Interception Strategy Based on Intermittent Information

A penetrator, p, attempts to cross a linear barrier patrolled by a searcher, S. S receives intermittent reports of P's position, P₁, P₂, …, but P knows only that S is somewhere on the barrier. After receiving report P₁, a time τ can elapse before the next report P₂ may reveal that S may be unable to intercept P even if he received continuous information thereafter. S attempts to select a position S (P₁) that maximizes τ, while P attempts to choose a course α that minimizes τ. If the searcher is faster than the penetrator (speed ratio λ > 1), values of α and S(P₁) that produce maximin τ are deduced. However, maximin τ < minimax τ, and P is obliged to use a mixed strategy in order to obtain the maximin. If the barrier is finite, contours of constant maximin τ are segments of conic sections. If λ < 1, S should modify the maximin τ strategy when P is close to the barrier. An indication is given of the frequency with which reports are needed as P approaches the barrier.