Quasi-Coordinate Search for a Randomly Moving Target

In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their search from the origin on the first line and other two searchers begin their search from the origin on the second line. But the motion of the two searchers on the first line is independent from the motion of the other two searchers on the second line. Here we introduce a model of search plan and investigate the expected value of the first meeting time between one of the searchers and the lost target. Also, we prove the existence of a search plan which minimizes the expected value of the first meeting time between one of the searchers and the target.