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

TL;DR

The paper addresses stability of decentralized vehicular admission control in large urban networks with uncertain, nonlinear macroscopic fundamental diagrams. It develops a passivity-based framework that yields scalable, locally verifiable stability conditions for a broad class of VAC dynamics, enabling heterogeneity across regions. Five VAC dynamics examples are shown to satisfy the conditions, and extensive simulations on 6- and 20-region networks demonstrate robust stabilization under modelling uncertainty and driver non-adherence, including scenarios with temporary control disruptions. The results offer a practical, distributed design approach that preserves stability without global recalibration, supporting scalable deployment in real urban networks.

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.

Figures (17)

• Figure 1: Predecessor-successor connectivity example for a vehicular network with four regions. Left-to-right: Network topology, predecessor-successor sets, node connectivity via directed edges.
• Figure 2: General form of region $i$ total inter-regional traffic flow $g_i(\rho_i)$ [veh/h], approximated by a nonlinear macroscopic fundamental diagram (MFD) area, due to flow variation and uncertaintiesMENELAOU2023.
• Figure 3: 6-region network topology and MFD characteristics.
• Figure 4: Admitted demand $[{\text{veh}}/{\text{h}}]$. Case-1: blue line. Case-2: black dotted line.
• Figure 5: Network density $[{\text{veh}}/{\text{km}}]$. The VAC schemes drive the solutions at the reference set-points even from the congested region and despite control authority disruptions. Case-1: blue line. Case-2: black dotted line.

Theorems & Definitions (17)

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