Software Tools for Network Modeling

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Software Tools for Network Modeling

• Kuki A.-Sztrik J.-Bolch G.
• University of Debrecen, Hungary
• University of Erlangen, Germany

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Content

• Introduction
• PEPSY-QNS
• WinPEPSY
• Using WinPEPSY

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Overview
Running programs compete for computing
resources,eg.
CPU
RAM
Peripheries, etc.
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The systems
Systems are working on large variety of machines
High level of complexity
System optimization is a very difficult task
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Modelling
Manufacturing systems
Computer systems, etc.
Queueing systems
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Queueing systems
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Queueing networks
One or more nodes
Job classes
One or more servers at each node
Serving principles
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Serving principles
FCFS - First Come First Served
LCFS - Last Come First Served
PS - Processzor Sharig
IS - Infinite Server
FCFS PRE, (FCFS NONPRE)
FCFS ASYM
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System characteristics
Throughput
Utilization
Average waiting times
Average queue length
Average response times, etc.
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Content

• Introduction
• PEPSY-QNS
• WinPEPSY
• Using WinPEPSY

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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)
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Modules
PEPSY-QNS consists of three modules
Interactive model input
Guided choice of analyzing method
Analyzing module
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System architecture
analyse
a_xx_data
eingabe
zusatz
auswahl
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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
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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
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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 -
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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
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Auswahl
Program auswahl results the following procedure
list
Usable Need further specification -------------
----------------------------------- Bounds Chyll
a Priomva2m Dekomp Sopenpfn Sim2
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Output file
Generated automatically (a_xx_name)
Short model description
System characteristics/job classes/nodes
Global system characteristics
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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
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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
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The same job with XPEPSY
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Node information
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Procedures of Analysis
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The Output screen
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Content

• Introduction
• PEPSY-QNS
• WinPEPSY
• Using WinPEPSY

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(No Transcript)
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WinPEPSY
Interactive graphical model description
WinPEPSY uses the methods programmed in PEPSY
Graphical output
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Model specification
Describe a new model with
Dialog box
Graphic tools
Model specification with dialog boxes gtgt
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Network type
Network type
Open
Closed
Mixed
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Network parameters
Number of
Nodes
Classes
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Type of nodes
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Serving rates
You can give serving rates
For each node
For each class
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Serving rates
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Routing the jobs
You can specify
Transition probabilities
Visiting rates
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Transition probabilities
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The described model
Here can be found the methods for the model
analysis
Model specification with graphic tools gtgt
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Drawing the nodes
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The model
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The results
The results of the other characteristics can be
obtained in the same form or in table form as
well.
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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
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Scenarios
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Scenarios
For example if you run the number of jobs in
Class 1 from 5 to 15
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Scenarios
The same results in table form
Note, that you can modify the serving rate
between 0,1 and 1.
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Content

• Introduction
• PEPSY-QNS
• WinPEPSY
• Using WinPEPSY

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Modelling finite-source (homogeneous) queueing
systems
Node 1 (M/M/n FCFS or IS)
Node 2 M/M/1 FCFS or PS
. . .
Waiting queue
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An example in WinPEPSY
Node 1 (M/M/6 FCFS) l0.025
Node 2 (M/M/1 FCFS) m0.25
. . .
Waiting queue
No. of jobs 6
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Sreenshot for the model
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Solution of the model
(Mean value analysis)
Results for Node 1
Results for Node 2
Utilisation
0,859
0,515
Average response time
6,558
0,845
Average Number of jobs
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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
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Analysis with scenarios
Serving rate at Node 2 between 0,1 and 0,3
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Analysis with scenarios
Serving rate at Node 1 between 0,01 and 0,03
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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 Muszaki Könyvkiadó
Budapest, 1979. 3 Sztrik J. Bevezetés a
sorbanállási elméletbe és alkalmazásaiba
Egyetemi jegyzet KLTE Debrecen, 1994.
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Thank you for your attention