Multi-Source Multi-Sink Nash Flows Over Time

TL;DR

This paper extends the concept of Nash flows over time from single-source single-sink networks to multi-source multi-sink networks, providing a new theoretical framework and algorithms for practical traffic modeling.

Contribution

It introduces a generalized model of thin flows with resetting for multi-terminal networks, enabling more realistic and applicable analysis of Nash flows over time.

Findings

Generalization of thin flows with resetting to multi-terminal networks

Development of an algorithm for computing multi-source multi-sink Nash flows

Enhanced understanding of dynamic traffic flow behavior in complex networks

Abstract

Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting'. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these result to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time.