An M/M/n queuing model simulation with Object Pascal and my Thread Pool Engine...

[aminer10]

Hello,

An M/M/n queuing model simulation with Object Pascal and my Thread Pool Engine.

Author: Amine Moulay Ramdane

Description:

It's harder and sometimes impossible to get analytical results

about waiting times and 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 for example at the M/M/n example MMn.pas 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/n queuig model...

If you look at MMn.pas , you will see that the InterArrival rate

is 3 and the Service rate is 4 , so, this will give us a theoretical

value of 1/(4-3) = 1, and the Object Pascal simulation give us 1.02.

You can download the M/M/n queuing model simulation from:

http://pages.videotron.com/aminer/

Language: FPC Pascal v2.2.0+ / Delphi 7+: http://www.freepascal.org/

Operating Systems: Win , Linux and Mac (x86).

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+

Disclaimer:

This software is provided on an "as-is" basis, with no warranties,

express or implied. The entire risk and liability of using it is yours.

Any damages resulting from the use or misuse of this software will be

the responsibility of the user.

Sincerely,

Amine Moulay Ramdane.

[aminer10]

I wrote:

>If you look at MMn.pas , you will see that the InterArrival rate

>is 3 and the Service rate is 4 , so, this will give us a theoretical

>value of 1/(4-3) = 1, and the Object Pascal simulation give us 1.02.

I mean for one server - M/M/1 - it givesa theorerical value
of 1/(4-3) = 1and 1.02 in the simulation..

But as you have noticed MMn.pascan simulatean M/M/n queuig model
with1 or many servers...



Sincerely,
Amine Moulay Ramdane.

[aminer10]

Hello ,

I have updated MMn.pas to version1.01 - i have corrected a bug -
and put it back inside the zip file that you can download from:

Welcome: http://pages.videotron.com/aminer/

Note: MMn.pas - n: numbers of servers - is queuing model simulation with
Object Pascal and my Thread Pool Engine.

Sincerely,
Amine Moulay Ramdane.

[aminer10]

Hello

Note: next time i will show you how to simulate
a more complex problem in Object Pascal...

Of course, if you want to simulate a 'general' distribution ,
like uniform or normal ,you can do it like this by changing
your variables inside MMn.pas:

Define your variables:

var InterArrivals: TUniformDistribution;
ServiceTimes: TUniformDistribution;

and after that:

InterArrivals:=TUniformDistribution.Create(420623,0,2);
ServiceTimes:=TUniformDistribution.Create(2990623,0,1.5);

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;

Welcome: http://pages.videotron.com/aminer/

That all.

Sincerely,
Amine Moulay Ramdane.