Software Tools for Software Tools for Network ModelingNetwork Modeling

Kuki A.-Sztrik J.-Bolch G.Kuki A.-Sztrik J.-Bolch G.

University of Debrecen, HungaryUniversity of Debrecen, HungaryUniversity of Erlangen, GermanyUniversity of Erlangen, Germany

ContentContent

•IntroductionIntroduction

•PEPSY-QNS

•WinPEPSY

•Using WinPEPSY

Overview

Running programs compete for computing resources,eg.

CPU

RAM

Peripheries, etc.

The systems

Systems are working on largevariety of machines

High level of complexity

System optimization is a very difficult task

Modelling

Manufacturing systems

Computer systems, etc.

Queueing systems

Queueing systemsWorld

Jobs

Jobs in waitingqueues

Jobs

Server 1 Server n….

Queueing networks

One or more nodesOne or more nodes

Job classesJob classes

One or more servers at each nodeOne or more servers at each node

Serving principlesServing principles

Serving principles

FCFS - First Come First ServedFCFS - First Come First Served

LCFS - Last Come First Served LCFS - Last Come First Served

PS - Processzor Sharig PS - Processzor Sharig

IS - Infinite ServerIS - Infinite Server

FCFS PRE, (FCFS NONPRE) FCFS PRE, (FCFS NONPRE)

FCFS ASYM FCFS ASYM

System characteristics

ThroughputThroughput

UtilizationUtilization

Average waiting timesAverage waiting times

Average queue lengthAverage queue length

Average response times, etc.Average response times, etc.

ContentContent

•Introduction

•PEPSY-QNSPEPSY-QNS

•WinPEPSY

•Using WinPEPSY

PEPSY-QNS(Performance Evaluation and Prediction SYstem

for Queueing NetworkS)

Developed at University of ErlangenDeveloped at University of Erlangen

Easy model description Easy model description

User friendly interface User friendly interface

More than 50 analyzing methodsMore than 50 analyzing methods

Graphical interface (XPEPSY)Graphical interface (XPEPSY)

Modules

PEPSY-QNS consists of three modules

Interactive model inputInteractive model input

Guided choice of analyzing method Guided choice of analyzing method

Analyzing module Analyzing module

Results

eingabe

zusatz

analyse

auswahl

a_xx_data

e_data

Modeldescription

Analyzing methods

System architecture

Type of the networkType of the network

Number of nodesNumber of nodes

Number of job classesNumber of job classes

Arrival rates (number of jobs)Arrival rates (number of jobs)

Service ratesService rates

Transition probabilitiesTransition probabilities

Type of nodesType of nodes

Procedure Eingabe

Type of nodes

(1) M/M/1-FCFS (2) M/M/m-FCFS (3) M/G/1-PS (4) M/G/0-IS (5) M/G/1-FCFS (6) M/G/m-FCFS (7) G/G/1-FCFS (8) G/G/m-FCFS (9) M/G/1-LCFS-PRE (10) M/M/1-FCFS-PRE(11) M/M/1-FCFS-NONPRE (12) M/G/m-PS(13) G/G/m-PS (14) M/G/1-FCFS-PRE(15) M/G/1-FCFS-NONPRE (16) M/M/m-FCFS-PRE(17) M/M/m-FCFS-NONPRE (18) M/G/m-FCFS-PRE(19) M/G/m-FCFS-NONPRE (20) M/M/m-FCFS-ASYM(21) M/G/m-FCFS-ASYM

(1) M/M/1-FCFS (2) M/M/m-FCFS (3) M/G/1-PS (4) M/G/0-IS (5) M/G/1-FCFS (6) M/G/m-FCFS (7) G/G/1-FCFS (8) G/G/m-FCFS (9) M/G/1-LCFS-PRE (10) M/M/1-FCFS-PRE(11) M/M/1-FCFS-NONPRE (12) M/G/m-PS(13) G/G/m-PS (14) M/G/1-FCFS-PRE(15) M/G/1-FCFS-NONPRE (16) M/M/m-FCFS-PRE(17) M/M/m-FCFS-NONPRE (18) M/G/m-FCFS-PRE(19) M/G/m-FCFS-NONPRE (20) M/M/m-FCFS-ASYM(21) M/G/m-FCFS-ASYM

Input data 1

NUMBER NODES: 4NUMBER CLASSES: 1

NODE SPECIFICATION node | name | type ---------+--------------------+--------------------- 1 | node 1 | M/M/1-FCFS 2 | node 2 | M/G/1-PS 3 | node 3 | M/G/1-PS 4 | node 4 | M/M/1-FCFS

CLASS SPECIFICATION class | arrival rate number of jobs ----------+---------------------------------- 1 | 0.3 -

CLASS SPECIFIC PARAMETERSCLASS 1

node | service_rate squared_coeff.--------------------+----------------------------------- node 1 | 1 1 node 2 | 2 1 node 3 | 2 1 node 4 | 1 1

Input data 2

SWITCHING PROBABILITIES

from/to | outside node 1 node 2 node 3 node 4 -----------+-------------------------------------------------------outside | 0.000000 1.000000 0.000000 0.000000 0.000000 node 1 | 0.000000 0.000000 0.333000 0.500000 0.167000 node 2 | 1.000000 0.000000 0.000000 0.000000 0.000000 node 3 | 1.000000 0.000000 0.000000 0.000000 0.000000 node 4 | 1.000000 0.000000 0.000000 0.000000 0.000000

Usable Need further specification

------------------------------------------------Bounds ChyllaPriomva2m DekompSopenpfn Sim2

Auswahl

Program ‘auswahl’ results the following procedure list:

Output file

Generated automatically (a_xx_name)Generated automatically (a_xx_name)

Short model description Short model description

System characteristics/job classes/nodes System characteristics/job classes/nodes

Global system characteristicsGlobal system characteristics

Output data 1

PERFORMANCE_INDICES FOR NET: angol

description of the network is in file 'e_angol'

the open net was analysed with method 'sopenpfn' .

jobclass 1

sopenpfn | lambda e 1/mue rho mvz maa mwz mwsl -----------+------------------------------------------------------------------------node 1 | 0.300 1.000 1.000 0.300 1.429 0.429 0.429 0.129 node 2 | 0.100 0.333 0.500 0.050 0.526 0.053 0.026 0.003 node 3 | 0.150 0.500 0.500 0.075 0.541 0.081 0.041 0.006 node 4 | 0.050 0.167 1.000 0.050 1.053 0.053 0.053 0.003

Output data 2

characteristic indices:

sopenpfn | lambda mvz maa ----------- +-------------------------- | 0.300 2.050 0.615

legend

e : average number of visits mue : service raterho : utilisation lambda : mean throughputmvz : average response timemaa : average number of jobsmwz : average waiting timemwsl: average queue-length

The same job with XPEPSY

Node information

Procedures of Analysis

The Output screen

ContentContent

•Introduction

•PEPSY-QNS

•WinPEPSYWinPEPSY

•Using WinPEPSY

WinPEPSY

Interactive graphical model descriptionInteractive graphical model description

WinPEPSY uses the methodsprogrammed in PEPSY

WinPEPSY uses the methodsprogrammed in PEPSY

Graphical outputGraphical output

Model specification

Describe a newmodel with

Graphic tools

Dialog box

Model specification with dialog boxes >>

Network type

Network type

Open

Closed

Mixed

Network parameters

Number of

Nodes

Classes

Type of nodes

Serving rates

You can give serving rates

For each node

For each class

Serving rates

Routing the jobs

You can specify

Transition probabilities

Visiting rates

Transition probabilities

The described model

Model specification with graphic tools >>

Here can be found the methods for the model analysis

Drawing the nodes

The model

The results

The results of the other characteristics can be obtained in the same form or in table form as well.

Scenarios

Number of jobsNumber of jobs

Serving rateServing rate

Transition probabilitiesTransition probabilities

Number of servers at a nodeNumber of servers at a node

You can run the value of a parameter between a specified range to obtain more sofisticated results.The parameter could be one of the followings:

Scenarios

ScenariosFor example if you run the number of jobs in Class 1 from 5 to 15:

ScenariosThe same results in table form:

Note, that you can modify the serving rate between 0,1 and 1.

ContentContent

•Introduction

•PEPSY-QNS

•WinPEPSY

•Using WinPEPSYUsing WinPEPSY

Modelling finite-source (homogeneous) queueing systems

Machine 1

Machine n

.

.

.

Node 1 (M/M/n FCFS or IS)

Waiting queue

Node 2M/M/1 FCFS or PS

An example in WinPEPSY

Machine 1

Machine 6

.

.

.

Node 1 (M/M/6 FCFS)=0.025

Waiting queue

Node 2(M/M/1 FCFS)

=0.25

No. of jobs: 6

Sreenshot for the model

Solution of the model(Mean value analysis)

Results for Node 1Results for Node 1

Utilisation Utilisation

Average response time Average response time

Average Number of jobsAverage Number of jobs

Results for Node 2Results for Node 2

0,8590,859 0,5150,515

6,5586,558

0,8450,845

Analysis with scenarios

Modify the value of serving rateModify the value of serving rate

At Node 2 between 0,1 and 0,3At Node 2 between 0,1 and 0,3

At Node 1 between 0,01 and 0,03At Node 1 between 0,01 and 0,03

Analysis with scenariosServing rate at Node 2 between 0,1 and 0,3Serving rate at Node 2 between 0,1 and 0,3

Analysis with scenariosServing rate at Node 1 between 0,01 and 0,03Serving rate at Node 1 between 0,01 and 0,03

References

[1] Bolch G., Greiner S., de Meer H., Trivedi K.S. Queueing Networks and Markov Chains John Wiley & Sons Inc. New York, 1998.

[2] Kleinrock L. Sorbanállás - Kiszolgálás; Bevezetés a tömegkiszolgálási rendszerek elméletébe Műszaki Könyvkiadó Budapest, 1979.

[3] Sztrik J. Bevezetés a sorbanállási elméletbe és alkalmazásaiba Egyetemi jegyzet KLTE Debrecen, 1994.

Thank you for your attentionThank you for your attention