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Optimal externalities in a parallel transportation network

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Abstract

We consider the Wardrop model with splittable traffic and externalities applied to the parallel transportation network. These externalities are introduced into the players’ latency functions as a tool of the system’s influence on the equilibrium distribution of traffic flows and also on the PoA values. In the general case, the externalities can be interpreted as elements of centralized control, which can be included, e.g., in traffic rules (speed-limit signs, controlled traffic lights), pricing policy for public transport, fuel, etc. This paper investigates the influence of traffic lane rules on the Price of Anarchy. We show that for the parallel transportation system there exist externality values such that the equilibrium and optimal profiles will coincide with one another and the Price of Anarchy will be equal to 1. Also we propose the socialization procedure of user behavior for which the parallel transportation system ensures an optimal profile of user behavior and the same value of the social costs as in the optimal profile with initial externalities.

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Authors and Affiliations

  1. Karelian Research Center, Institute of Applied Mathematical Research, Russian Academy of Sciences, ul. Pushkinskaya 11, Petrozavodsk, Russia, 185910

    Julia V. Chirkova & Vladimir V. Mazalov

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  1. Julia V. Chirkova
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  2. Vladimir V. Mazalov
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Correspondence to Julia V. Chirkova.

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This work is supported by the Russian Science Foundation (grant No. 22-11-20015)

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Chirkova, J.V., Mazalov, V.V. Optimal externalities in a parallel transportation network. Optim Lett 16, 1971–1989 (2022). https://doi.org/10.1007/s11590-022-01864-y

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