Applied Mathematics & Information Sciences

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A lost target is a random walker on one of n disjoint lines, and the purpose is to detect the target as fast as possible. On each line there are two searchers starting the search from the origin of their line, where they follow the so called coordinate search. One common measure of effectiveness for the search process is the expected time of search. This type of search has been addressed and solved in the literature for the case where the target is located. In this paper, we introduce a new model of search and prove that the expected value of the first meeting time between one of the searchers and the lost target is finite. Also, we show the existence of the optimal search plan which minimizes the expected value. An application is also given to illustrate our results.

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