Abstract
This paper considers a network comprised of parallel routes with the Bureau of Public Road (BPR) latency function and suggests an optimal distribution method for incoming traffic flow. The authors analytically derive a system of equations defining the optimal distribution of the incoming flow with minimum social costs, as well as a corresponding system of equations for the Wardrop equilibrium in this network. In particular, the Wardrop equilibrium is applied to the competition model with rational consumers who use the carriers with minimal cost, where cost is equal to the price for service plus the waiting time for the service. Finally, the social costs under the equilibrium and under the optimal distribution are compared. It is shown that the price of anarchy can be infinitely large in the model with strategic pricing.
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Acknowledgements
This research is supported by the Russian Fund for Basic Research (projects 16-51-55006, 16-01-00183), the National Natural Science Foundation of China (project 61661136002) and Tsinghua University Initiative Scientific Research Grant (project 20151080397).
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Lien, J.W., Mazalov, V.V., Melnik, A.V., Zheng, J. (2016). Wardrop Equilibrium for Networks with the BPR Latency Function. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_4
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