Dynamic flows with adaptive route choice

Graf, Lukas; Harks, Tobias; Sering, Leon

doi:10.1007/s10107-020-01504-2

Cited by 27 publications

(65 citation statements)

References 23 publications

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“…An extension that is maximal with respect to α is called a phase in the construction of an equilibrium and the existence of equilibria on the whole R + then follows by a limit argument over the phases. In the same spirit, Graf, Harks and Sering [10] established a similar characterization for IDE flows and also derived an α-extension property.…”

Section: Introductionmentioning

confidence: 87%

A finite time combinatorial algorithm for instantaneous dynamic equilibrium flows

Graf

Harks

2022

Math. Program.

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Instantaneous dynamic equilibrium (IDE) is a standard game-theoretic concept in dynamic traffic assignment in which individual flow particles myopically select en route currently shortest paths towards their destination. We analyze IDE within the Vickrey bottleneck model, where current travel times along a path consist of the physical travel times plus the sum of waiting times in all the queues along a path. Although IDE have been studied for decades, several fundamental questions regarding equilibrium computation and complexity are not well understood. In particular, all existence results and computational methods are based on fixed-point theorems and numerical discretization schemes and no exact finite time algorithm for equilibrium computation is known to date. As our main result we show that a natural extension algorithm needs only finitely many phases to converge leading to the first finite time combinatorial algorithm computing an IDE. We complement this result by several hardness results showing that computing IDE with natural properties is NP-hard.

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Section: Introductionmentioning

confidence: 87%

A finite time combinatorial algorithm for instantaneous dynamic equilibrium flows

Graf

Harks

2022

Math. Program.

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“…In particular, Sering and Vargas Koch [27] consider spillback effects, which is the study how an a priori bound on the amount of flow that can be waiting on a queue affects the equilibrium behavior. Graf and Harks [14] consider a related model in which flow particles are myopic in that they make local routing decisions based on the current status of the network, without anticipating the whole future evolution. Finally, Scarsini, Schröder, and Tomala [25] consider a discrete variant of the problem and look at the simpler parallel-link networks, but add the complication that the inflow varies over time in a periodic fashion.…”

Section: Further Related Literaturementioning

confidence: 99%

On the Price of Anarchy for Flows over Time

2022

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Dynamic network flows, or network flows over time, constitute an important model for real-world situations in which steady states are unusual, such as urban traffic and the internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper, we study dynamic equilibria in the deterministic fluid queuing model in single-source, single-sink networks—arguably the most basic model for flows over time. In the last decade, we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the price of anarchy, measured as the worst-case ratio between the minimum time required to route a given amount of flow from the source to the sink and the time a dynamic equilibrium takes to perform the same task. Our main result states that, if we could reduce the inflow of the network in a dynamic equilibrium, then the price of anarchy is bounded by a factor, parameterized by the longest path length that converges to [Formula: see text], and this is tight. This significantly extends a result by Bhaskar et al. (SODA 2011). Furthermore, our methods allow us to determine that the price of anarchy in parallel-link and parallel-path networks is exactly 4/3. Finally, we argue that, if a certain, very natural, monotonicity conjecture holds, the price of anarchy in the general case is exactly [Formula: see text].

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“…In order to be able to analyze the connection between the packet routing model and flows over time in the following sections, we briefly introduce the multi-commodity flow over time model which is studied in [4,10,25,26]. This model extends the network flow concept by a continuous time component.…”

Section: Flows Over Timementioning

confidence: 99%

Convergence of a Packet Routing Model to Flows Over Time

Sering

Koch

Ziemke

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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The mathematical approaches for modeling dynamic traffic can roughly be divided into two categories: discrete packet routing models and continuous flow over time models. Despite very vital research activities on models in both categories, the connection between these approaches was poorly understood so far. In this work we build this connection by specifying a (competitive) packet routing model, which is discrete in terms of flow and time, and by proving its convergence to the intensively studied model of flows over time with deterministic queuing. More precisely, we prove that the limit of the convergence process, when decreasing the packet size and time step length in the packet routing model, constitutes a flow over time with multiple commodities. In addition, we show that the convergence result implies the existence of approximate equilibria in the competitive version of the packet routing model. This is of significant interest as exact pure Nash equilibria, similar to almost all other competitive models, cannot be guaranteed in the multi-commodity setting.Moreover, the introduced packet routing model with deterministic queuing is very application-oriented as it is based on the network loading module of the agent-based transport simulation MATSim. As the present work is the first mathematical formalization of this simulation, it provides a theoretical foundation and an environment for provable mathematical statements for MATSim. CCS Concepts: • Theory of computation → Algorithmic game theory; Network games; Network flows; Exact and approximate computation of equilibria; Routing and network design problems; • Mathematics of computing → Network flows.

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Dynamic flows with adaptive route choice

Cited by 27 publications

References 23 publications

A finite time combinatorial algorithm for instantaneous dynamic equilibrium flows

A finite time combinatorial algorithm for instantaneous dynamic equilibrium flows

On the Price of Anarchy for Flows over Time

Convergence of a Packet Routing Model to Flows Over Time

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