Software Tools for Network Modeling. Content IntroductionIntroduction PEPSY-QNS WinPEPSY Using...
Transcript of Software Tools for Network Modeling. Content IntroductionIntroduction PEPSY-QNS WinPEPSY Using...
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