Routing Games over Time with FIFO Policy

Ismaili, Anisse

doi:10.1007/978-3-319-71924-5_19

Cited by 22 publications

(17 citation statements)

References 30 publications

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“…Such computability is in sharp contrast with previous hardness results on related games of atomic dynamic flows, e.g., NP-completeness for determining NE existence (Werth et al 2014) and NPhardness for computing a best response (Hoefer et al 2009, Ismaili 2017.…”

Section: Contributionscontrasting

confidence: 75%

“…The paradox differs from ours in that it involves route changes (see Section 4.2). Under the model of Scarsini et al (2018), Ismaili (2017) shows many negative results when multiple origin-destination pairs are involved, including non-existence of an NE, and the NP-hardness and inapproximability of computing a best response, etc.…”

Section: Atomic Dynamic Flow Gamesmentioning

confidence: 99%

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Atomic Dynamic Flow Games: Adaptive vs. Nonadaptive Agents

Cao

Chen

et al. 2021

Operations Research

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We propose a game model for selfish routing of atomic agents, who compete for use of a network to travel from their origins to a common destination as quickly as possible. We follow a frequently used rule that the latency an agent experiences on each edge is a constant transit time plus a variable waiting time in a queue. A key feature that differentiates our model from related ones is an edge-based tie-breaking rule for prioritizing agents in queueing when they reach an edge at the same time. We study both nonadaptive agents (each choosing a one-off origin–destination path simultaneously at the very beginning) and adaptive ones (each making an online decision at every nonterminal vertex they reach as to which next edge to take). On the one hand, we constructively prove that a (pure) Nash equilibrium (NE) always exists for nonadaptive agents and show that every NE is weakly Pareto optimal and globally first-in first-out. We present efficient algorithms for finding an NE and best responses of nonadaptive agents. On the other hand, we are among the first to consider adaptive atomic agents, for which we show that a subgame perfect equilibrium (SPE) always exists and that each NE outcome for nonadaptive agents is an SPE outcome for adaptive agents but not vice versa.

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Section: Contributionscontrasting

confidence: 75%

Section: Atomic Dynamic Flow Gamesmentioning

confidence: 99%

Atomic Dynamic Flow Games: Adaptive vs. Nonadaptive Agents

Cao

Chen

et al. 2021

Operations Research

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“…Our results reveal that this is in fact not true: there are multi-commodity instances with finitely lasting bounded inflows that admit IDE flows cycling forever. For the discrete version of this model using the natural discrete version of our equi-librium concept, such a behavior was already discovered in Ismaili [12,Theorem 8], though his instance makes critical use of edges with zero transit time (which we do not allow) and the instantaneous travel time always increases when there is positive inflow into an edge, even when the edge inflow rate is smaller than the rate capacity. In particular, players may observe increased instantaneous travel time, although no player is in fact delayed.…”

Section: Related Workmentioning

confidence: 91%

“…Since all edges vw i are active at time θ k , we have v (θ k ) = c vw i (θ k ) + w i (θ k ) and, thus, a flow with constant inflow rates satisfies (12) and (13)…”

Section: Existence Of Ide Flows In Single-sink Networkmentioning

confidence: 99%

Dynamic flows with adaptive route choice

2020

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We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation of IDE flows for multi-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.

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“…For multi-commodity games pure Nash equilibria do not exist in general. This follows from the example presented by Ismaili [14], which we adapt to our model here. Proposition 2.1.…”

Section: Competitive Packet Routing Gamementioning

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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Routing Games over Time with FIFO Policy

Cited by 22 publications

References 30 publications

Atomic Dynamic Flow Games: Adaptive vs. Nonadaptive Agents

Atomic Dynamic Flow Games: Adaptive vs. Nonadaptive Agents

Dynamic flows with adaptive route choice

Convergence of a Packet Routing Model to Flows Over Time

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