Finding Equilibrium in Transport Networks by Simulation and Investigation of Behaviors
The goal of this paper is to find Wardrop equilibrium
in transport networks at case of uncertainty situations, where the
uncertainty comes from lack of information. We use simulation tool
to find the equilibrium, which gives only approximate solution, but
this is sufficient for large networks as well. In order to take the
uncertainty into account we have developed an interval-based
procedure for finding the paths with minimal cost using the
Dempster-Shafer theory. Furthermore we have investigated the users-
behaviors using game theory approach, because their path choices
influence the costs of the other users- paths.
[1] A. Nagurney, "Spatial Equilibrium in Transport Networks", in
Handbook of Transport Geography and Spatial Systems, Handbooks in
Transport Vol. 5, ed. David Hensher, et al., Elsevier, 2004, pp. 583-608.
[2] D. E. Kaufman, J. Nonis, and R. L. Smith, "A mixed integer linear
programming model for dynamic route guidance", Transportation
Research Part B: Methodological, Volume 32, Issue 6, August 1998, pp.
431-440.
[3] D. Boyce, D. H. Lee and B. Ran: Analytical Models of the Dynamic
Traffic Assignment Problem, Networks and Spatial Economics, Vol. 1,
Numbers 3-4, September, 2001, pp. 377-390.
[4] I. Chabini, H. Jiang, P. Macneille, and R. Miller, "Parallel
Implementation of Dynamic Traffic Assignment Models", Presented at
the 2003 IEEE International Conference on Systems, Man &
Cybernetics, Washington DC, October 2003.
[5] Q. Yang: A Simulation Laboratory for Evaluation of Dynamic Traffic
Management Systems, PhD thesis, Massachusetts Institute of
Technology, Cambridge, Massachusetts, June 1997.
[6] H. Miller, Y. Wu, M. Hung, "Gis-Based Dynamic Traffic Congestion
Modeling To Support Time-Critical Logistics", Published in the
Proceedings of the Hawai-i International IEEE Conference on System
Science, January 5-8, Maui, Hawaii, 1999.
[7] Y. Wu, H. Miller, M. Hung, "A GIS-based decision support system for
analysis of route choice in congested urban road networks", Journal of
Geographical Systems, 2001. No. 3 pp. 3-24.
[8] A. Rapoport, T. Kugler, S. Dugar, and E. J. Gisches, "Choice of routes in
congested traffic networks: Experimental tests of the Braess Paradox",
Games and Economic Behavior, Volume 65, Issue 2, March 2009, pp.
538-571.
[9] S. J. Li, G. Y. Chen, "Multiclass, Two-criteria Traffic Network
Equilibrium Models and Vector Variational Inequalities", Systems
Engineering - Theory & Practice, Volume 28, Issue 1, January 2008, pp.
141-145.
[10] L.C. Davis, "Realizing Wardrop equilibria with real-time traffic
information", Physica A: Statistical Mechanics and its Applications,
Volume 388, Issue 20, 15 October 2009, pp. 4459-4474.
[11] V. Henn, M. Ottomanelli, "Handling uncertainty in route choice models:
From probabilistic to possibilistic approaches", European Journal of
Operational Research, Volume 175, Issue 3, 16 December 2006, pp.
1526-1538.
[12] Y. M. Nie, "Equilibrium analysis of macroscopic traffic oscillations",
Transportation Research Part B: Methodological, Volume 44, Issue 1,
January 2010, pp. 62-72.
[13] B. Raney, K. Nagel, "Iterative route planning for large-scale modular
transportation simulations", Future Generation Computer Systems,
Volume 20, Issue 7, 1 October 2004, pp. 1101-1118.
[14] A. L.C. Bazzan, F. Kl├╝gl, "Case studies on the Braess Paradox:
Simulating route recommendation and learning in abstract and
microscopic models", Transportation Research Part C: Emerging
Technologies, Volume 13, Issue 4, August 2005, pp. 299-319.
[15] S. Rosswog, C. Gawron, S. Hasselberg, R. Böning, P. Wagner,
"Computational aspects in traffic simulation problems", Future
Generation Computer Systems, Volume 17, Issue 5, March 2001, pp.
659-665.
[16] D. Braess, "Uber ein Paradoxon der Verkehrsplanung,"
Unternehmenforschung, 1968, 12, pp. 258-268.
[17] J. G. Wardrop, "Some Theoretical Aspects of Road Traffic Research,"
Proceedings of the Institute of Civil Engineers, Part II, 1952, pp. 325-
378.
[18] G. Szűcs, Gy. Sallai, "Route Planning with Uncertain Information using
Dempster-Shafer theory", 3rd International Conference Engineering
Management and Service Sciences (EMS 2009), Session of City
Operation and Development, in Beijing, China, September 20-22, 2009.
[19] M. Florian, M. Mahut, N. Tremblay, "Application of a simulation-based
dynamic traffic assignment model", European Journal of Operational
Research 189, 2008, pp. 1381-1392.
[20] R. Axelrod, "Effective choice in the prisoner-s dilemma" J. Conflict
Resolution, 24, 1980, pp. 3-25.
[21] R. Axelrod, "The Evolution of Cooperation" (Revised edition) Perseus
Books Group, 2006.
[22] J. Baron, "Thinking and Deciding", (Third Edition), Cambridge
University Press, 2000.
[23] Gy. Szabó, G. Fáth, "Evolutionary games on graphs", Physics Reports
446, 2007, pp. 97-216.
[24] S. Azhar, A. McLennan, J.H. Reif, "Computation of equilibriain
noncooperative games", Computers & Mathematics with Applications,
Volume 50, Issues 5-6, September 2005, Pages 823-854.
[25] G. Szűcs, Gy. Sallai: "Finding Equilibrium in Transport Networks by
Simulation in case of Lack of Information", "International Conference
on Innovation, Engineering Management and Technology", WASET
conference 65, Tokyo, 2010 May 26-28. pp. 172-176.
[1] A. Nagurney, "Spatial Equilibrium in Transport Networks", in
Handbook of Transport Geography and Spatial Systems, Handbooks in
Transport Vol. 5, ed. David Hensher, et al., Elsevier, 2004, pp. 583-608.
[2] D. E. Kaufman, J. Nonis, and R. L. Smith, "A mixed integer linear
programming model for dynamic route guidance", Transportation
Research Part B: Methodological, Volume 32, Issue 6, August 1998, pp.
431-440.
[3] D. Boyce, D. H. Lee and B. Ran: Analytical Models of the Dynamic
Traffic Assignment Problem, Networks and Spatial Economics, Vol. 1,
Numbers 3-4, September, 2001, pp. 377-390.
[4] I. Chabini, H. Jiang, P. Macneille, and R. Miller, "Parallel
Implementation of Dynamic Traffic Assignment Models", Presented at
the 2003 IEEE International Conference on Systems, Man &
Cybernetics, Washington DC, October 2003.
[5] Q. Yang: A Simulation Laboratory for Evaluation of Dynamic Traffic
Management Systems, PhD thesis, Massachusetts Institute of
Technology, Cambridge, Massachusetts, June 1997.
[6] H. Miller, Y. Wu, M. Hung, "Gis-Based Dynamic Traffic Congestion
Modeling To Support Time-Critical Logistics", Published in the
Proceedings of the Hawai-i International IEEE Conference on System
Science, January 5-8, Maui, Hawaii, 1999.
[7] Y. Wu, H. Miller, M. Hung, "A GIS-based decision support system for
analysis of route choice in congested urban road networks", Journal of
Geographical Systems, 2001. No. 3 pp. 3-24.
[8] A. Rapoport, T. Kugler, S. Dugar, and E. J. Gisches, "Choice of routes in
congested traffic networks: Experimental tests of the Braess Paradox",
Games and Economic Behavior, Volume 65, Issue 2, March 2009, pp.
538-571.
[9] S. J. Li, G. Y. Chen, "Multiclass, Two-criteria Traffic Network
Equilibrium Models and Vector Variational Inequalities", Systems
Engineering - Theory & Practice, Volume 28, Issue 1, January 2008, pp.
141-145.
[10] L.C. Davis, "Realizing Wardrop equilibria with real-time traffic
information", Physica A: Statistical Mechanics and its Applications,
Volume 388, Issue 20, 15 October 2009, pp. 4459-4474.
[11] V. Henn, M. Ottomanelli, "Handling uncertainty in route choice models:
From probabilistic to possibilistic approaches", European Journal of
Operational Research, Volume 175, Issue 3, 16 December 2006, pp.
1526-1538.
[12] Y. M. Nie, "Equilibrium analysis of macroscopic traffic oscillations",
Transportation Research Part B: Methodological, Volume 44, Issue 1,
January 2010, pp. 62-72.
[13] B. Raney, K. Nagel, "Iterative route planning for large-scale modular
transportation simulations", Future Generation Computer Systems,
Volume 20, Issue 7, 1 October 2004, pp. 1101-1118.
[14] A. L.C. Bazzan, F. Kl├╝gl, "Case studies on the Braess Paradox:
Simulating route recommendation and learning in abstract and
microscopic models", Transportation Research Part C: Emerging
Technologies, Volume 13, Issue 4, August 2005, pp. 299-319.
[15] S. Rosswog, C. Gawron, S. Hasselberg, R. Böning, P. Wagner,
"Computational aspects in traffic simulation problems", Future
Generation Computer Systems, Volume 17, Issue 5, March 2001, pp.
659-665.
[16] D. Braess, "Uber ein Paradoxon der Verkehrsplanung,"
Unternehmenforschung, 1968, 12, pp. 258-268.
[17] J. G. Wardrop, "Some Theoretical Aspects of Road Traffic Research,"
Proceedings of the Institute of Civil Engineers, Part II, 1952, pp. 325-
378.
[18] G. Szűcs, Gy. Sallai, "Route Planning with Uncertain Information using
Dempster-Shafer theory", 3rd International Conference Engineering
Management and Service Sciences (EMS 2009), Session of City
Operation and Development, in Beijing, China, September 20-22, 2009.
[19] M. Florian, M. Mahut, N. Tremblay, "Application of a simulation-based
dynamic traffic assignment model", European Journal of Operational
Research 189, 2008, pp. 1381-1392.
[20] R. Axelrod, "Effective choice in the prisoner-s dilemma" J. Conflict
Resolution, 24, 1980, pp. 3-25.
[21] R. Axelrod, "The Evolution of Cooperation" (Revised edition) Perseus
Books Group, 2006.
[22] J. Baron, "Thinking and Deciding", (Third Edition), Cambridge
University Press, 2000.
[23] Gy. Szabó, G. Fáth, "Evolutionary games on graphs", Physics Reports
446, 2007, pp. 97-216.
[24] S. Azhar, A. McLennan, J.H. Reif, "Computation of equilibriain
noncooperative games", Computers & Mathematics with Applications,
Volume 50, Issues 5-6, September 2005, Pages 823-854.
[25] G. Szűcs, Gy. Sallai: "Finding Equilibrium in Transport Networks by
Simulation in case of Lack of Information", "International Conference
on Innovation, Engineering Management and Technology", WASET
conference 65, Tokyo, 2010 May 26-28. pp. 172-176.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:52010", author = "Gábor Szűcs and Gyula Sallai", title = "Finding Equilibrium in Transport Networks by Simulation and Investigation of Behaviors", abstract = "The goal of this paper is to find Wardrop equilibrium
in transport networks at case of uncertainty situations, where the
uncertainty comes from lack of information. We use simulation tool
to find the equilibrium, which gives only approximate solution, but
this is sufficient for large networks as well. In order to take the
uncertainty into account we have developed an interval-based
procedure for finding the paths with minimal cost using the
Dempster-Shafer theory. Furthermore we have investigated the users-
behaviors using game theory approach, because their path choices
influence the costs of the other users- paths.", keywords = "Dempster-Shafer theory, S-O and U-Otransportation network, uncertainty of information, Wardropequilibrium.", volume = "4", number = "5", pages = "521-6", }
