1. CPN Models of Transport Systems Michal Zarnay Slovakia

2. 22.10.2007Department of Transport Networks, University of Zilina2/38 Michal Zarnay Department of Transport Networks Faculty of Management Science and Informatics University of Zilina Slovak Republic

3. 22.10.2007Department of Transport Networks, University of Zilina3/38 Department of Transport Networks modelling by means of optimisation and simulation focus mainly on transport systems Villon – tool for simulation of complex transport nodes

4. Villon

5. CPN Model of Railway Marshalling Yard Technology

6. 22.10.2007Department of Transport Networks, University of Zilina6/38 CPN Model of Railway Marshalling Yard Technology Aim Timed version Un-timed version

7. 22.10.2007Department of Transport Networks, University of Zilina7/38 CPN Model of Railway Marshalling Yard Technology To test abilities of CPN for modelling of technological process in transportation systems

8. 22.10.2007Department of Transport Networks, University of Zilina8/38 Model’s Characteristics resources used: –tracks –locomotives –personnel 2 technological flowcharts –incoming train processing –outgoing train processing

9. Incoming Train Processing

10. Outgoing Train Processing

11. 22.10.2007Department of Transport Networks, University of Zilina11/38 CPN Model of Railway Marshalling Yard Technology Aim Timed version Un-timed version

12. 22.10.2007Department of Transport Networks, University of Zilina12/38 Coloured Petri Net Model of Marshalling Yard 1 principal net and 3 subnets 72 transitions 137 places Short demonstration

13. 22.10.2007Department of Transport Networks, University of Zilina13/38 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

14. 22.10.2007Department of Transport Networks, University of Zilina14/38 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

15. 22.10.2007Department of Transport Networks, University of Zilina15/38 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 trains13 Nodes in state space156307025 Arcs in state space202376507 Calculation time [s]01286

16. 22.10.2007Department of Transport Networks, University of Zilina16/38 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 modelnon-timed model Processed wagons 10152050101520 Nodes in state space 156199490207210576278114255 Arcs in state space 2022696252718306224411596520 Calculation time [s] 011518467

17. 22.10.2007Department of Transport Networks, University of Zilina17/38 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 trains1 incoming train Modelling of tracks individuallygroupindividuallygroup Nodes in state space 95952485137292 Arcs in state space 1136595395565117 Calculation time [s] 243911

18. 22.10.2007Department of Transport Networks, University of Zilina18/38 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 individuallygroup Nodes in state space 753156 Arcs in state space 1073202 Calculation time [s] 20

19. 22.10.2007Department of Transport Networks, University of Zilina19/38 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 train101112131415 Nodes in state space 3633730211021146081821521899 Arcs in state space 93012299536807502666378077501 Calculation time [s] 3813192431

20. 22.10.2007Department of Transport Networks, University of Zilina20/38 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

21. CPN Model of Simple Transportation System with Banker's Algorithm for Deadlock Avoidance

22. 22.10.2007Department of Transport Networks, University of Zilina22/38 CPN Model of Simple Transp. System with Banker's Algorithm Aim Without deadlock avoidance algorithm With Banker’s algorithm State space issues

23. 22.10.2007Department of Transport Networks, University of Zilina23/38 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

24. 22.10.2007Department of Transport Networks, University of Zilina24/38 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

25. 22.10.2007Department of Transport Networks, University of Zilina25/38 Station Layout

26. Technology Flowchart: Version 1

27. Technology Flowchart: Version 2

28. 22.10.2007Department of Transport Networks, University of Zilina28/38 CPN Model of Simple Transp. System with Banker's Algorithm Aim Without deadlock avoidance algorithm With Banker’s algorithm State space issues

29. 22.10.2007Department of Transport Networks, University of Zilina29/38 Banker’s Algorithm deadlock avoidance algorithm three versions: –A – basic algorithm –B – shorter calculation for some states –C – more complicates – accepts more states

30. 22.10.2007Department of Transport Networks, University of Zilina30/38 CPN Model of Simple Transp. System with Banker's Algorithm Aim Without deadlock avoidance algorithm With Banker’s algorithm State space issues

31. 22.10.2007Department of Transport Networks, University of Zilina31/38 Results (1) – Table Deadlock States -ABC 2 trains (I)1000 3 trains (I)306000 4 trains (I)00 2 trains (II)6000 3 trains (II)760000 4 trains (II)000

32. 22.10.2007Department of Transport Networks, University of Zilina32/38 Results (2) – Table State Space Size -ABC 2 trains (I)180027986 11142 3 trains (I)17940823362 83920 4 trains (I)46327 2 trains (II)207989978 12172 3 trains (II)22850029338 35920 4 trains (II)58279 71443

33. 22.10.2007Department of Transport Networks, University of Zilina33/38 Results (3) – Table Calculation Time [s] -ABC 2 trains (I)1636159126 3 trains (I)132524974916323 4 trains (I)19371843 2 trains (II)2309894144 3 trains (II)239637977731185 4 trains (II)305232704962

34. 22.10.2007Department of Transport Networks, University of Zilina34/38 Issues in State Space Analysis For large configurations: SS calculation froze –cursor feedback: hourglass –processor utilization: minimal

35. 22.10.2007Department of Transport Networks, University of Zilina35/38 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

36. 22.10.2007Department of Transport Networks, University of Zilina36/38 Summary – Use of CPN CPN –not used for deadlock avoidance –used for quick model building = environment for testing of the Banker’s algorithm

37. 22.10.2007Department of Transport Networks, University of Zilina37/38 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

38. Thank you for your attention! Michal.Zarnay@fri.uniza.sk