Cascading Waves of Fluctuation in Time-delay Multi-agent Rendezvous

We develop a framework to assess the risk of cascading failures when a team of agents aims to solve the distributed rendezvous problem in time in the presence of exogenous noise and communication time-delay. The notion of value-at-risk (VaR) measure is used to evaluate the risk of cascading failures (i.e., network-based waves of large fluctuations) when some agents have failed to rendezvous. Furthermore, an explicit formula is obtained to calculate the risk of higher-order cascading failures recursively. Finally, from a risk-aware design perspective, we report an evaluation of the most vulnerable sequence of agents in various communication graphs.