On the Sequential Search for Spatially-Distributed Events
Arnold I. Barnett, John Mazzarino · SIAM Journal on Algebraic and Discrete Methods · 1980
Events arise at two points according to independent Poisson processes; their durations are independent and identically distributed random variables. An observer can make visits to the two points, and, on any particular visit to either point, can detect all events then going on there. There is a “dead time” associated with travel from one point to the other. The problem is: What should the observer’s visiting strategy be if his goal is to maximize the steady-state fraction of events he observes at least once? We prove a series of theorems about an optimal search strategy that ultimately provide the basis of an algorithm shown to converge to that strategy.