Convergence of approximate and packet routing equilibria to Nash flows over time

Olver, Neil ORCID: 0000-0001-8897-5459, Sering, Leon and Vargas Koch, Laura (2023) Convergence of approximate and packet routing equilibria to Nash flows over time. In: Proceedings of the 64th IEEE Symposium on Foundations of Computer Science (FOCS. Annual IEEE Symposium on Foundations of Computer Science,64. IEEE Computer Society Press, 123 - 133. ISBN 9798350318951

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Abstract

We consider a dynamic model of traffic that has received a lot of attention in the past few years. Infinitesimally small agents aim to travel from a source to a destination as quickly as possible. Flow patterns vary over time, and congestion effects are modeled via queues, which form based on the deterministic queueing model whenever the inflow into a link exceeds its capacity.Are equilibria in this model meaningful as a prediction of traffic behavior? For this to be the case, a certain notion of stability under ongoing perturbations is needed. Real traffic consists of discrete, atomic “packets”, rather than being a continuous flow of non-atomic agents. Users may not choose an absolutely quickest route available, if there are multiple routes with very similar travel times. We would hope that in both these situations - a discrete packet model, with packet size going to 0, and ε-equilibria, with ε - going to 0 - equilibria converge to dynamic equilibria in the flow over time model. No such convergence results were known.We show that such a convergence result does hold in single-commodity instances for both of these settings, in a unified way. More precisely, we introduce a notion of “strict” ε-equilibria, and show that these must converge to the exact dynamic equilibrium in the limit as ε→0. We then show that results for the two settings mentioned can be deduced from this with only moderate further technical effort.

Item Type:	Book Section
Official URL:	https://ieeexplore.ieee.org/xpl/conhome/1000292/al...
Additional Information:	© 2023 IEEE
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	21 Nov 2023 12:33
Last Modified:	20 Dec 2024 00:20
URI:	http://eprints.lse.ac.uk/id/eprint/120818

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