Risk of Collision and Detachment in Vehicle Platooning: Time-Delay–Induced Limitations and Tradeoffs

We quantify the value-at-risk of intervehicle collision and detachment for a class of platoons, in presence of communication time-delay and stochastic noise. Closed-form expressions for the risk measures are obtained as functions of Laplacian eigen-spectrum as well as their explicit approximations. We quantify several hard limits and fundamental tradeoffs among the risk measures, network connectivity, communication time-delay, and statistics of exogenous stochastic noise. Simultaneous presence of noise and time-delay in a platoon reveals an idiosyncratic behavior risk of collision and detachment, for instance, weakening (improving) network connectivity may result in lower (higher) levels of risk. We support our theoretical findings via multiple simulations.