Computational Studies on Detecting a Diffusing Target in a Square Region  by a Stationary or Moving Searcher

Wang, Hongyun; Zhou, Hong

doi:10.4236/ajor.2015.52005

Cited by 2 publications

(1 citation statement)

References 18 publications

(11 reference statements)

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“…Fernando and Sritharan computed the non-detection probability of infinitely many diffusing Brownian targets by a moving searcher which traveled along a deterministic path with constant speed in the two-dimensional plane [20]. Wang and Zhou conducted numerical studies to calculate the non-detection probability of a randomly moving target by a stationary or moving searcher in a square search region [21]. They also considered the search problem where a target moves between a hiding area and an operating area via multiple pathways where the searchers are equipped with either cookie-cutter sensors [22] or stochastically intermittent sensors [23].…”

Section: Introductionmentioning

confidence: 99%

Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

Wang¹,

Zhou²

2016

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We revisit one of the classical search problems in which a diffusing target encounters a stationary searcher. Under the condition that the searcher's detection region is much smaller than the search region in which the target roams diffusively, we carry out an asymptotic analysis to derive the decay rate of the non-detection probability. We consider two different geometries of the search region: a disk and a square, respectively. We construct a unified asymptotic expression valid for both of these two cases. The unified asymptotic expression shows that the decay rate of the nondetection probability, to the leading order, is proportional to the diffusion constant, is inversely proportional to the search region, and is inversely proportional to the logarithm of the ratio of the search region to the searcher's detection region. Furthermore, the second term in the unified asymptotic expansion indicates that the decay rate of the non-detection probability for a square region is slightly smaller than that for a disk region of the same area. We also demonstrate that the asymptotic results are in good agreement with numerical solutions.

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Section: Introductionmentioning

confidence: 99%

Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

Wang¹,

Zhou²

2016

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Searching for a Target Traveling between a Hiding Area and an Operating Area over Multiple Routes

Wang¹,

Zhou²

2015

AJOR

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We consider the problem of searching for a target that moves between a hiding area and an operating area over multiple fixed routes. The search is carried out with one or more cookie-cutter sensors, which can detect the target instantly once the target comes within the detection radius of the sensor. In the hiding area, the target is shielded from being detected. The residence times of the target, respectively, in the hiding area and in the operating area, are exponentially distributed. These dwell times are mathematically described by Markov transition rates. The decision of which route the target will take on each travel to and back from the operating area is governed by a probability distribution. We study the mathematical formulation of this search problem and analytically solve for the mean time to detection. Based on the mean time to capture, we evaluate the performance of placing the searcher(s) to monitor various travel route(s) or to scan the operating area. The optimal search design is the one that minimizes the mean time to detection. We find that in many situations the optimal search design is not the one suggested by the straightforward intuition. Our analytical results can provide operational guidances to homeland security, military, and law enforcement applications.

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Computational Studies on Detecting a Diffusing Target in a Square Region by a Stationary or Moving Searcher

Cited by 2 publications

References 18 publications

Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

Non-Detection Probability of a Diffusing Target by a Stationary Searcher in a Large Region

Searching for a Target Traveling between a Hiding Area and an Operating Area over Multiple Routes

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