Stability of vehicular admission control schemes in urban traffic networks under modelling uncertainty

TL;DR

This paper analyzes the stability of decentralized vehicular admission control schemes in urban traffic networks considering modeling uncertainties, providing scalable conditions for stability guarantees using passivity theory.

Contribution

It introduces a passivity-based framework to ensure stability of VAC schemes under uncertainty in large-scale, heterogeneous urban traffic networks.

Findings

Stability conditions are scalable and locally verifiable.

Numerical simulations validate the theoretical stability guarantees.

The framework applies to networks with nonlinear dynamics and uncertain parameters.

Abstract

Urban transportation networks face significant challenges due to traffic congestion, leading to adverse environmental and socioeconomic impacts. Vehicular admission control (VAC) strategies have emerged as a promising solution to alleviate congestion. By leveraging information and communication technologies, VAC strategies regulate vehicle entry into the network to optimize different traffic metrics of interest over space and time. Despite the significant development of VAC strategies, their stability at the presence of modelling uncertainty remains under-explored. This paper investigates the stability properties of a class of decentralized VAC schemes under modelling uncertainty. Specifically, we consider large-scale, heterogeneous urban traffic networks characterised by nonlinear dynamics and concave macroscopic fundamental diagrams with bounded uncertainty between flow, density, and speed. In this context, we examine a broad class of decentralized VAC dynamics, described by general nonlinear forms. Using passivity theory, we derive scalable, locally verifiable conditions on the design of VAC schemes, that enable stability guarantees in the presence of modelling uncertainty. Several examples are presented to illustrate the applicability of the proposed design framework. Our analytical results are validated through numerical simulations on a 6 and a 20-region system, demonstrating their effectiveness and practical relevance.