Optimal randomized surveillance patterns to detect intruders approaching a military installation

Abstract

This thesis addresses a two-person zero-sum game between an intruder and a defender of a military installation. The intruder attempts to penetrate the military installation by choosing one of its many entry points, each of which is monitored by a surveillance camera and may require a different amount of time to transit. Although the real-time video of each surveillance camera is fed to a surveillance room simultaneously, the defender has only one surveillance monitor and can monitor only one entry point at a time. We consider a discrete-time model such that the intruder will be detected if, during his travel time, the defender spends one time unit monitoring the entry point chosen by the intruder. The problem facing the defender is how to switch among entry points to monitor from one time unit to the next, in order to maximize the detection probability of the intruder. The intruder's goal is, of course, to infiltrate without being detected, and so he wishes to minimize this probability. We formulate the problem as a two-person zero-sum game, and develop a linear program to solve it. Numerical experiments provide insights into the design of such surveillance systems.