Bicriteria Nash Flows over Time

TL;DR

This paper studies Nash flows over time in traffic networks with deadlines, analyzing their existence, structure, and efficiency loss, and provides bounds for parallel networks with different performance metrics.

Contribution

It introduces a variant of the fluid queuing model with deadlines, characterizes Nash flows, and analyzes the price of anarchy for this setting.

Findings

Nash flows over time exist and have a specific structure.

The price of anarchy can be unbounded in general networks.

Tight bounds are established for parallel path networks.

Abstract

Flows over time are a natural way to incorporate flow dynamics that arise in various applications such as traffic networks. In this paper we introduce a natural variant of the deterministic fluid queuing model in which users aim to minimize their costs subject to arrival at their destination before a pre-specified deadline. We determine the existence and the structure of Nash flows over time and fully characterize the price of anarchy for this model. The price of anarchy measures the ratio of the quality of the equilibrium and the quality of the optimum flow, where we evaluate the quality using two different natural performance measures: the throughput for a given deadline and the makespan for a given amount of flow. While it turns out that both prices of anarchy can be unbounded in general, we provide tight bounds for the important subclass of parallel path networks. Surprisingly, the two performance measures yield different results here.