Network Equilibrium under Cumulative Prospect Theory and Endogenous Stochastic Demand and Supply
In this paper we consider a network whose travel demands and road capacities are endogenously considered to be random variables. With stochastic demand and supply the route travel times are also random variables. In this scenario travelers choose their routes under travel time uncertainties. Several evidences suggest that the decision making process under uncertainty is significantly different from that without uncertainty. Therefore, the paper applies the decision framework of cumulative prospect theory (CPT) to capture this difference. We first formulate a stochastic network model whose travel demands and link capacities follow lognormal distributions. The stochastic travel times can then be derived under a given route choice modeling framework. For the route choice, we consider a modeling framework where the perceived value and perceived probabilities of travel time outcomes are obtained via transformations following CPT. We then formulate an equilibrium condition similar to that of User Equilibrium in which travelers choose the routes that maximizes their perceived utility values in the face of transformed stochastic travel times. Conditions are established guaranteeing existence (but not uniqueness) of this equilibrium. The paper then proposes a solution algorithm for the proposed model which is then tested with a test network.
KeywordsRoute Choice Network Equilibrium Transportation Research Part Cumulative Prospect Theory Probability Weighting Function
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This research was partially supported by a grant from the Research Committee of the Hong Kong Polytechnic University (Project No. A-PH65) and a General Research Fund from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 5271/08E).
- Avineri, E. and Prashker, J.N. (2003). Sensitivity to uncertainty - need for a paradigm shift. Traveler Behavior and Values 2003, 90-98.Google Scholar
- Barberis, N. and Huang, M. (2005). Stocks as lotteries: the implications of probability weighting for security prices. Yale School of Management Working Paper, http://badger.som.yale.edu/faculty/ncb25/pw35b.pdf.
- Connors, R.D. and Sumalee, A. (2009). A network equilibrium model with travellers' perception of stochastic travel times. Transportation Research Part B (In Press).Google Scholar
- Davies, G. and Satchell, S. (2004). Continuous cumulative prospect theory and individual asset allocation. Cambridge Working Papers in Economics Faculty of Economics (formerly DAE), http://www.dectech.org/Links/DaviesandSatchell-CPT.pdf.
- de Jong, G., Kroes, E., Plasmeijer, R., Sanders, P. and Warffemius, P. (2004). The value of reliability. Paper presented at the European Transport Conference, Strasbourg, France.Google Scholar
- Jou, R.C., Kitamura, R., Weng, M.C. and Chen, C.C. (2008). Dynamic commuter departure time choice under uncertainty. Transportation Research Part A, 42(5), 774–783.Google Scholar
- Michea, A., and Polak, J.W. (2006). Modelling risky choice behaviour: evaluating alternatives to expected utility theory. Paper presented at the 11th International Conference on Travel Behaviour Research, Kyoto, Japan.Google Scholar
- Noland, R.B. and Small, K.A. (1995). Travel time uncertainty, departure time choice and the cost of the morning commute. Transportation Research Record, 1493, 150-158.Google Scholar
- Wardrop, J. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers, 1(2), 325-378.Google Scholar
- Wu, J., Mehta, N.B. and Zhang, J. (2005). A flexible lognormal sum approximation method. Paper presented at the IEEE Global Telecommunication Conference GLOBECOM'05.Google Scholar