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Software Tools for Network Modeling. Kuki A.-Sztrik J.-Bolch G. University of Debrecen, Hungary University of Erlangen, Germany. Content. Introduction PEPSY-QNS WinPEPSY Using WinPEPSY. Overview. Running programs compete for computing resources,eg. CPU. RAM. Peripheries, etc.

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Software tools for network modeling
Software Tools for Network Modeling

Kuki A.-Sztrik J.-Bolch G.

University of Debrecen, Hungary

University of Erlangen, Germany


Content
Content

  • Introduction

  • PEPSY-QNS

  • WinPEPSY

  • Using WinPEPSY


Overview
Overview

Running programs compete

for computing resources,eg.

CPU

RAM

Peripheries, etc.


The systems
The systems

Systems are working on large

variety of machines

High level of complexity

System optimization is

a very difficult task


Modelling
Modelling

Manufacturing systems

Computer systems, etc.

Queueing systems


Queueing systems

World

Jobs

Jobs in waiting

queues

….

Server 1

Server n

Jobs

Queueing systems


Queueing networks
Queueing networks

One or more nodes

Job classes

One or more servers at each node

Serving principles


Serving principles
Serving principles

FCFS - First Come First Served

LCFS - Last Come First Served

PS - Processzor Sharig

IS - Infinite Server

FCFS PRE, (FCFS NONPRE)

FCFS ASYM


System characteristics
System characteristics

Throughput

Utilization

Average waiting times

Average queue length

Average response times, etc.


Content1
Content

  • Introduction

  • PEPSY-QNS

  • WinPEPSY

  • Using WinPEPSY


Pepsy qns
PEPSY-QNS

(Performance Evaluation and Prediction SYstem

for Queueing NetworkS)

Developed at University of Erlangen

Easy model description

User friendly interface

More than 50 analyzing methods

Graphical interface (XPEPSY)


Modules
Modules

PEPSY-QNS consists of three modules

Interactive model input

Guided choice of analyzing method

Analyzing module


System architecture
System architecture

e_data

Results

Model

description

Analyzing methods

analyse

a_xx_data

eingabe

zusatz

auswahl


Procedure Eingabe

Type of the network

Number of nodes

Number of job classes

Type of nodes

Arrival rates (number of jobs)

Service rates

Transition probabilities


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


Input data 1
Input data 1

CLASS SPECIFIC PARAMETERS

CLASS 1

node | service_rate squared_coeff.

--------------------+-----------------------------------

node 1 | 1 1

node 2 | 2 1

node 3 | 2 1

node 4 | 1 1

NUMBER NODES: 4

NUMBER 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 -


Input data 2
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


Auswahl

Program ‘auswahl’ results the following procedure list:

Usable Need further specification

------------------------------------------------

Bounds Chylla

Priomva2m Dekomp

Sopenpfn Sim2


Output file
Output file

Generated automatically (a_xx_name)

Short model description

System characteristics/job classes/nodes

Global system characteristics


Output data 1
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
Output data 2

characteristic indices:

sopenpfn | lambda mvz maa

----------- +--------------------------

| 0.300 2.050 0.615

legend

e : average number of visits mue : service rate

rho : utilisation lambda : mean throughput

mvz : average response time

maa : average number of jobs

mwz : average waiting time

mwsl: average queue-length






Content2
Content

  • Introduction

  • PEPSY-QNS

  • WinPEPSY

  • Using WinPEPSY


Winpepsy
WinPEPSY

Interactive graphical model description

WinPEPSY uses the methods

programmed in PEPSY

Graphical output


Model specification
Model specification

Describe a new

model with

Dialog box

Graphic tools

Model specification with dialog boxes >>


Network type
Network type

Network type

Open

Closed

Mixed


Network parameters
Network parameters

Number of

Nodes

Classes



Serving rates
Serving rates

You can give serving rates

For each node

For each class



Routing the jobs
Routing the jobs

You can specify

Transition probabilities

Visiting rates



The described model
The described model

Here can be found the

methods for the model

analysis

Model specification with graphic tools >>




The results
The results

The results of the other characteristics can be

obtained in the same form or in table form as well.


Scenarios
Scenarios

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:

Number of jobs

Serving rate

Transition probabilities

Number of servers at a node



Scenarios2
Scenarios

For example if you run the number of jobs in Class 1

from 5 to 15:


Scenarios3
Scenarios

The same results in table form:

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


Content3
Content

  • Introduction

  • PEPSY-QNS

  • WinPEPSY

  • Using WinPEPSY


Modelling finite source homogeneous queueing systems

Machine 1

Machine n

Modelling finite-source (homogeneous) queueing systems

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

Node 2

M/M/1 FCFS or PS

.

.

.

Waiting queue


An example in winpepsy

Machine 1

Machine 6

An example in WinPEPSY

Node 1 (M/M/6 FCFS)

l=0.025

Node 2

(M/M/1 FCFS)

m=0.25

.

.

.

Waiting queue

No. of jobs: 6



Solution of the model
Solution of the model

(Mean value analysis)

Results for Node 1

Results for Node 2

0,859

Utilisation

0,515

Average response time

6,558

0,845

Average Number of jobs


Analysis with scenarios
Analysis with scenarios

Modify the value of serving rate

At Node 2 between 0,1 and 0,3

At Node 1 between 0,01 and 0,03


Analysis with scenarios1
Analysis with scenarios

Serving rate at Node 2 between 0,1 and 0,3


Analysis with scenarios2
Analysis with scenarios

Serving rate at Node 1 between 0,01 and 0,03


References
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.



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