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Dynamic Traffic Assignment for Electric Vehicles

Authors Lukas Graf , Tobias Harks, Prashant Palkar

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Lukas Graf
  • Universität Augsburg, Germany
Tobias Harks
  • Universität Augsburg, Germany
Prashant Palkar
  • Universität Augsburg, Germany


We are grateful to the anonymous reviewers for their valuable feedback on this paper. Additionally, we thank the organizers and participants of the 2022 Dagstuhl seminar on "Dynamic Traffic Models in Transportation Science" where we had many helpful and inspiring discussions on the topic of this paper.

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Lukas Graf, Tobias Harks, and Prashant Palkar. Dynamic Traffic Assignment for Electric Vehicles. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 6:1-6:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


We initiate the study of dynamic traffic assignment for electrical vehicles addressing the specific challenges such as range limitations and the possibility of battery recharge at predefined charging locations. We pose the dynamic equilibrium problem within the deterministic queueing model of Vickrey and as our main result, we establish the existence of an energy-feasible dynamic equilibrium. There are three key modeling-ingredients for obtaining this existence result: 1) We introduce a walk-based definition of dynamic traffic flows which allows for cyclic routing behavior as a result of recharging events en route. 2) We use abstract convex feasibility sets in an appropriate function space to model the energy-feasibility of used walks. 3) We introduce the concept of capacitated dynamic equilibrium walk-flows which generalize the former unrestricted dynamic equilibrium path-flows. Viewed in this framework, we show the existence of an energy-feasible dynamic equilibrium by applying an infinite dimensional variational inequality, which in turn requires a careful analysis of continuity properties of the network loading as a result of injecting flow into walks. We complement our theoretical results by a computational study in which we design a fixed-point algorithm computing energy-feasible dynamic equilibria. We apply the algorithm to standard real-world instances from the traffic assignment community illustrating the complex interplay of resulting travel times, energy consumption and prices paid at equilibrium.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Network flows
  • Networks → Traffic engineering algorithms
  • Electromobility
  • Dynamic Traffic Assignment
  • Dynamic Flows
  • Fixed Point Algorithm


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