Stability of Information-Based Routing in Dynamic Transportation Networks

TL;DR

This paper analyzes how specific real-time traffic information signals can ensure stable, unique equilibria in dynamic transportation networks, reducing congestion and travel time while maintaining system stability.

Contribution

It introduces a class of density-dependent traffic information that guarantees equilibrium existence, uniqueness, and stability in joint density and routing dynamics.

Findings

Identifies information signals that ensure stable equilibria in traffic networks.

Demonstrates reduction in total travel time through designed information signals.

Ensures traffic densities remain within free-flow conditions over time.

Abstract

Recent studies on transportation networks have shown that real-time route guidance can inadvertently induce congestion or oscillatory traffic patterns. Nevertheless, such technologies also offer a promising opportunity to manage traffic non-intrusively by shaping the information delivered to users, thereby mitigating congestion and enhancing network stability. A key step toward this goal is to identify information signals that ensure the existence of an equilibrium with desirable stability and convergence properties. This challenge is particularly relevant when traffic density and routing dynamics evolve concurrently, as increasingly occurs with digital signaling and real-time navigation technologies. To address this, we analyze a parallel-path transportation network with a single origin-destination pair, incorporating joint traffic density and logit-based routing dynamics that evolve at the same timescale. We characterize a class of density-dependent traffic information that guarantees a unique equilibrium in the free-flow regime, ensures its asymptotic stability, and keeps traffic densities within the free-flow region for all time. The theoretical results are complemented by a numerical case study demonstrating how the framework can inform the design of traffic information that reduces total travel time without compromising credibility.