Stability of Information-Based Routing in Dynamic Transportation Networks

TL;DR

The paper addresses stability of joint density–routing dynamics in a parallel-path transportation network under real-time information. It develops an information-design framework that characterizes a density-dependent signal class $u$ ensuring a unique, asymptotically stable free-flow equilibrium within the coupled system where density dynamics and logit routing co-evolve at the same timescale. By leveraging fixed-point arguments, softmax Lipschitz properties, and a Lyapunov function, it provides existence, uniqueness, and global stability conditions, along with a positively invariant free-flow region. A numerical example demonstrates how affine information signals can improve network efficiency (lower total travel time) while maintaining credibility, illustrating the practical impact for real-time navigation platforms and traffic management. The results lay groundwork for optimizing information signals under stability constraints and invite extension to more general network topologies and regimes.

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.

Figures (5)

• Figure 1: Equilibrium link densities with respect to $\eta$ when users are provided with real travel-time information $\tau(x)$ (top), and designed information $u(x)$ with $\gamma=0$ (bottom).
• Figure 2: Comparison of total travel times experienced by the drivers at equilibrium, when provided with different travel-time information.
• Figure 3: Credibility of the designed information $u(x)$ with different values of $\gamma$, quantified by $\|\tau(x)-u(x)\|$.
• Figure 4: Trajectory of link densities and routing ratios under the designed $u(x)$ with $\eta=20$ and $\gamma=0.1$.
• Figure 5: $100$ trajectories of $x(t)/\bar{x}$ and $r(t)/\bar{f}$ starting from $x^0\in\mathcal{X}\times \mathcal{R}'$ under the designed $u(x)$ with $\eta=20$ and $\gamma=0.1$.

Theorems & Definitions (14)

• Proposition 1
• proof
• Remark 1
• Lemma 1
• proof
• Remark 2
• Proposition 2
• proof
• Proposition 3
• proof