On the Coordinated Search Problem on the Plane
Mohamed Abd Allah El-hadidy, Abd El-Moneim Anwar Mohamed, Hala Ali Fergany
Abstract
Two unit- speed searchers at (0,0) seek a randomly located target on the plane
accoirding to a known unsymmetric continous distribution. The objective is to
minimize the expected time for the searchers to return to (0,0) after one of them has
found the target. We find a necessary conditions which make the search strategy be
optimal when the target has a bivariate Balakrishnan skew--normal distribution. The
search strategy is derived using a dynamic programming algorithm. An example is
given to show the applications of this technique. The problem has applications to
parallel processing and to the optimal choice of drilling depths in the search for an
underground mineral.
DOUBLE-ACTING SEARCH FOR
A RANDOMLY MOVING TARGET
Abd-El-Moneim A.M. Teamah1, Hamdy M. Abou-Gabal2 §
1,2Department of Mathematics
Faculty of Science
Tanta University
Tanta, EGYPT
1e-mail: [email protected]
2e-mail:
[email protected]
Abstract: A target is assumed to move randomly according to a stochastic
process on a straight line. Two searchers S1 and S2 start looking for the
target, S1 starts looking for the target from some point ao and S2 starts from
some other point bo on the line to detect the target. Each of the searchers
moves continuously along the line in both directions from his starting point. In
this paper we show the existence of a search plan such that the expected value
of the first meeting time of the lost target is minimum
Searching For a Randomly Moving Target
Abd-Elmoneim A. M.Teamah
Assistant Professor in Mathematical statistics
Department of Mathematics, Faculty of Science
Tanta University, Tanta, Egypt
[email protected]
Abstract
This paper addressed the problem of searching for a randomly
moving target on one of two disjoint lines. One common measure of
effectiveness for the search process is the expected time of the search.
This type of search has been addressed for a case of a line .Here the
author calculated the expected value of the first meeting time of the target
and show the existence of a search plan which minimizes it
Existence of a periodic search strategy for a parabolic spiral
target motion in the plane
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Abd El-Moneim Anwar Mohamed,
Mohamed Abd Allah El-Hadidy
Abstract
This paper investigates a periodic search problem for a parabolic spiral moving target
in the plane in which any information of the target position is not always available to
the searcher. We have one searcher that starts searching for the target from (0, 0). The
problem is mathematically formulated as an allocation of searching effort which is the
expected value of the first meeting time between the searcher and the target. We study
the same method which is detailed on the real line by Mohamed et al. (Appl. Math.
Model. 7214:53–4:74, 50::) in the case of the plane to find the conditions from
which the expected value is finite.