On the linear cooperative search technique for a lost target with multiple searchers (Q2113815)

Summary: We discuss the linear cooperative search model to detect a hidden and randomly located target on one of the \(n\)-intersected roads (real lines). The searching process starts from the origin with \(n\) searchers. Each one of these roads has one unit speed searcher. We get the expected value of the searching time until the \((n - 1)\) searchers return to the origin after the target has been detected by the other searcher. We obtain the optimal distances for these \(n\) searchers to get the optimal search strategy which minimises the expected time of return. An interesting case with numerical results is studied when the target's position has a truncated normal distribution.