cpn models of transport systems michal zarnay slovakia
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CPN Models of Transport Systems
Michal Zarnay
Slovakia
22.10.2007 Department of Transport Networks, University of Zilina 2/38
Michal Zarnay
Department of Transport Networks
Faculty of Management Science and Informatics
University of Zilina
Slovak Republic
22.10.2007 Department of Transport Networks, University of Zilina 3/38
Department of Transport Networks
• modelling by means of optimisation and simulation
• focus mainly on transport systems
• Villon – tool for simulation of complex transport nodes
Villon
CPN Model of Railway Marshalling Yard
Technology
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CPN Model of Railway Marshalling Yard
Technology• Aim
• Timed version
• Un-timed version
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CPN Model of Railway Marshalling Yard
Technology
To test abilities of CPN for modelling of technological process
in transportation systems
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Model’s Characteristics
• resources used:– tracks– locomotives– personnel
• 2 technological flowcharts– incoming train processing– outgoing train processing
1 3
5
Arrival Announcem.
Examiner Movement
Track Assignment
7 24Train Movement
14
15
Technical Inspection
11
Documents Take-over
Securing of Wagons
19Documents Processing Traffic
Inspection, Labels
12
Train Loco Uncoupling
10Coupler Movement
Train Loco Displacement
Coupler Release
22 23
Shunter Release
24 26 27 28
Hump Loco Coupling
Hump Loco Movement
Feeding to Hump
Primary Humping
29
Hump Loco Release
30
2
4
Train Arrival
Shunter Movement
Preparation for Humping
8Examiner Release
202 Transiteurs Release
16
Transiteur Movement
2 Transiteurs Movement
17
Transiteur Release
13
6
9
2118
25
Examiner Assignment
Transiteur Assignment
Coupler Assignment
Shunter Assignment
Hump Loco Assignment
2 Transiteurs Assignment
Incoming Train Processing
Outgoing Train Processing2 3 4 8
10
Coupler Movement
Train set Coupling
Shunt Loco Assignment
Arrival Announcement
20
13
11
Coupler Movement
Examiner Movement
Train Mov. to Dep. Track
23
Transiteur Assignment
15
Technical Inspection
21
24List of Wagons
Train set coupling Completion
27
Coupler Release
Train Loco Movement
28
Brake Test
34
Train Documentation
35Train
Departure
Shunt Loco Uncoupling
Shunt Loco Coupling
9
Track Assignment
16
Coupler Assignment
Train Loco Coupling
30
14
Shunt Loco Release
Examiner Release
107
6
Coupler Release
17
18
Coupler Release
32
Train Doc. Completing
Train Doc. Delivery
33
Transiteur Release
25
26
Transiteur Release
31
Transiteur Movement
1 5
22
19
12
29
Coupler Assignment
Shunt Loco Movement
Transiteur Movement
Coupler Assignment
Transiteur Assignment
Coupler Movement
Examiner Assignment
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CPN Model of Railway Marshalling Yard
Technology• Aim
• Timed version
• Un-timed version
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Findings
• Coloured Petri net is able to model technological handling of train in marshalling yard and has some advantages
• Size and complexity of models for reasonable transport nodes is big + state space explosion
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State Space Explosion
• depends on:– number of incoming trains in the model– number of wagons in a train– number of potential destination stations for
wagons– if the trains and wagons are labeled uniquely
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Table 1
Change in number of incoming trains – timed model, both incoming and outgoing trains have 10 wagons and all wagons have the same destination
Processed incoming trains 1 3
Nodes in state space 156 307025
Arcs in state space 202 376507
Calculation time [s] 0 1286
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Table 2
Change in number of wagons in incoming train – 1 incoming train only, 10 wagons in outgoing trains and all wagons have the same destination
timed model non-timed model
Processed wagons 10 15 20 50 10 15 20
Nodes in state space 156 199 490 2072 1057 6278 114255
Arcs in state space 202 269 625 2718 3062 24411 596520
Calculation time [s] 0 1 1 5 1 8 467
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Table 3
Change in number of different colours for resources - timed model, only technology of incoming train is carried out, 10 wagons in incoming train; all wagons have the same destination
3 incoming trains 1 incoming train
Modelling of tracks individually group individually group
Nodes in state space 95952 4851 372 92
Arcs in state space 113659 5395 565 117
Calculation time [s] 243 9 1 1
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Table 4
Change in number of different colours for resources - timed model, both technologies carried out, 10 wagons in incoming train; all wagons have the same destination
1 incoming train
Modelling of tracks individually group
Nodes in state space 753 156
Arcs in state space 1073 202
Calculation time [s] 2 0
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Table 5
Variable state space size for random number of wagons between 10 and 15 for incoming train – non-timed model, 1 incoming train; all wagons have the same destination and 10 wagons in outgoing train
Wagons in 1 incoming train 10 11 12 13 14 15
Nodes in state space 3633 7302 11021 14608 18215 21899
Arcs in state space 9301 22995 36807 50266 63780 77501
Calculation time [s] 3 8 13 19 24 31
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State Space Explosion
• depends on:– number of incoming trains in the model– number of wagons in a train– number of potential destination stations for
wagons– if the trains and wagons are labeled uniquely
CPN Modelof Simple Transportation
System with Banker's Algorithm for Deadlock Avoidance
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CPN Model of Simple Transp. System with Banker's Algorithm
• Aim
• Without deadlock avoidance algorithm
• With Banker’s algorithm
• State space issues
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CPN Model of Simple Transp. System with Banker's Algorithm
To study deadlock situations in simulation of transport nodes’
technology
and
To find a method to avoid them
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Model’s Characteristics
• concurrent activities in a process• flexible routing available in process• repeated allocation and de-allocation of
resources during execution of a process• professions for handling of resources
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Station Layout
Technology Flowchart: Version 1
Technology Flowchart: Version 2
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CPN Model of Simple Transp. System with Banker's Algorithm
• Aim
• Without deadlock avoidance algorithm
• With Banker’s algorithm
• State space issues
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Banker’s Algorithm
• deadlock avoidance algorithm
• three versions:– A – basic algorithm– B – shorter calculation for some states– C – more complicates – accepts more states
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CPN Model of Simple Transp. System with Banker's Algorithm
• Aim
• Without deadlock avoidance algorithm
• With Banker’s algorithm
• State space issues
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Results (1) – Table
Deadlock States - A B C2 trains (I) 1 0 0 0
3 trains (I) 306 0 0 0
4 trains (I) 0 0
2 trains (II) 6 0 0 0
3 trains (II) 760 0 0 0
4 trains (II) 0 0 0
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Results (2) – Table
State Space Size - A B C2 trains (I) 18002 7986 7986 11142
3 trains (I) 179408 23362 23362 83920
4 trains (I) 46327 46327
2 trains (II) 20798 9978 9978 12172
3 trains (II) 228500 29338 29338 35920
4 trains (II) 58279 58279 71443
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Results (3) – Table
Calculation Time [s] - A B C2 trains (I) 163 61 59 126
3 trains (I) 13252 497 491 6323
4 trains (I) 1937 1843
2 trains (II) 230 98 94 144
3 trains (II) 23963 797 773 1185
4 trains (II) 3052 3270 4962
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Issues in State Space Analysis
• For large configurations: SS calculation froze– cursor feedback: hourglass– processor utilization: minimal
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Summary – Banker’s Alg.
• Model was used for Banker’s algorithm implementation for deadlock avoidance– state space reduction:
• same size for A and B• C less restrictive than A and B
– calculation time:• B can get solution in shorter time than A• longest for C
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Summary – Use of CPN
• CPN– not used for deadlock avoidance– used for quick model building = environment
for testing of the Banker’s algorithm
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Future Plans
• Implementation of Banker’s algorithm in specialised simulation tool Villon
• Looking into possibilities of DAP based on Petri net structure– category of RAS used is complex
