson & Susan Riedel)
SOLUTIONS MANUAL: Electric Circuits 9th Ed by Nilsson, Riedel
SOLUTIONS MANUAL: Electric Machinery 6th ed. A.E. Fitzgerald,Kingsley,Umans
SOLUTIONS MANUAL: Electric Machinery and Power System Fundamentals (Chapman)
SOLUTIONS MANUAL: Electric Machinery Fundamentals (4th Ed., Chapman)
SOLUTIONS MANUAL: Electric Machines Analysis and Design Applying MATLAB,Jim Cathey
SOLUTIONS MANUAL: Electric Machines By D. P. Kothari, I. J. Nagrath
SOLUTIONS MANUAL: Electrical Engineering - Principles and Applications 5E Hambley
SOLUTIONS MANUAL: Electrical Engineering Principles and Applications (3rd Ed., Allan R. Hambley)
SOLUTIONS MANUAL: Electrical Engineering Principles and Applications (4th Ed., Allan R. Hambley)
SOLUTIONS MANUAL: Electrical Machines, Drives and Power Systems (6th Ed., Theodore Wildi)
SOLUTIONS MANUAL: Electromagnetic Fields and Energy by Haus, Melcher
SOLUTIONS MANUAL: Electromagnetics Problem Solver (Problem Solvers) By The Staff of REA
SOLUTIONS MANUAL: Electromagnetism. Principles and Applications by LORRAIN, PAUL ; CORSON, DAVID
SOLUTIONS MANUAL: Electromechanical Dynamics Part 1, 2, 3 by Herbert H. Woodson, James R. Melcher
SOLUTIONS MANUAL: Electronic Circuit Analysis, 2nd Ed., by Donald Neamen
SOLUTIONS MANUAL: Electronic Devices 6th ed and electronic devices Electron Flow Version 4th ed, Floyd
SOLUTIONS MANUAL: Electronic Devices and Circuit Theory 10th Ed by Boylestad, Nashelsky
SOLUTIONS MANUAL: Electronic Devices and Circuit Theory 8th Ed by Robert Boylestad
SOLUTIONS MANUAL: Electronic Physics Strabman
SOLUTIONS MANUAL: Electronics & Communication Engineering 5th ED by Kanodia
SOLUTIONS MANUAL: Electronics, 2nd Ed., by Allan R. Hambley
SOLUTIONS MANUAL: Elementary Differential Equations ( Werner E. Kohler, Johnson)
SOLUTIONS MANUAL: Elementary Differential Equations and Boundary Value Problems (8th Ed., Boyce & Diprima)
SOLUTIONS MANUAL: Elementary Linear Algebra 5th edition by Stanley I. Grossman
SOLUTIONS MANUAL: Elementary Linear Algebra by Matthews
SOLUTIONS MANUAL: Elementary Linear Algebra with Applications (9th Ed., Howard Anton & Chris Rorres)
SOLUTIONS MANUAL: Elementary Linear Algebra with Applications 9E by Kolman, Hill
SOLUTIONS MANUAL: Elementary mechanics & thermodynamics jhon w.Nobury
SOLUTIONS MANUAL: ELEMENTARY NUMBER THEORY AND ITS APPLICATIONS, (5TH EDITION, Bart Goddard, Kenneth H. Rosen)
SOLUTIONS MANUAL: Elementary Number Theory and Its Applications, 6th Ed by Kenneth H. Rosen
SOLUTIONS MANUAL: Elementary Principles of Chemical Processes (3rd Ed., Felder & Rousseau)
SOLUTIONS MANUAL: Elementary Statistics Using The Graphing Calculator 9 Ed by MILTON LOYER
SOLUTIONS MANUAL: Elementary Statistics Using the Graphing Calculator For the TI-83-84 Plus (Mario F. Triola)
SOLUTIONS MANUAL: ELEMENTARY SURVEYING 13th ED by Ghilani,Wolf
SOLUTIONS MANUAL: Elements of Information Theory - M. Cover, Joy A. Thomas
SOLUTIONS MANUAL: Elements of Chemical Reaction Engineering 4th Edition by Fogler
SOLUTIONS MANUAL: Elements of Chemical Reaction Engineering by Fogler hubbard, hamman , johnson , 3rd edition
SOLUTIONS MANUAL: Elements of Deductive Inference by Bessie, Glennan
SOLUTIONS MANUAL: Elements of Electromagnetics , 2 ed by Matthew N. O. Sadiku
SOLUTIONS MANUAL: Elements of Electromagnetics , 3ed by Matthew N. O. Sadiku
SOLUTIONS MANUAL: Elements of Forecasting in Business, Finance, Economics and Government by Diebold
SOLUTIONS MANUAL: Embedded Microcomputer Systems Real Time Interfacing, 2nd Edition , Jonathan W. Valvano
SOLUTIONS MANUAL: Embedded System Design by Vahid, Givargis
SOLUTIONS MANUAL: Engineering and Chemical Thermodynamics (Koretsky)
SOLUTIONS MANUAL: ENGINEERING BIOMECHANICS (STATICS) by Angela Matos, Eladio Pereira, Juan Uribe and Elisandra Valentin
SOLUTIONS MANUAL: Engineering Circuit Analysis 6Ed, Luay Shaban
SOLUTIONS MANUAL: Engineering Circuit Analysis 6th ed by Hayt
SOLUTIONS MANUAL: Engineering Circuit Analysis 7th Ed. by William H. Hayt Jr
SOLUTIONS MANUAL: Engineering Economic Analysis 9th ED by Newnan
SOLUTIONS MANUAL: Engineering Economy and the Decision-Making Process (Joseph C. Hartman)
SOLUTIONS MANUAL: Engineering Economy, 14 Ed by Sullivan
SOLUTIONS MANUAL: Engineering Electromagnetics 6E by William H. Hayt Jr. and John A. Buck
SOLUTIONS MANUAL: Engineering Electromagnetics 7E by William H. Hayt Jr. and John A. Buck
SOLUTIONS MANUAL: Engineering Fluid Mechanics - 8th Ed by Crowe, Elger & Roberson
SOLUTIONS MANUAL: Engineering Fluid Mechanics 7th Ed by Crowe and Donald
SOLUTIONS MANUAL: Engineering Materials Science, by Milton Ohring
SOLUTIONS MANUAL: Engineering Mathematics (4th Ed., John Bird)
SOLUTIONS MANUAL: Engineering Mechanics - Dynamics by Boresi, Schmidt
SOLUTIONS MANUAL: Engineering Mechanics - Dynamics, 5th Ed (J. L. Meriam, L. G. Kraige)
SOLUTIONS MANUAL: Engineering Mechanics - Dynamics, 6th Ed (J. L. Meriam, L. G. Kraige)
SOLUTIONS MANUAL: Engineering Mechanics - Statics (10th Edition) by Russell C. Hibbeler
SOLUTIONS MANUAL: Engineering Mechanics - Statics (11th Edition) by Russell C. Hibbeler
SOLUTIONS MANUAL: Engineering Mechanics - Statics by Boresi, Schmidt
SOLUTIONS MANUAL: Engineering Mechanics - Statics, 4th Ed (J. L. Meriam, L. G. Kraige)
SOLUTIONS MANUAL: Engineering Mechanics - Statics, 6th Ed (J. L. Meriam, L. G. Kraige)
SOLUTIONS MANUAL: Engineering Mechanics : Dynamics (11th Ed., Hibbeler)
SOLUTIONS MANUAL: Engineering Mechanics by Manoj Kumar Harbola
SOLUTIONS MANUAL: Engineering Mechanics Dynamic (10th Edition) hibbeler
SOLUTIONS MANUAL: Engineering Mechanics Dynamics (12th Ed., Hibbeler)
SOLUTIONS MANUAL: Engineering Mechanics Dynamics, Bedford & Fowler, 5th Edition
SOLUTIONS MANUAL: Engineering Mechanics Dynamics, by R. C. Hibbeler, 3rd
SOLUTIONS MANUAL: Engineering Mechanics Statics (12th Ed., Hibbeler)
SOLUTIONS MANUAL: Engineering Mechanics Statics, Bedford & Fowler, 5th Edition
SOLUTIONS MANUAL: Engineering Mechanics, Dynamics 2nd E by Riley, Sturges
SOLUTIONS MANUAL: Engineering Mechanics, Statics 2nd E by Riley, Sturges
SOLUTIONS MANUAL: Engineering Statistics (4th Ed., Douglas Montgomery, George Runger & Norma Faris Hubele)
SOLUTIONS MANUAL: Engineering Vibration 3rd Ed by Inman
SOLUTIONS MANUAL: Equilibrium Statistical Physics, 2nd E by Plischke, Bergersen
SOLUTIONS MANUAL: Erosion and sedimentation by Pierre Y. Julien
SOLUTIONS MANUAL: Essentials of Corporate Finance 6th Ed by Ross,Westerfield,Jordan
SOLUTIONS MANUAL: Essentials of Corporate Finance 7th Ed by Ross,Westerfield,Jordan
SOLUTIONS MANUAL: Essentials of Soil Mechanics and Foundations: Basic Geotechnics (7th Ed., David F. McCarthy)
SOLUTIONS MANUAL: Experimental Methods for Engineers 8th ED by Holman
SOLUTIONS MANUAL: Feedback Control of Dynamic Systems (4th Ed., Franklin, Powell & Emami-Naeini)
SOLUTIONS MANUAL: Feedback Control of Dynamic Systems (5th Ed., Franklin, Powell & Emami-Naeini)
SOLUTIONS MANUAL: Feedback Control of Dynamic Systems 6th E by Franklin, Powell, Naeini
SOLUTIONS MANUAL: Field and Wave Electromagnetics 2nd Ed by David K. Cheng
SOLUTIONS MANUAL: Financial Accounting 6th E with Annual Report by Libby, Short
SOLUTIONS MANUAL: Financial Accounting 6th Ed by Harrison
SOLUTIONS MANUAL: Financial Accounting An Integrated Approach, 6th Ed by Gibbins
SOLUTIONS MANUAL: Financial Management- Principles and Applications, 10th Ed by Keown, Scott
SOLUTIONS MANUAL: Financial Management- Theory and Practice 12 th ED by Brigham, Ehrhardt
SOLUTIONS MANUAL: Financial Reporting and Analysis Using Financial Accounting Information 10th Ed by Gibson
SOLUTIONS MANUAL: Financial Reporting and Analysis, 3E by Revsine, Collins, Johnson
SOLUTIONS MANUAL: Finite Element Techniques in Structural Mechanics Ross
SOLUTIONS MANUAL: First Course in Abstract Algebra, 3rd Ed by Joseph J. Rotman
SOLUTIONS MANUAL: First Course in Probability (7th Ed., Sheldon Ross)
SOLUTIONS MANUAL: Fluid Mechanics (5th Ed., White)
SOLUTIONS MANUAL: Fluid Mechanics 4th Ed by Cohen, Kundu
SOLUTIONS MANUAL: Fluid Mechanics 4th Edition by Frank M. White
SOLUTIONS MANUAL: Fluid Mechanics and Thermodynamics of Turbomachinery (5th Ed., S.L. Dixon)
SOLUTIONS MANUAL: Fluid Mechanics by CENGEL
SOLUTIONS MANUAL: Fluid Mechanics Egon Krause
SOLUTIONS MANUAL: Fluid Mechanics for Chemical Engineers, 3rd Ed by Noel de Nevers
SOLUTIONS MANUAL: Fluid Mechanics Fundamentals and Applications by Çengel & Cimbala
SOLUTIONS MANUAL: Fluid Mechanics with Engineering Applications, 10th Edition, by Finnemore
SOLUTIONS MANUAL: Foundations of Analog and Digital Electronic Circuits by Agarwal, Lang
SOLUTIONS MANUAL: Foundations of Applied Combinatorics by Bender, Williamson
SOLUTIONS MANUAL: Foundations of Colloid Science 2e , Hunter
SOLUTIONS MANUAL: Foundations of Electromagnetic Theory by John R. Reitz, Frederick J. Milford
SOLUTIONS MANUAL: Foundations of Mathematical Economics by Michael Carter
SOLUTIONS MANUAL: Foundations of Modern Macroeconomics 2nd Ed by Heijdra, Reijnders, Romp
SOLUTIONS MANUAL: Fourier and Laplace Transform - Antwoorden
SOLUTIONS MANUAL: Fractal Geometry Mathematical Foundations and Applications, 2nd Ed Kenneth Falcone
SOLUTIONS MANUAL: fracture mechanics ; fundamentals and applications, 2E, by T.L. Anderson
SOLUTIONS MANUAL: From Polymers to Plastics By A.K. van der Vegt
SOLUTIONS MANUAL: Fundamental Methods of Mathematical Economics 4th E by Chiang,Wainwright
SOLUTIONS MANUAL: Fundamental Quantum Mechanics for Engineers by Leon van Dommelen
SOLUTIONS MANUAL: Fundamentals of Advanced Accounting By Fischer, Taylor
SOLUTIONS MANUAL: Fundamentals of Aerodynamics ( 3 Ed., Anderson)
SOLUTIONS MANUAL: Fundamentals of Aerodynamics (2 Ed., Anderson)
SOLUTIONS MANUAL: Fundamentals of Aircraft Structural Analysis by Howard D. Curtis
SOLUTIONS MANUAL: Fundamentals of Applied Electromagnetics (5th Ed., Fawwaz T. Ulaby)
SOLUTIONS MANUAL: Fundamentals of Chemical Reaction Engineering by Davis
SOLUTIONS MANUAL: Fundamentals of Complex Analysis ( 3rd Ed., E. Saff & Arthur Snider )
SOLUTIONS MANUAL: Fundamentals of Computer Organization and Architecture by Abd-El-Barr, El-Rewini
SOLUTIONS MANUAL: Fundamentals of Corporate Finance 8th edition by Ross
SOLUTIONS MANUAL: Fundamentals of Corporate Finance 9th edition by Ross
SOLUTIONS MANUAL: Fundamentals of Corporate Finance, 4th Edition (Brealey, Myers, Marcus)
SOLUTIONS MANUAL: Fundamentals of Differential Equations 7E Kent Nagle, B. Saff, Snider
SOLUTIONS MANUAL: Fundamentals of Differential Equations and Boundary Value Problems, 6th Ed by Nagle ,Saff, Snider
SOLUTIONS MANUAL: Fundamentals of Digital Logic with VHDL Design (1st Ed., Stephen Brown Vranesic)
SOLUTIONS MANUAL: Fundamentals of Electric Circuits (2nd.ed.) by C.K.Alexander M.N.O.Sadiku
SOLUTIONS MANUAL: Fundamentals of Electric Circuits (4E., Charles Alexander & Matthew Sadiku)
SOLUTIONS MANUAL: Fundamentals of Electromagnetics with Engineering Applications (Stuart Wentworth)
SOLUTIONS MANUAL: Fundamentals of Electronic Circuit Design , Comer
SOLUTIONS MANUAL: Fundamentals of Engineering Economics 2nd E by Chan S. Park
SOLUTIONS MANUAL: FUNDAMENTALS OF ENGINEERING ELECTROMAGNETICS, by DAVID CHENG
SOLUTIONS MANUAL: Fundamentals of Engineering Thermodynamics, 6th Ed (Michael J. Moran, Howard N. Shapiro)
SOLUTIONS MANUAL: Fundamentals of Engineering Thermodynamics, 7th Ed (Michael J. Moran, Howard N. Shapiro)
SOLUTIONS MANUAL: Fundamentals of Financial Management 12th edition James C. Van Horne, Wachowicz
SOLUTIONS MANUAL: Fundamentals of Fluid Mechanics 5th Ed Munson Young Okiishi
SOLUTIONS MANUAL: Fundamentals of Fluid Mechanics 6th Ed by Munson
SOLUTIONS MANUAL: Fundamentals of Fluid Mechanics, 4E (Bruce R. Munson, Donald F. Young, Theodore H.)
SOLUTIONS MANUAL: Fundamentals of Heat and Mass Transfer - 5th Edition F.P. Incropera D.P. DeWitt
SOLUTIONS MANUAL: Fundamentals of Heat and Mass Transfer (4th Ed., Incropera, DeWitt)
SOLUTIONS MANUAL: Fundamentals of Heat and Mass Transfer (6th Ed., Incropera, DeWitt)
SOLUTIONS MANUAL: Fundamentals of Hydraulic Engineering Systems 4th E by Houghtalen,Akan,Hwang
SOLUTIONS MANUAL: Fundamentals of Investments, 4 th ed by Jordan and Miller
SOLUTIONS MANUAL: Fundamentals of Investments, 5th E by Jordan, Miller
SOLUTIONS MANUAL: Fundamentals of Investments, 6th E by Jordan, Miller,Dolvin
SOLUTIONS MANUAL: Fundamentals of Logic Design, 5th Ed., by Charles Roth
SOLUTIONS MANUAL: Fundamentals of Machine Component Design (3rd Ed., Juvinall)
SOLUTIONS MANUAL: Fundamentals of Machine Component Design 4th Ed by Juvinall
SOLUTIONS MANUAL: Fundamentals of Machine Elements 2nd E by Bernard Hamrock
SOLUTIONS MANUAL: Fundamentals of Machine Elements by Bernard Hamrock
SOLUTIONS MANUAL: Fundamentals of Manufacturing 2nd Edition by Philip D. Rufe
SOLUTIONS MANUAL: Fundamentals of Materials Science and Engineering- An Integrated Approach, 3rd Ed by Callister
SOLUTIONS MANUAL: Fundamentals of Microelectronics by Behzad Razavi
SOLUTIONS MANUAL: Fundamentals of Modern Manufacturing 3rd Ed by Mikell P. Groover
SOLUTIONS MANUAL: Fundamentals of Modern Manufacturing: Materials, Processes, and Systems (2nd Ed., Mikell P. Groover)
SOLUTIONS MANUAL: Fundamentals of Modern Manufacturing: Materials, Processes, and Systems 4th Ed.by Groover
SOLUTIONS MANUAL: Fundamentals of Momentum, Heat and Mass Transfer, 4th Ed by Welty,Wilson
SOLUTIONS MANUAL: Fundamentals of Momentum, Heat and Mass Transfer, 5th Ed by Welty,Wilson
SOLUTIONS MANUAL: Fundamentals of Organic Chemistry, 5E, by T. W. Graham Solomons
SOLUTIONS MANUAL: Fundamentals of Physics (7th Ed., David Halliday, Robert Resnick & Jearl Walker)
SOLUTIONS MANUAL: Fundamentals of Physics 9th Ed by Resnick, Walker, Halliday
SOLUTIONS MANUAL: Fundamentals of Physics, 8th Edition Halliday, Resnick, Walker
SOLUTIONS MANUAL: Fundamentals of Power Semiconductor Devices By Jayant Baliga
SOLUTIONS MANUAL: Fundamentals of Probability, with Stochastic Processes (3rd Ed., Saeed Ghahramani)
SOLUTIONS MANUAL: Fundamentals of Quantum Mechanics (C.L. Tang)
SOLUTIONS MANUAL: Fundamentals of Semiconductor Devices, 1st Edition by Anderson
SOLUTIONS MANUAL: Fundamentals of Signals and Systems Using the Web and Matlab (3rd Ed., Kamen & Bonnie S Heck)
SOLUTIONS MANUAL: Fundamentals of Solid-State Electronics by Chih-Tang Sah
SOLUTIONS MANUAL: Fundamentals of Structural Analysis 3rd Ed by Leet
SOLUTIONS MANUAL: Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel
SOLUTIONS MANUAL: Fundamentals of Thermodynamics 5th Ed by Sonntag, Borgnakke and Van Wylen
SOLUTIONS MANUAL: Fundamentals of Thermodynamics 6th Ed by Sonntag, Borgnakke & Van Wylen
SOLUTIONS MANUAL: Fundamentals of Thermodynamics 7th Ed by Borgnakke, Sonntag
SOLUTIONS MANUAL: Fundamentals of Wireless Communication by Tse and Viswanath
SOLUTIONS MANUAL: Fundamentals of Wireless Communication by Tse, Viswanath
SOLUTIONS MANUAL: Fundamentals of Digital Signal Processing using MATLAB, 2nd Ed by Schilling, Harris
SOLUTIONS MANUAL: Gas Dynamics (3rd Ed., John & Keith)
SOLUTIONS MANUAL: General Chemistry 9 Edition by Ebbings, Gammon
SOLUTIONS MANUAL: General Chemistry, 8th Edition by Ralph H. Petrucci; William S. Harwood; Geoffrey Herring
SOLUTIONS MANUAL: Geometry - A High School Course by S. Lang and G. Murrow
SOLUTIONS MANUAL: Geometry ( Glencoe )
SOLUTIONS MANUAL: Geometry and Discrete Mathematics Addison Wesley
SOLUTIONS MANUAL: Green Engineering - Environmentally Conscious Design of Chemical Processes by Shonnard, Allen
SOLUTIONS MANUAL: Guide to Energy Management, 6th Edition by Klaus Dieter E. Pawlik
SOLUTIONS MANUAL: Guide to Energy Management, Fifth Edition, Klaus-Dieter E. Pawlik
SOLUTIONS MANUAL: HARCOURT MATHEMATICS 12 Advanced Functions and Introductory Calculus
SOLUTIONS MANUAL: Harcourt Mathematics 12 Geometry and Discrete Mathematics
SOLUTIONS MANUAL: Heat and Mass Transfer: A Practical Approach (3rd. Ed., Cengel)
SOLUTIONS MANUAL: Heat Transfer A Practical Approach ,Yunus A. Cengel 2d ed
SOLUTIONS MANUAL: Heating, Ventilating and Air Conditioning Analysis and Design, 6th Edition McQuiston, Parker, Spitler
SOLUTIONS MANUAL: Higher Algebra 3rd edition by Hall and Knight
SOLUTIONS MANUAL: HIGH-SPEED NETWORKS AND INTERNETS 2 ED STALLINGS
SOLUTIONS MANUAL: History of Mathematics: Brief Version (Victor J. Katz)
SOLUTIONS MANUAL: Hydraulics in Civil and Environmental Engineering 4 E by Chadwick , Morfett
SOLUTIONS MANUAL: Hydraulics in Civil and Environmental Engineering 4th Ed by Chadwick , Borthwick
SOLUTIONS MANUAL: Industrial Organization Theory & Applications by Shy
SOLUTIONS MANUAL: Intermediate Accounting - IFRS Edition Vol.1 by Kieso, Weygandt, Warfield
SOLUTIONS MANUAL: Intermediate Accounting 12th ed by Kieso
SOLUTIONS MANUAL: Intermediate Accounting 13 ed by Kieso
SOLUTIONS MANUAL: Intermediate Accounting 14 ed by Kieso
SOLUTIONS MANUAL: INTERMEDIATE ACCOUNTING, 6th Edition, by Spiceland, Sepe
SOLUTIONS MANUAL: Intermediate Algebra - Concepts & Applications 8th Ed by Bittinger, Ellenbogen
SOLUTIONS MANUAL: Introduction to Algorithms, 2nd Ed by Cormen, Leiserson
SOLUTIONS MANUAL: Introduction to Applied Modern Physics by Henok Abebe
SOLUTIONS MANUAL: Introduction to Chemical Engineering Thermodynamics (7th Ed., Smith & Van Ness)
SOLUTIONS MANUAL: Introduction to Commutative Algebra by M. F. Atiyah
SOLUTIONS MANUAL: Introduction to Digital Signal Processing (in Serbian) by Lj. Milic and Z. Dobrosavljevic
SOLUTIONS MANUAL: Introduction to Econometrics (2nd ed., James H. Stock & Mark W. Watson)
SOLUTIONS MANUAL: Introduction to Electric Circuits 7th Edition by Dorf, Svaboda
SOLUTIONS MANUAL: Introduction to Electric Circuits, 6E, Dorf
SOLUTIONS MANUAL: Introduction to Electrodynamics (3rd Ed., David J. Griffiths)
SOLUTIONS MANUAL: Introduction to Elementary Particles 2nd Ed by David Griffiths
SOLUTIONS MANUAL: Introduction to Environmental Engineering and Science (3rd Ed., Gilbert M. Masters & Wendell P. Ela)
SOLUTIONS MANUAL: Introduction to Environmental Engineering and Science, Edition 2, Masters
SOLUTIONS MANUAL: Introduction to Ergonomics 2E by Robert Bridger
SOLUTIONS MANUAL: Introduction to Flight 7th ED by John D. Anderson
SOLUTIONS MANUAL: Introduction to Fluid Mechanics ( 7 E., Robert Fox, Alan McDonald & Philip )
SOLUTIONS MANUAL: Introduction to Fluid Mechanics (6E., Robert Fox, Alan McDonald & Philip)
SOLUTIONS MANUAL: Introduction to fluid mechanics 5th edition by Alan T. McDonald, Robert W Fox
SOLUTIONS MANUAL: Introduction to Fourier Optics 3rd Ed by Joseph W. Goodman
SOLUTIONS MANUAL: Introduction to Graph Theory 2E - West
SOLUTIONS MANUAL: Introduction to Heat Transfer by Vedat S. Arpaci, Ahmet Selamet, Shu-Hsin Kao
SOLUTIONS MANUAL: Introduction to Hydrology 5th Edition by Warren Viessman Jr., Gary L. Lewis
SOLUTIONS MANUAL: Introduction to Java Programming, Comprehensive Version 7th Ed by Liang
SOLUTIONS MANUAL: Introduction to Linear Algebra, 3rd Ed., by Gilbert Strang
SOLUTIONS MANUAL: Introduction to Linear Algebra, 4th Ed by Gilbert Strang
SOLUTIONS MANUAL: Introduction to Management Accounting, 14 ED by Horngren, Schatzberg
SOLUTIONS MANUAL: Introduction to Materials Science for Engineers (6th Ed., Shackelford)
SOLUTIONS MANUAL: Introduction to Materials Science for Engineers 7th E by Shackelford
SOLUTIONS MANUAL: Introduction to Mathematical Statistics (6th Ed., Hogg, Craig & McKean)
SOLUTIONS MANUAL: Introduction to Mechatronics and Measurements Systems 2nd Ed by Alciatore, Histand
SOLUTIONS MANUAL: Introduction to Mechatronics and Measurements Systems 3rd Ed by Alciatore, Histand
SOLUTIONS MANUAL: Introduction to Nuclear And Particle Physics 2nd E by Bromberg, Das, Ferbel
SOLUTIONS MANUAL: Introduction to Operations Research - 7th ed by Frederick Hillier, Gerald Lieberman
SOLUTIONS MANUAL: Introduction to Probability 2nd Ed by Bertsekas and Tsitsiklis
SOLUTIONS MANUAL: Introduction to Probability by Dimitri P. Bertsekas and John N. Tsitsiklis
SOLUTIONS MANUAL: Introduction to Probability by Grinstead, Snell
SOLUTIONS MANUAL: Introduction to Probability Models 10th Ed by M. Ross
SOLUTIONS MANUAL: Introduction to Probability Models 9th Ed by M. Ross
SOLUTIONS MANUAL: Introduction to Quantum Mechanics (2nd Ed., David J. Griffiths)
SOLUTIONS MANUAL: Introduction to Quantum Mechanics 1st edition (1995) by David J. Griffiths
SOLUTIONS MANUAL: Introduction to Queueing Theory 2nd Edition by R.B. Cooper
SOLUTIONS MANUAL: Introduction to Scientific Computation and Programming, 1st Edition by Daniel Kaplan
SOLUTIONS MANUAL: Introduction to Signal Processing by S. J. Orfanidis
SOLUTIONS MANUAL: Introduction to Signal Processing by Sophocles J. Orfanidis
SOLUTIONS MANUAL: Introduction to Solid State Physics 8th Ed by Kittel & Charles
SOLUTIONS MANUAL: Introduction to Statistical Physics by Kerson Huang
SOLUTIONS MANUAL: Introduction to Statistical Physics by Silvio Salinas
SOLUTIONS MANUAL: Introduction to Statistical Quality Control (4th Ed., Douglas C. Montgomery)
SOLUTIONS MANUAL: Introduction to Statistical Quality Control (5th Ed., Douglas C. Montgomery)
SOLUTIONS MANUAL: Introduction to the Theory of Computation by Ching Law
SOLUTIONS MANUAL: Introduction to the Thermodynamics of Materials 3 E by Gaskell
SOLUTIONS MANUAL: Introduction to Thermal and Fluids Engineering by Kaminski, Jensen
SOLUTIONS MANUAL: Introduction to Thermal Systems Engineering Moran Shapiro Munson
SOLUTIONS MANUAL: Introduction to VLSI Circuits and Systems, by John P. Uyemura
SOLUTIONS MANUAL: Introduction to Wireless Systems by P.M Shankar
SOLUTIONS MANUAL: Introductory Circuit Analysis 11 E by Boylestad
SOLUTIONS MANUAL: Introductory Econometrics A Modern Approach, 3Ed by Jeffrey Wooldridge
SOLUTIONS MANUAL: Introductory Mathematical Analysis for Business, Economics and the Life and Social Sciences, 12th E By Haeussler,Paul,Wood
SOLUTIONS MANUAL: Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences, 13 E by Haeussler,Paul,Wood
SOLUTIONS MANUAL: Introductory Quantum Optics (Christopher Gerry & Peter Knight)
SOLUTIONS MANUAL: Introdution to Accounting 3rd Ed by Marriott, Mellett
SOLUTIONS MANUAL: Introdution to Solid State Physics, 8th Edition by Kittel
SOLUTIONS MANUAL: Investment Analysis & Portfolio Management, 7e by Reilly, Brown
SOLUTIONS MANUAL: Investment Analysis and Portfolio Management 7th Edition by Frank K. et al. Reilly
SOLUTIONS MANUAL: Investments by Charles P. Jones
SOLUTIONS MANUAL: IT Networking Labs by Cavaiani
SOLUTIONS MANUAL: IT Networking Labs by Tom Cavaiani
SOLUTIONS MANUAL: Java How to program 7th Ed by Deitel
SOLUTIONS MANUAL: Journey into Mathematics An Introduction to Proofs ,Joseph Rotman
SOLUTIONS MANUAL: Kinematics, Dynamics, and Design of Machinery, 2nd Ed., Waldron & Kinzel
SOLUTIONS MANUAL: Kinetics of Catalytic Reactions by M. Albert Vannice
SOLUTIONS MANUAL: LabVIEW for Engineers by Larsen
SOLUTIONS MANUAL: Laser Fundamentals (2nd Ed., William T. Silfvast)
SOLUTIONS MANUAL: Learning SAS in the Computer Lab 3rd ED by Elliott, Morrell
SOLUTIONS MANUAL: Lectures on Corporate Finance 2006, 2 Ed by Bossaerts, Oedegaard
SOLUTIONS MANUAL: Linear Algebra - 2 Ed - Poole
SOLUTIONS MANUAL: Linear Algebra and Its Applications 3rd ed by David C. Lay
SOLUTIONS MANUAL: Linear Algebra Done Right, 2nd Ed by Sheldon Axler
SOLUTIONS MANUAL: Linear Algebra with Applications (6th Ed., S. Leon)
SOLUTIONS MANUAL: Linear Algebra with Applications 3rd Ed by Otto Bretscher
SOLUTIONS MANUAL: Linear Algebra With Applications, 2nd Edition by W. Keith Nicholson
SOLUTIONS MANUAL: Linear Algebra, 4th Ed, by Stephen H. Friedberg , Arnold J. Insel , Lawrence E. Spence
SOLUTIONS MANUAL: Linear Algebra, by J. Hefferon
SOLUTIONS MANUAL: Linear Circuit Analysis Time Domain, Phasor and Laplace.., 2nd Ed, Lin
SOLUTIONS MANUAL: Linear Circuit Analysis, 2nd Ed by DeCarlo , Pen-Min Lin
SOLUTIONS MANUAL: Linear dynamic systems and signals by Zoran Gajic
SOLUTIONS MANUAL: Linear Systems And Signals, 1stE, B P Lathi
SOLUTIONS MANUAL: Logic and Computer Design Fundamentals, 2E, by Morris Mano and Charles Kime
SOLUTIONS MANUAL: Logic and Computer Design Fundamentals, 3d edition by Morris Mano and Charles Kime
SOLUTIONS MANUAL: Logic and Computer Design Fundamentals, 4/E, by Morris Mano and Charles Kime
SOLUTIONS MANUAL: Machine Design : An Integrated Approach (3rd Ed., Norton)
SOLUTIONS MANUAL: Machines and Mechanisms - Applied Kinematic Analysis, 3E by David H. Myszka
SOLUTIONS MANUAL: Macroeconomics A European Text 2nd Ed by Mertens, Weder
SOLUTIONS MANUAL: Managerial Accounting 11th Ed by Garrison & Noreen
SOLUTIONS MANUAL: Managerial Accounting 13th E by Garrison, Noreen, Brewer
SOLUTIONS MANUAL: Managing Business and Professional Communication 2nd ed Carley H. Dodd
SOLUTIONS MANUAL: Managing Business Process Flows: Principles of Operations Management(2nd Ed., Anupind, Chopra, Deshmukh, et al)
SOLUTIONS MANUAL: Managing Engineering and Technology (4th, Morse & Babcock)
SOLUTIONS MANUAL: Manufacturing Processes for Engineering Materials (5th Ed. Kalpakjian & Smith)
SOLUTIONS MANUAL: Materials - engineering, science, properties, and design
SOLUTIONS MANUAL: Materials and Processes in Manufacturing (9th Ed., E. Paul DeGarmo, J. T. Black,Kohser)
SOLUTIONS MANUAL: Materials- Engineering, Science, Processing and Design 2nd ED by Ashby
SOLUTIONS MANUAL: Materials for Civil and Construction Engineers 3rd ED by Mamlouk, Zaniewski
SOLUTIONS MANUAL: Materials Science and Engineering- An Introduction ( 7th Ed., William D. Callister, Jr.)
SOLUTIONS MANUAL: Materials Science and Engineering- An Introduction (6th Ed., William D. Callister, Jr.)
SOLUTIONS MANUAL: MATH 1010 - Applied Finite Mathematics - 2009 by D.W. Trim
SOLUTIONS MANUAL: MATH 1010 - Applied Finite Mathematics by D.W. Trim
SOLUTIONS MANUAL: Mathematical Analysis, Second Edition by Tom M. Apostol
SOLUTIONS MANUAL: Mathematical Methods for Physicists 5 Ed, Arfken
SOLUTIONS MANUAL: Mathematical Methods for Physics and Engineering, (3rd Ed., Riley,Hobson)
SOLUTIONS MANUAL: Mathematical Methods in the Physical Sciences; 3 edition by Mary L. Boas
SOLUTIONS MANUAL: Mathematical Models in Biology An Introduction (Elizabeth S. Allman & John A. Rhodes)
SOLUTIONS MANUAL: Mathematical Proofs - A Transition to Advanced Mathematics 2nd Ed by Chartrand, Polimeni, Zhang
SOLUTIONS MANUAL: Mathematical Techniques 4th ED by D W Jordan & P Smith
SOLUTIONS MANUAL: Mathematics for Economists, by Carl P. Simon , Lawrence E. Blume
SOLUTIONS MANUAL: Mathematics for Management Science - A Bridging Course by Tulett
SOLUTIONS MANUAL: Mathematics for Physicists by Susan Lea
SOLUTIONS MANUAL: Matrix Analysis and Applied Linear Algebra by Meyer
SOLUTIONS MANUAL: Matter and Interactions, 3rd Ed VOL 1 by Chabay, Sherwood
SOLUTIONS MANUAL: Matter and Interactions, 3rd Ed VOL 2 by Chabay, Sherwood
SOLUTIONS MANUAL: McGraw-Hill Ryerson Calculus & Advanced Function by Dearling, Erdman, et all
SOLUTIONS MANUAL: Mechanical Behavior of Materials 3rd Ed by Norman E. Dowling
SOLUTIONS MANUAL: Mechanical Engineering Design 8th Ed by Shigley & Budynas
SOLUTIONS MANUAL: Mechanical Engineering Design 9th Ed by Shigley & Budynas
SOLUTIONS MANUAL: Mechanical Engineering Design, 7th Ed. by Mischke, Shigley
SOLUTIONS MANUAL: Mechanical Measurements (6th Ed., Beckwith, Marangoni & Lienhard)
SOLUTIONS MANUAL: Mechanical Vibrations (3rd Ed., Rao)
SOLUTIONS MANUAL: Mechanical Vibrations 4th Ed SI Units by Rao
SOLUTIONS MANUAL: Mechanics of Aircraft Structures, 2nd Ed by Sun
SOLUTIONS MANUAL: Mechanics of Fluids (8th Ed., Massey)
SOLUTIONS MANUAL: Mechanics of Fluids 3rd ED Vol 1 by Merle C. Potter
SOLUTIONS MANUAL: Mechanics of Fluids 4th ED by I.H. Shames
SOLUTIONS MANUAL: Mechanics of Materials 5 edition by James M. Gere
SOLUTIONS MANUAL: Mechanics of Materials (6th Ed., Riley, Sturges & Morris)
SOLUTIONS MANUAL: Mechanics of Materials 4 E by Russell C. Hibbeler
SOLUTIONS MANUAL: Mechanics of Materials 4th Ed by Beer Johnston
SOLUTIONS MANUAL: Mechanics of Materials 8th E by Russell C. Hibbeler
SOLUTIONS MANUAL: Mechanics Of Materials Beer Johnston 3rd
SOLUTIONS MANUAL: Mechanics of Materials, 2nd Ed by Roy R. Craig
SOLUTIONS MANUAL: Mechanics of Materials, 6E, by Russell C. Hibbeler
SOLUTIONS MANUAL: Mechanics of Materials, 6th Edition - James M. Gere & Barry Goodno
SOLUTIONS MANUAL: Mechanics of Materials, 7E, by Russell C. Hibbeler
SOLUTIONS MANUAL: Mechanics of Materials, 7th Edition - James M. Gere & Barry Goodno
SOLUTIONS MANUAL: mechanics of solids by C. T. F. Ross
SOLUTIONS MANUAL: Mechanism Design Analysis and Synthesis (4th Edition) by Erdman, Sandor, Kota
SOLUTIONS MANUAL: MEMS and Microsystems Design, Manufacture and Nanoscale Engineering 2nd ED by Tai-Ran Hsu
SOLUTIONS MANUAL: Microeconomic Analysis, 3rd Ed., by H. Varian
SOLUTIONS MANUAL: Microeconomic Theory Basic Principles and Extensions 9E ( South-Western ) by Walter Nicholson
SOLUTIONS MANUAL: Microeconomic Theory by Segal Tadelis Hara Chiaka Hara Steve Tadelis
SOLUTIONS MANUAL: Microeconomic Theory, by Mas-Colell, Whinston, Green
SOLUTIONS MANUAL: Microeconomics, 6th Ed by Pyndick, Rubinfeld
SOLUTIONS MANUAL: Microelectronic Circuit Analysis and Design, 3rd Edition, by D. Neamen
SOLUTIONS MANUAL: Microelectronic Circuit Design (3rd Ed., Richard Jaeger & Travis Blalock)
SOLUTIONS MANUAL: Microelectronic Circuit Design 4th ED by Jaeger, Blalock
SOLUTIONS MANUAL: Microelectronic Circuits By Adel Sedra 5th Edition
SOLUTIONS MANUAL: Microelectronic Circuits, 4th Ed. by Sedra and Smith
SOLUTIONS MANUAL: Microelectronic Circuits, 5th Ed. by Sedra and Smith
SOLUTIONS MANUAL: Microelectronics Digital and Analog Circuits and Systems by Millman
SOLUTIONS MANUAL: Microelectronics I & II by Dr.Chang
SOLUTIONS MANUAL: Microelectronics,Solution MANUAL,5thEd,MAZ
SOLUTIONS MANUAL: Microprocessors and Interfacing, Revised 2nd Edition by Douglas V Hall
SOLUTIONS MANUAL: Microwave and Rf Design of Wireless Systems, 1st Edition, by Pozar
SOLUTIONS MANUAL: Microwave Engineering, 2nd Ed., by David M. Pozar
SOLUTIONS MANUAL: Microwave Engineering, 3rd Ed., by David M. Pozar
SOLUTIONS MANUAL: Microwave Transistor Amplifiers Analysis and Design, 2nd Ed., by Guillermo Gonzalez
SOLUTIONS MANUAL: Mobile Communications 2nd ed by Jochen Schiller
SOLUTIONS MANUAL: Modern Control Engineering 3rd Ed. - K. OGATA
SOLUTIONS MANUAL: Modern Control Engineering 4th Ed. - K. OGATA
SOLUTIONS MANUAL: Modern Control Engineering 5 Ed. - K. OGATA
SOLUTIONS MANUAL: Modern Control Systems 11E by Richard C Dorf and Robert H. Bishop
SOLUTIONS MANUAL: Modern Control Systems 9 E by Richard C Dorf and Robert H. Bishop
SOLUTIONS MANUAL: Modern Control Systems, 12th Ed by Dorf, Bishop
SOLUTIONS MANUAL: Modern Digital and Analog Communication Systems, 3rd Ed., by Lathi
SOLUTIONS MANUAL: Modern Digital Electronics 3 Ed by R P Jain
SOLUTIONS MANUAL: Modern Digital Electronics,3E by R P JAIN
SOLUTIONS MANUAL: Modern Digital Signal Processing-Roberto Cristi
SOLUTIONS MANUAL: MODERN OPERATING SYSTEMS 2nd ed A.S.TANENBAUM
SOLUTIONS MANUAL: Modern Organic Synthesis An Introduction by George Zweifel, Michael Nantz
SOLUTIONS MANUAL: Modern Physics 2nd E by Randy Harris
SOLUTIONS MANUAL: Modern Physics 4th ed by Mark Llewellyn
SOLUTIONS MANUAL: Modern Physics 4th ed by Tipler, Llewellyn
SOLUTIONS MANUAL: Modern Physics for Scientists and Engineers 3rd E by Thornton and Rex
SOLUTIONS MANUAL: Modern Portfolio Theory and Investment Analysis, 7th Ed by Gruber,Goetzmann
SOLUTIONS MANUAL: MODERN POWER SYSTEM ANALYSIS 3rd E by Kothari,Nagrath
SOLUTIONS MANUAL: Modern Quantum Mechanics (Revised Edition) by J. J. Sakurai
SOLUTIONS MANUAL: Modern Thermodynamics - From Heat Engines to Dissipative Structures by Kondepudi, Prigogine
SOLUTIONS MANUAL: Modern Thermodynamics - From Heat Engines to Dissipative Structures Vol 1 by Kondepudi, Prigogine
SOLUTIONS MANUAL: Molecular Driving Forces 2nd ED ( vol.1 ) by Dill, Bromberg
SOLUTIONS MANUAL: Molecular Symmetry and Group Theory by Robert L. Carter
SOLUTIONS MANUAL: Molecular Thermodynamics of Fluid-Phase Equilibria 3rd Ed by Prausnitz, Lichtenthaler
SOLUTIONS MANUAL: Multinational Business Finance 10 E by Stonehill, Moffett, Eiteman
SOLUTIONS MANUAL: Multivariable Calculus, 4th Edition, JAMES STEWART
SOLUTIONS MANUAL: Multivariable Calculus, 5th Edition, JAMES STEWART
SOLUTIONS MANUAL: Multivariable Calculus, Applications and Theory by Kenneth Kuttler
SOLUTIONS MANUAL: Nanoengineering of Structural, Functional and Smart Materials, Mark J. Schulz, Ajit D. Kelkar
SOLUTIONS MANUAL: Network Flows: Theory, Algorithms, and Applications by Ravindra K. Ahuja , Thomas L. Magnanti , James B. Orlin
SOLUTIONS MANUAL: Networks and Grids - Technology and Theory by Thomas G. Robertazzi
SOLUTIONS MANUAL: Neural networks and learning machines 3rd edition by Simon S. Haykin
SOLUTIONS MANUAL: Nonlinear Programming 2nd Edition , Dimitri P.Bertsekas
SOLUTIONS MANUAL: Numerical Analysis 8th ED by BURDEN & FAIRES
SOLUTIONS MANUAL: Numerical Computing with MATLAB by Moler
SOLUTIONS MANUAL: Numerical Methods for Engineers (3rd Ed. Steven C. Chapra)
SOLUTIONS MANUAL: Numerical Methods for Engineers (5th Ed. Steven C. Chapra)
SOLUTIONS MANUAL: Numerical Methods Using Matlab, 4E by Mathews, Kurtis K. Fink
SOLUTIONS MANUAL: Numerical Solution of Partial Differential Equations- An Introduction (2nd Ed., K. W. Morton &D)
SOLUTIONS MANUAL: Operating System Concepts, 6E, Silberschatz, Galvin, Gagne
SOLUTIONS MANUAL: Operating System Concepts, 7E, Silberschatz, Galvin, Gagne
SOLUTIONS MANUAL: Operating systems Internals and Design principles 4th Edition Stallings
SOLUTIONS MANUAL: Operating systems Internals and Design principles 5th Edition Stallings
SOLUTIONS MANUAL: Operations Management 5th Ed by Nigel Slack, Chambers, Johnston
SOLUTIONS MANUAL: Optical Fiber Communications 3rd E by Gerd Keiser
SOLUTIONS MANUAL: Optical Properties of Solids 2nd Ed by Mark Fox
SOLUTIONS MANUAL: Optics 4th Edition by Hecht E., Coffey M., Dolan P
SOLUTIONS MANUAL: Optimal Control Theory An Introduction By Donald E. Kirk
SOLUTIONS MANUAL: Optimal State Estimation Dan Simon
SOLUTIONS MANUAL: Optimization of Chemical Processes by Edgar
SOLUTIONS MANUAL: Options, Futures and Other Derivatives, 4E, by John Hull
SOLUTIONS MANUAL: Options, Futures and Other Derivatives, 5E, by John Hull
SOLUTIONS MANUAL: Options, Futures, and Other Derivatives 7th Ed by John C. Hull
SOLUTIONS MANUAL: Orbital Mechanics for Engineering Students 2nd ED by Curtis
SOLUTIONS MANUAL: Orbital Mechanics for Engineering Students by Curtis
SOLUTIONS MANUAL: ORDINARY DIFFERENTIAL EQUATIONS by Adkins, Davidson
SOLUTIONS MANUAL: Organic Chemistry - Clayden et.al.
SOLUTIONS MANUAL: Organic Chemistry 10th E by SOLOMONS,FRYHLE,JOHNSON
SOLUTIONS MANUAL: Organic Chemistry 2nd ed by Schore
SOLUTIONS MANUAL: Organic Chemistry 2nd Edition by Hornback
SOLUTIONS MANUAL: Organic Chemistry 5th Ed by Brown, Foote, Iverson, Ansyln
SOLUTIONS MANUAL: Organic Chemistry 7ed, McMurry
SOLUTIONS MANUAL: Organic Chemistry, 4E., by Carey, Atkins
SOLUTIONS MANUAL: Organic Chemistry, 5E., by Carey, Atkins
SOLUTIONS MANUAL: Organic Chemistry, 6 Ed by Wade, Jan Simek
SOLUTIONS MANUAL: Organic Chemistry, 8th Ed by Carey, Atkins
SOLUTIONS MANUAL: Organic Chemistry, 8th Ed by Wade, Jan Simek
SOLUTIONS MANUAL: Organic Chemistry, by David R. Klein
SOLUTIONS MANUAL: Parallel & Distributed Computation Numerical Methods by Bertsekas & Tsitsiklis
SOLUTIONS MANUAL: Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers (2nd Ed., Barry Wilkinson & Michael Allen)
SOLUTIONS MANUAL: Partial Differential Equations with Fourier Series and Boundary Value Problems 2nd Ed by NAKHL E H. ASMAR
SOLUTIONS MANUAL: Physical Basis of Biochemistry 2nd Ed by Bergethon, Hallock
SOLUTIONS MANUAL: Physical Chemistry (7E, Peter Atkins & Julio de Paula)
SOLUTIONS MANUAL: Physical Chemistry 8E Atkins, Trapp, Cady, Giunta
SOLUTIONS MANUAL: Physical Chemistry by Prem Dhawan
SOLUTIONS MANUAL: Physical Chemistry by Thomas Engel & Philip Reid
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==============================================================================
TOPIC: NatSys Lock-free Queue vs LMAX Disruptor vs boost::lockfree::queue
http://groups.google.com/group/comp.programming.threads/t/7d8862a3ca3cfbe0?hl=en
==============================================================================
== 1 of 2 ==
Date: Wed, Jan 15 2014 8:35 am
From: Alexander Krizhanovsky
I've been asked many times how our lock-free queue differs from LMAX Disruptor. The last time is in discussion at Hacker News. In LinkedIn discussions I also was asked about boost::lockfree::queue (it appeared in Boost recently). So I'm writing the post to share the answers.
http://natsys-lab.blogspot.ru/2014/01/natsys-lock-free-queue-in-comparison.html
== 2 of 2 ==
Date: Wed, Jan 15 2014 2:19 pm
From: "Chris M. Thomasson"
> "Alexander Krizhanovsky" wrote in message
> news:b0f0ec88-399a-407a-87a2-41c9c5df7007@googlegroups.com...
> I've been asked many times how our lock-free queue differs from LMAX
> Disruptor.
FWIW, check this out:
https://groups.google.com/d/topic/lock-free/acjQ3-89abE/discussion
AFAICT, it is the basically the best one can get wrt a _single_ MPMC strict
bi-directional FIFO Queue.
==============================================================================
TOPIC: Scalable RWLock and FIFO fairness
http://groups.google.com/group/comp.programming.threads/t/a2868b50b829fb53?hl=en
==============================================================================
== 1 of 1 ==
Date: Thurs, Jan 23 2014 12:34 pm
From: aminer
Hello all,
Please read this about the Windows event object:
http://msdn.microsoft.com/en-us/library/windows/desktop/ms682655(v=vs.85).aspx
It says: "Do not assume a first-in, first-out (FIFO) order"
So i have thought more about this, and if you have noticed i have
designed and implemented two variations of my scalable RWLock, one that
is called LW_RWLOCK that scales and that is not starvation free and that
uses more CPU ressources, and another one that is called RWLock that
scales and that is not stavation free on the reader side and that uses
less CPU ressources, so i have thought more about the second one that is
called RWLock that uses my SemMonitor on the writer side and that uses a
portable event object on the reader side, and i think it is not
starvation free on the reader side cause the Windows event object that i
am using on the reader side of my scalable RWLock is not FIFO fair, so i
have thought more about this and i think that i have to upgrade my
SemaMonitor to support the set() and reset() methos as in the Windows
event object but my SemaMonitor will be FIFO fair so
it will be starvation free , the windows event object is not,
after that i will enhanced and upgrade my new SemaMonitor on the reader
side of my
scalable RWLock so that it supports many requirements such us:
1- It will use my new SemaMonitor on both the reader and writer side
so it will use less CPU ressources.
2- It will scale on multicores
3- It will be FIFO fair on both the reader and the writer side
so it will be starvation free.
So i will soon upgrade my SemaCondVar and SemaMonitor and my scalable
RWLock so stay tuned.
Thank you,
Amine Moulay Ramdane.
==============================================================================
TOPIC: Again my scalable RWLock and FIFO fairness
http://groups.google.com/group/comp.programming.threads/t/1474a413ea8fa68f?hl=en
==============================================================================
== 1 of 1 ==
Date: Thurs, Jan 23 2014 1:53 pm
From: aminer
Hello,
I have thought more about my scalable RWLock , i mean my second
variation that scales and that is not FIFO fair and starvation free on
the reader side, if you use the Windows manual event object and call the
Setevent() and Resetevent() methods it will not be starvation free, so
i will not use the Windows manual event object, so i have to implement
this Setevent() and Resetevent methods inside my SemaMonitor and
SemaCondvar objects so that my scalable RWLock be FIFO fair , but i have
thought more and if you let my RWLock algorithm as it is, it will not be
starvation free cause i am looping back inside my scalable RWLock and
entering again my SemaMonitor but even if my SemaMonitor is FIFO fair my
RWLock will not be FIFO fair cause i am looping back and
entering again my SemaMonitor, so the solution is that i have to change
the following code:
if (FCount3^.fcount3 = 0)
then break
else
begin
LockedExchangeAdd(FCount1^[myid].fcount1,-1);
end;
with:
if (FCount3^.fcount3 = 0)
then break
So i have to not decrement and looping back.
Look here at my LW_RWLOCK algorithm:
http://pages.videotron.com/aminer/rwlock1.html
But with this change in my code my scalable RWLock algorithm will favor
more the reader threads than the writer threads, but it will be FIFO
fair and starvation free and this variation of my scalable RWLOCK will
support the all following requirements:
1- it will use my new SemaMonitor on both the reader and writer side
so it will use less CPU ressources.
2- It will scale on multicores
3- It will be FIFO fair on both the reader and the writer side
so it will be starvation free.
So i will ugrade soon my SemaMonitor and my SemaCondvar
and my scalable RWLock to support all those requirements.
Thank you,
Amine Moulay Ramdane.
==============================================================================
TOPIC: I have to be smart and scalable RWLOCK
http://groups.google.com/group/comp.programming.threads/t/9b91bbd7fc319c85?hl=en
==============================================================================
== 1 of 1 ==
Date: Thurs, Jan 23 2014 2:37 pm
From: aminer
Hello all,
I have to be smart more than that, so be smart with me...
In my previous post i have told you that i have to upgrade my
SemaCondvar and SemaMonitor objects, but i have thought more
and i think i have to not upgrade it, the solution is that i
have to delete the following code inside my TRWLOCK.RLock() method:
if (FCount3^.fcount3 = 0)
then break
else
begin
LockedExchangeAdd(FCount1^[myid].fcount1,-1);
end;
look here at my LW_RWLOCK algorithm:
http://pages.videotron.com/aminer/rwlock1.html
But that's not all and that's not enough, i have to avoid the
enhancement of my previous post so that my scalable RWLock algorithm
will not favor more the reader side , cause if it favor more the reader
side the write side can starve for a long time and this is bad , so i
have thought more and i think i have found a solution for that , if you
look at the interface of my SemaCondvar and SemaMonitor objects look
here: http://pages.videotron.com/aminer/
I have implemented a method called "function WaitersBlocked:integer"
this WaitersBlocked() method will return how many waiters are blocked
and this is enough to implement a much clever algorithm that do not
favor more the reader side, so i have to use my SemaMonitor on
both the reader side and the writer side of my scalable RWLock and on
the reader side i have have also to look at how much Waiters there is
Waiters Blocked on both the reader side and writer side by calling on
both the reader and the write side, if there is no writers threads on
the writer side i will call the SignalAll() method of my SemaMonitor to
wake up all the waiters on the reader side, but if the there is more
than 1 waiter threads on the writer side i will signal only one thread
of the waiters on the reader side, so that i give a chance to the other
writer threads to run, and by using this new algorithm the writers side
will not starve for a long time, and my new scalable RWLock algorithm
will support all the following requirements:
1- it will use my new SemaMonitor on both the reader and writer side
so it will use less CPU ressources.
2- It will scale on multicores
3- It will be FIFO fair on both the reader and the writer side
so it will be starvation free.
So i will upgrade soon my scalable RWLock to support all those requirements.
Thank you,
Amine Moulay Ramdane.
==============================================================================
TOPIC: Intelligence...
http://groups.google.com/group/comp.programming.threads/t/eb2b878ee4caef93?hl=en
==============================================================================
== 1 of 8 ==
Date: Thurs, Jan 23 2014 3:57 pm
From: aminer
Hello all,
I was reading and reading again my algorithm of my scalable RWLock,
and i have discovered what is intelligence and what is to be smart..
if you look at my algorithm here:
http://pages.videotron.com/aminer/rwlock1.html
you will notice that this algorithm consists of different parts
that you have to assemble to make this scalable RWLock algorithm, and
the action and it's speed to assemble those parts constitutes what we
call intelligence , so i think a man that is smart is only a machine
that is faster and that finds the parts of the algorithm faster and that
assemble the final algorithm from those parts faster.
So i think intelligence and also conscience is in fact a faster machine
with some data in it that organizes data in a form that is smart, but
how life have evolved in a more intelligent and smart form as to be
human ? i think it is just a long and dumb process, so to create
intelligence and conscience we have first to be inspired by the laws of
our mother nature and to create a more faster machines.
Thank you,
Amine Moulay Ramdane.
== 2 of 8 ==
Date: Thurs, Jan 23 2014 4:07 pm
From: Melzzzzz
On Thu, 23 Jan 2014 18:58:02 -0800
aminer <aminer@toto.net> wrote:
>
> Hello all,
>
>
> So i think intelligence and also conscience is in fact a faster
> machine with some data in it that organizes data in a form that is
> smart, but how life have evolved in a more intelligent and smart form
> as to be human ? i think it is just a long and dumb process, so to
> create intelligence and conscience we have first to be inspired by
> the laws of our mother nature and to create a more faster machines.
In 1987 my math professor showed us proof that algorithm for making
algorithms does not exists...
--
Click OK to continue...
== 3 of 8 ==
Date: Thurs, Jan 23 2014 4:47 pm
From: aminer
On 1/23/2014 4:07 PM, Melzzzzz wrote:
> On Thu, 23 Jan 2014 18:58:02 -0800
> aminer <aminer@toto.net> wrote:
>
>>
>> Hello all,
>>
>>
>> So i think intelligence and also conscience is in fact a faster
>> machine with some data in it that organizes data in a form that is
>> smart, but how life have evolved in a more intelligent and smart form
>> as to be human ? i think it is just a long and dumb process, so to
>> create intelligence and conscience we have first to be inspired by
>> the laws of our mother nature and to create a more faster machines.
>
> In 1987 my math professor showed us proof that algorithm for making
> algorithms does not exists...
>
So if this proof exists that means that i have forgot something,
that means that the thing that gives human intelligence is not
an algorithm.
Amine Moulay Ramdane.
== 4 of 8 ==
Date: Thurs, Jan 23 2014 4:55 pm
From: Melzzzzz
On Thu, 23 Jan 2014 19:48:19 -0800
aminer <aminer@toto.net> wrote:
> On 1/23/2014 4:07 PM, Melzzzzz wrote:
> > On Thu, 23 Jan 2014 18:58:02 -0800
> > aminer <aminer@toto.net> wrote:
> >
> >>
> >> Hello all,
> >>
> >>
> >> So i think intelligence and also conscience is in fact a faster
> >> machine with some data in it that organizes data in a form that is
> >> smart, but how life have evolved in a more intelligent and smart
> >> form as to be human ? i think it is just a long and dumb process,
> >> so to create intelligence and conscience we have first to be
> >> inspired by the laws of our mother nature and to create a more
> >> faster machines.
> >
> > In 1987 my math professor showed us proof that algorithm for making
> > algorithms does not exists...
> >
>
>
> So if this proof exists that means that i have forgot something,
> that means that the thing that gives human intelligence is not
> an algorithm.
>
>
>
We are analog, slow computers, that can make algorithms.
--
Click OK to continue...
== 5 of 8 ==
Date: Thurs, Jan 23 2014 5:09 pm
From: aminer
On 1/23/2014 4:55 PM, Melzzzzz wrote:
> On Thu, 23 Jan 2014 19:48:19 -0800
> aminer <aminer@toto.net> wrote:
>
>> On 1/23/2014 4:07 PM, Melzzzzz wrote:
>>> On Thu, 23 Jan 2014 18:58:02 -0800
>>> aminer <aminer@toto.net> wrote:
>>>
>>>>
>>>> Hello all,
>>>>
>>>>
>>>> So i think intelligence and also conscience is in fact a faster
>>>> machine with some data in it that organizes data in a form that is
>>>> smart, but how life have evolved in a more intelligent and smart
>>>> form as to be human ? i think it is just a long and dumb process,
>>>> so to create intelligence and conscience we have first to be
>>>> inspired by the laws of our mother nature and to create a more
>>>> faster machines.
>>>
>>> In 1987 my math professor showed us proof that algorithm for making
>>> algorithms does not exists...
>>>
>>
>>
>> So if this proof exists that means that i have forgot something,
>> that means that the thing that gives human intelligence is not
>> an algorithm.
>>
>>
>>
> We are analog, slow computers, that can make algorithms.
>
Even if this proof exist, we can still have algorithms that
create a finite number of algorithms and creates more
specialized algorithms. That's what we are doing with machines and
computers, and that also brings hope to humanity.
Amine Moulay Ramdane.
== 6 of 8 ==
Date: Thurs, Jan 23 2014 5:16 pm
From: Melzzzzz
On Thu, 23 Jan 2014 20:10:10 -0800
aminer <aminer@toto.net> wrote:
> On 1/23/2014 4:55 PM, Melzzzzz wrote:
> > On Thu, 23 Jan 2014 19:48:19 -0800
> > aminer <aminer@toto.net> wrote:
> >
> >> On 1/23/2014 4:07 PM, Melzzzzz wrote:
> >>> On Thu, 23 Jan 2014 18:58:02 -0800
> >>> aminer <aminer@toto.net> wrote:
> >>>
> >>>>
> >>>> Hello all,
> >>>>
> >>>>
> >>>> So i think intelligence and also conscience is in fact a faster
> >>>> machine with some data in it that organizes data in a form that
> >>>> is smart, but how life have evolved in a more intelligent and
> >>>> smart form as to be human ? i think it is just a long and dumb
> >>>> process, so to create intelligence and conscience we have first
> >>>> to be inspired by the laws of our mother nature and to create a
> >>>> more faster machines.
> >>>
> >>> In 1987 my math professor showed us proof that algorithm for
> >>> making algorithms does not exists...
> >>>
> >>
> >>
> >> So if this proof exists that means that i have forgot something,
> >> that means that the thing that gives human intelligence is not
> >> an algorithm.
> >>
> >>
> >>
> > We are analog, slow computers, that can make algorithms.
> >
>
>
> Even if this proof exist, we can still have algorithms that
> create a finite number of algorithms and creates more
> specialized algorithms. That's what we are doing with machines and
> computers, and that also brings hope to humanity.
>
>
What I want to say is that we are not digital computers. We are
not driven by algorithm...although we can simulate digital
computer but badly...
--
Click OK to continue...
== 7 of 8 ==
Date: Thurs, Jan 23 2014 5:23 pm
From: aminer
On 1/23/2014 5:16 PM, Melzzzzz wrote:
> On Thu, 23 Jan 2014 20:10:10 -0800
> aminer <aminer@toto.net> wrote:
>
>> On 1/23/2014 4:55 PM, Melzzzzz wrote:
>>> On Thu, 23 Jan 2014 19:48:19 -0800
>>> aminer <aminer@toto.net> wrote:
>>>
>>>> On 1/23/2014 4:07 PM, Melzzzzz wrote:
>>>>> On Thu, 23 Jan 2014 18:58:02 -0800
>>>>> aminer <aminer@toto.net> wrote:
>>>>>
>>>>>>
>>>>>> Hello all,
>>>>>>
>>>>>>
>>>>>> So i think intelligence and also conscience is in fact a faster
>>>>>> machine with some data in it that organizes data in a form that
>>>>>> is smart, but how life have evolved in a more intelligent and
>>>>>> smart form as to be human ? i think it is just a long and dumb
>>>>>> process, so to create intelligence and conscience we have first
>>>>>> to be inspired by the laws of our mother nature and to create a
>>>>>> more faster machines.
>>>>>
>>>>> In 1987 my math professor showed us proof that algorithm for
>>>>> making algorithms does not exists...
>>>>>
>>>>
>>>>
>>>> So if this proof exists that means that i have forgot something,
>>>> that means that the thing that gives human intelligence is not
>>>> an algorithm.
>>>>
>>>>
>>>>
>>> We are analog, slow computers, that can make algorithms.
>>>
>>
>>
>> Even if this proof exist, we can still have algorithms that
>> create a finite number of algorithms and creates more
>> specialized algorithms. That's what we are doing with machines and
>> computers, and that also brings hope to humanity.
>>
>>
>
> What I want to say is that we are not digital computers. We are
> not driven by algorithm...although we can simulate digital
> computer but badly...
>
>
And what i mean is that computers and machines are becoming faster and
more powerfull than human at doing different things , and even though
this proof exists , algorithms inside machines and computers can still
create a finite number of algorithms , and all that brings hope
to humanity..
Amine Moulay Ramdane.
== 8 of 8 ==
Date: Thurs, Jan 23 2014 5:33 pm
From: Melzzzzz
On Thu, 23 Jan 2014 20:24:05 -0800
aminer <aminer@toto.net> wrote:
> On 1/23/2014 5:16 PM, Melzzzzz wrote:
> > On Thu, 23 Jan 2014 20:10:10 -0800
> > aminer <aminer@toto.net> wrote:
> >
> >> On 1/23/2014 4:55 PM, Melzzzzz wrote:
> >>> On Thu, 23 Jan 2014 19:48:19 -0800
> >>> aminer <aminer@toto.net> wrote:
> >>>
> >>>> On 1/23/2014 4:07 PM, Melzzzzz wrote:
> >>>>> On Thu, 23 Jan 2014 18:58:02 -0800
> >>>>> aminer <aminer@toto.net> wrote:
> >>>>>
> >>>>>>
> >>>>>> Hello all,
> >>>>>>
> >>>>>>
> >>>>>> So i think intelligence and also conscience is in fact a faster
> >>>>>> machine with some data in it that organizes data in a form that
> >>>>>> is smart, but how life have evolved in a more intelligent and
> >>>>>> smart form as to be human ? i think it is just a long and dumb
> >>>>>> process, so to create intelligence and conscience we have first
> >>>>>> to be inspired by the laws of our mother nature and to create a
> >>>>>> more faster machines.
> >>>>>
> >>>>> In 1987 my math professor showed us proof that algorithm for
> >>>>> making algorithms does not exists...
> >>>>>
> >>>>
> >>>>
> >>>> So if this proof exists that means that i have forgot something,
> >>>> that means that the thing that gives human intelligence is not
> >>>> an algorithm.
> >>>>
> >>>>
> >>>>
> >>> We are analog, slow computers, that can make algorithms.
> >>>
> >>
> >>
> >> Even if this proof exist, we can still have algorithms that
> >> create a finite number of algorithms and creates more
> >> specialized algorithms. That's what we are doing with machines and
> >> computers, and that also brings hope to humanity.
> >>
> >>
> >
> > What I want to say is that we are not digital computers. We are
> > not driven by algorithm...although we can simulate digital
> > computer but badly...
> >
> >
>
>
>
> And what i mean is that computers and machines are becoming faster
> and more powerfull than human at doing different things , and even
> though this proof exists , algorithms inside machines and computers
> can still create a finite number of algorithms , and all that brings
> hope to humanity..
Problem is that algorithm can't create algorithm...
So digital machines can only function within own algorithm...
--
Click OK to continue...
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