Abstract
We present the cooperation between two searchers start at the origin to seek for the pipeline hole. The pipeline searched with random distances and velocities through the time by each searcher. There is no available information about the target position to the searchers all the time. We study this problem in the case of bounded asymmetric and unbounded symmetric hole distribution.Rather than finding the expected value of the time detection, we find the optimal search plan which minimizes this detection time. The effectiveness of this model is illustrated using a numerical example.
Highlights
The Linear search problem for a lost target either located or moved is often a time-critical issue, when the target is very important, e.g., searching for a bomb in the street
If the hole has a symmetric distribution about the origin, the expected value of the time to detect it is given by: E(Ω(φ))
The searchers search the pipeline with random distances and velocities through the time
Summary
The Linear search problem for a lost target either located or moved is often a time-critical issue, when the target is very important, e.g., searching for a bomb in the street. Obtaining the optimal search plan which minimizes the expected value of the first meeting time between the searcher and the target. A linear search method has been presented to find a Brownian target motion such as El-Rayes et al.[14], Mohamed et al.[15] and El-Hadidy [23]. They discussed the finiteness of finite and an optimal search plan. Beside that we determine the optimal search strategy that minimizes the expected value of the time for detecting this hole. The paper concludes with a discussion of the results and directions for the future research
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