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.
The systems
Systems are working on large
variety of machines
High level of complexity
System optimization is
a very difficult task
Modelling
Manufacturing systems
Computer systems, etc.
Queueing systems
Queueing systems
World
Jobs
Jobs in waiting
queues
Server 1
….
Server n
Jobs
Queueing networks
One or more nodes
Job classes
One or more servers at each node
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
Throughput
Utilization
Average waiting times
Average queue length
Average response times, etc.
Content
•Introduction
•PEPSY-QNS
•WinPEPSY
•Using WinPEPSY
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
PEPSY-QNS consists of three modules
Interactive model input
Guided choice of analyzing method
Analyzing module
System architecture
analyse
eingabe
e_data
zusatz
auswahl
a_xx_data
Results
Model
description
Analyzing methods
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
NUMBER NODES: 4
NUMBER CLASSES: 1
CLASS SPECIFIC PARAMETERS
CLASS 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
node
| service_rate squared_coeff.
--------------------+----------------------------------node 1
|
1
1
node 2
|
2
1
node 3
|
2
1
node 4
|
1
1
CLASS SPECIFICATION
class | arrival rate number of jobs
----------+---------------------------------1 | 0.3
-
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
Priomva2m
Sopenpfn
Chylla
Dekomp
Sim2
Output file
Generated automatically (a_xx_name)
Short model description
System characteristics/job classes/nodes
Global 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
rho : utilisation
mvz : average response time
maa : average number of jobs
mwz : average waiting time
mwsl: average queue-length
mue
: service rate
lambda : mean throughput
The same job with XPEPSY
Node information
Procedures of Analysis
The Output screen
Content
•Introduction
•PEPSY-QNS
•WinPEPSY
•Using WinPEPSY
WinPEPSY
Interactive graphical model description
WinPEPSY uses the methods
programmed in PEPSY
Graphical output
Model specification
Describe a new
model with
Dialog box
Graphic tools
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
Here can be found the
methods for the model
analysis
Model specification with graphic tools >>
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
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
Scenarios
Scenarios
For example if you run the number of jobs in Class 1
from 5 to 15:
Scenarios
The same results in table form:
Note, that you can modify the serving rate between 0,1 and 1.
Content
•Introduction
•PEPSY-QNS
•WinPEPSY
•Using WinPEPSY
Modelling finite-source
(homogeneous) queueing systems
Node 1 (M/M/n FCFS or IS)
Node 2
M/M/1 FCFS or PS
Machine 1
.
.
.
Machine n
Waiting queue
An example in WinPEPSY
Node 1 (M/M/6 FCFS)
l=0.025
Node 2
(M/M/1 FCFS)
m=0.25
Machine 1
.
.
.
Waiting queue
Machine 6
No. of jobs: 6
Sreenshot for the model
Solution of the model
(Mean value analysis)
Results for Node 1
0,859
Results for Node 2
Utilisation
0,515
Average response time
6,558
Average Number of jobs
0,845
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 scenarios
Serving rate at Node 2 between 0,1 and 0,3
Analysis with scenarios
Serving 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 attention