A target is assumed to move randomly on one of two disjoint lines 1 L and 2 L according to a stochastic process ( ) { } , S t t + ∈ ℜ . We have two searchers start looking for the lost target from some points on the two lines separately. Each of the searchers moves continuously along his line in both directions of his starting point. When the target is valuable as a person lost on one of disjoint roads, or is serious as a car filled with explosives which moves randomly in one of disjoint roads, in these cases the search effort must be unrestricted and then we can use more than one searcher. In this paper we show the existence of a search plan such that the expected value of the first meeting time between the target and one of the two searchers is minimum.

We consider the coordinated search problem ,where the lost target is located on one of the two intersection lines excipt the point of intersection of the lines ,and the the point of intersection lines is the origin .We have four searchers who start together from the origin , where every two searchers aim to detect the lost target on their line .The position of the target is a random variable , which has unsymmetric distribution. In this paper we will find the expected value of the first meeting time for the searchers to return to starting point (the origin) after one of them has found the target and the optimal search plan to find it. We show that the previous studies are special cases from our studies.

This paper presents the search technique for a lost target. A lost target is random walker on one of two intersected real lines, and the purpose is to detect the target as fast as possible. We have four searchers start from the point of intersection, they follow the so called Quasi-Coordinated search plan. The expected value of the first meeting time between one of the searchers and the target is investigated, also we show the existence of the optimal search strategy which minimizes this first meeting time. IntroductionThe search problem for a randomly moving target is very interesting because it may arise in many real world situations such as searching for lost persons on roads, the cancer cells in the human body and missing black box of a plane crash in the depth of the sea or ocean, also searching for a gold mine underground, Landmines and navy mines, a faulty unit in a large linear system such as electrical power lines, telephone lines, and mining system, and so on (see [1], [2],[3], [4] and [5]).The aim of search, in many cases (see [6], and [7]) is to calculate the expected cost of detecting the target and is to obtain the search plan, which minimizes this expected cost. In the case of linear search for stationary or randomly moving targets many studies are made (see [8]-[26]).The coordinated search method is one of the famous search methods which consider the searchers starting together from the origin and moving, seeking for 350Applied Mathematics a random walk target. Therefore, coordinated search technique is one of many techniques which studied previously on the line where the located targets have symmetric and unsymmetric distributions (see [27], [28], [29] and [30]), this technique has been illustrated on the circle with a known radius and the target equally likely to be anywhere on its circumference (see [31]), also this technique has been discussed in the plane when the located target has symmetric and asymmetric distribution (see [32] and [33]). There is obviously some similarity