Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations

This paper is concerned with a novel mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of events that can not be easily forecast. Prominent examples range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion in the Boston area using an aerial robot). Motivated by these examples, this paper focuses on problems where the precise occurrence time of the events is not known {\em a priori}, but some statistics for their inter-arrival times are available from past observations. The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. Provided with only one robot, it is crucial to optimize these objectives in a balanced way, so that they are optimized at each station simultaneously. Our main theoretical result is that this complex mobile sensor scheduling problem can be reduced to a convex program, which can be solved in polynomial time. In other words, a globally optimal solution can be computed in time that is polynomial in the number of locations. We also provide computational experiments that validate our theoretical results.