The Price of Anarchy for Instantaneous Dynamic Equilibria

TL;DR

This paper analyzes the efficiency loss of instantaneous dynamic equilibrium flows over time, providing bounds on the price of anarchy in deterministic queueing models with complex network instances.

Contribution

It establishes upper and lower bounds on the price of anarchy for IDE in flow over time models, advancing understanding of their efficiency.

Findings

Upper bound of order O(U·τ) for single-sink instances

Lower bound of order Ω(U·log τ) demonstrated with complex instances

Provides insights into the efficiency of IDE in dynamic network flows

Abstract

We consider flows over time within the deterministic queueing model and study the solution concept of instantaneous dynamic equilibrium (IDE) in which flow particles select at every decision point a currently shortest path. The length of such a path is measured by the physical travel time plus the time spent in queues. Although IDE have been studied since the eighties, the efficiency of the solution concept is not well understood. We study the price of anarchy for this model and show an upper bound of order $\mathcal{O}(U\cdot \tau)$ for single-sink instances, where $U$ denotes the total inflow volume and $\tau$ the sum of edge travel times. We complement this upper bound with a family of quite complex instances proving a lower bound of order $\Omega(U\cdot\log\tau)$.