Risk of Cascading Failures in Multi-agent Rendezvous with Communication Time Delay

We develop a framework to assess the risk of cascading failures when a team of agents aims to rendezvous in time in the presence of exogenous noise and communication time-delay. The notion of value-at-risk (VaR) measure is adopted to quantify the risk of an agent failing to rendezvous with other agents when it is given that another agent has experienced a large fluctuation. It is shown that the risk of cascading failures depends on the Laplacian spectrum of the underlying communication graph, time-delay, and noise statistics. Furthermore, we exploit the structure of several standard graphs to show how the cascading risk behaves differently for various graph topologies. Finally, our theoretical results are supported by several simulation case studies.