Risk of Cascading Collisions in Network of Vehicles with Delayed Communication

This work explores cascading failures in networked control systems by employing a platoon of vehicles that exchange information over a time-delayed communication graph as a model. We study the roles of network connectivity, system dynamics, communication time-delay, and uncertainty in the emergence of these failure phenomena. Our results yield closed-form expressions for the average value-at-risk (AV@R), which we utilize as a coherent risk measure to quantify the cascading effect of vehicle collisions within a platoon. These findings are further extended with several standard communication graphs with symmetries to reveal the impact of graph design parameters on the risk of cascading collisions. By presenting the boundedness of the steady-state statistics of the inter-vehicle distances, we present 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 findings pave the way for the development of a robust framework designed to mitigate the risk of cascading collisions in vehicle platoons by exploring how platoon reacts to the various existing failures and the change of communication links.