Entropic Value-at-Risk for Inter-Vehicle Collision in Platoons: Network- and Delay-Induced Bounds on Risk Due to Extreme Events

Abstract

Safe operation of connected vehicle platoons under stochastic disturbances and time-delayed dynamics requires accurate quantification of rare but dangerous events, such as inter-vehicle collisions. We propose a rigorous framework for quantifying the risk of inter-vehicle collisions in connected vehicle platoons subject to time-delayed stochastic dynamics. We adopt the \emph{entropic value-at-risk} (EVaR) as a conservative metric to capture \emph{risk due to extreme events}, highlighting its advantages over conventional Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). By expressing the inter-vehicle distance covariance in terms of the Laplacian eigenvalues of the communication network, we derive \emph{network-and time-delay-induced bounds} on both the minimum inherent risk and the worst-case risk. Specifically, the algebraic connectivity dictates the maximum EVaR, while the largest Laplacian eigenvalue determines the minimum risk inherently induced by the network structure. Numerical simulations illustrate how network topology and time delay shape collision risk, offering actionable insights for the safe design of vehicle platoons operating under stochastic disturbances.