Risk of Cascading Collisions in Network of Vehicles with Delayed Communication

TL;DR

This work develops an AV@R-based framework to quantify the risk of cascading collisions in vehicle platoons under time delays and input uncertainty. By deriving closed-form expressions for inter-vehicle distance statistics in the steady state and conditioning on observed failures, it yields tractable AV@R risks across general graphs and on symmetric topologies such as complete graphs, path graphs, and p-cycle graphs. The paper reveals fundamental limits on achievable cascading risk imposed by time delays and graph connectivity, and it provides practical insights for risk-aware design of communication topologies to mitigate cascading collisions. Case studies demonstrate how failure properties and topology choices influence risk profiles, offering guidance on where to strengthen or sparsify links to balance single-collision and cascading risks in real-world platooning. Overall, the framework enables safety-aware planning for large-scale networked vehicle systems with delays and stochastic disturbances.

Abstract

This paper establishes and explores a framework to analyze the risk of cascading failures in a platoon of autonomous vehicles, accounting for communication time-delays and input uncertainty. Our proposed framework yields closed-form expressions for cascading collisions, which we quantify using the coherent Average Value-at-Risk ($\AVAR$) to assess the cascading effect of vehicle collisions within the platoon. We investigate how factors such as network connectivity, system dynamics, communication delays, and uncertainty contribute to the emergence of cascading failures. Our findings are extended to standard communication graphs with symmetries, allowing us to evaluate the risk of cascading collisions from a platoon design perspective. Furthermore, by discovering the boundedness of the inter-vehicle distances, we reveal the best achievable risk of cascading collision with general graph topologies, which is further specified for special communication graph, such as the complete graph. Our theoretical results pave the way for the development of a safety-aware framework aimed at mitigating the risk of cascading collisions in vehicle platoons.

Figures (17)

• Figure 1: Schematics of platoon ensemble of autonomous vehicles. Speed and distance control is adjusted automatically with feedback laws using information communicated over a virtual network.
• Figure 2: Change of the set $C_{\delta}$ with different distributions of the inter-vehicle distance.
• Figure 3: The risk of cascading collision $\mathcal{A}^{i,j}_{\varepsilon}$ in a path graph. The x-axis denotes the vehicle number and the y-axis represents the risk value $\mathcal{A}^{i,j}_{\varepsilon}$. The second row shows the risk profile after adding an edge to the path graph. The existing collision is shown by the red hexagram and the case $\mathcal{A}^{i,j}_{\varepsilon} = \infty$ is shown by the yellow triangle.
• Figure 4: The above figure illustrates the concept of snapshots of multiple vehicle pairs within a platoon.
• Figure 5: The risk partition on the axis of $\kappa_\varepsilon = (\sqrt{2\pi} \varepsilon\exp(\iota_{\varepsilon}^2))^{-1}$.