ON THE BEST LOCATION OF SIGNAL DETECTORS

An event may occur anywhere in a planar area or on a linear region suc h as a route. One or more detectors are to be located within this regi on with the objective of maximizing the smallest probability of the de tection of an event anywhere in the region. In other words, the minimu m protection in the region is to be maximized. The probability that an event is detected by a detector is a decreasing function of the dista nce. For example, the probability may decrease with some power (say, 2 ) of distance, or this decrease could be approximately exponential wit h distance. Two solution procedures are proposed for the problem on a line segment: a mathematical programming model and a specially designe d algorithm. The problem in an area is solved by a univariate search, a Demjanov-type algorithm, a mathematical programming model, and simul ated annealing. Computational experience is reported.