A Game Theoretic Approach to the Determination of Hyperpaths in Transportation Networks
In transit assignment, the common lines problem leads to the notion of a hyperpath, which is a set of paths that when used according to the “take whichever attractive line arrives next” strategy minimises the expected travel time. Similarly, the game theoretic approach to risk-averse traffic assignment leads to the generation of a set of paths which minimises expected travel time when a pessimistic assumption is made about on-trip events. The equivalence between the hyperpath of transit assignment and the set of paths generated by a multi-agent, zero sum game is shown in this paper. In particular, game theory is used to show that the path split probabilities proposed by Spiess and Florian (1989) are optimal for the risk-averse traveller who needs to make an on-the-spot decision between alternative routes. An alternative two-agent (single demon), zero-sum game is considered. The results of the multiple- and two-agent games are compared on a small example network, showing that the single demon game can lead to denser hyperpaths.
KeywordsTravel Time Transportation Network Route Choice Transit Network Transportation Research Part
Unable to display preview. Download preview PDF.
- Ahuja, R.K., Magnanti, T.L. and Orlin, J.B. (1993). Network Flows: Theory, Algorithms, and Applications. Prentice Hall, New Jersey, 308-316.Google Scholar
- Billi, C., Gentile, G., Nguyen, S. and Pallottino, S. (2004). Rethinking the wait model at transit stops. Proceedings TRISTAN-Workshop, Guadelupe.Google Scholar
- Cassir, C. and Bell, M.G.H. (2000). The N+M person game approach to network reliability. Reliability of Transport Networks (Eds. M.G.H. Bell and C. Cassir), Research Studies Press, Baldock (Herts.), U.K., 91-102.Google Scholar
- Cassir, C., Bell, M.G.H. and Schmöcker, J.D. (2003). A Normative Assessment of Transport Network Reliability Based on Game Theory, Edited by Bell, M.G.H. and Iida Y., The Network Reliability of Transport, Pergamon.Google Scholar
- Kato, H., Kaneko, Y. and Inoue, M. (2007). Choice of Travel Demand Forecast Models: Comparative Analysis in Urban Rail Route Choice. Presented at the European Transport Conference, 17-19 October, Leiden, The Netherlands.Google Scholar
- Nagae, T. and Akamatsu, T. (2007). An efficient algorithm for a maximin routing model for hazardous materials. Proceedings of the 3rd International Symposium on Transport Network Reliability (INSTR), Delft, Holland, 19-20 July.Google Scholar
- Nökel, K. and Wekeck, S. (2007). Choice Models in Frequency-Based Transit Assignment. Presented at the European Transport Conference, 17-19 October, Leiden, The Netherlands.Google Scholar
- Szeto, W.Y., O'Brien, L. and O'Mahony, M. (2007). Generalisation of the risk-averse traffic assignment. Proceedings of the 17th ISTTT, Elsevier: Oxford, 127-155.Google Scholar