Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations

This paper describes 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. Application areas 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 using an aerial robot). Motivated particularly by these examples, this paper focuses on problems where the precise occurrence times of the events are not known {\em a priori}, but statistics for their inter-arrival times are available. 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. The paper considers the case when one robot is tasked with optimizing the event observations in a balanced manner. We prove that this complex mobile sensor scheduling problem can be efficiently reduced to a quasi-convex optimization problem in one variable. Our result implies a linear time algorithm that computes the unique optimal schedule (a cyclic policy). If certain statistics are available, the problem can be solved in constant time. That is, the running time of the resulting algorithm is independent of the number of stations! This leads to constant- and logarithmic-time algorithms for online scenarios where new stations are added and some other existing one are removed from the problem on the fly. We demonstrate the performance of the proposed algorithm in simulations.