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

Abstract

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.

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

“…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]. In contrast, the two-sided search problem is traditionally addressed by formulating the problem as a game-theory problem [24] [25].…”

Performance of Stochastically Intermittent Sensors in Detecting a Target Traveling between Two Areas

“…In a recent work [5] we considered the problem of searching for a target that travels between a hiding area and an operating area via multiple routes. By assuming certain behaviors of the moving target, we obtained analytic expressions for the mean time to detection and thereby were able to determine the optimal placement of m cookie-cutter sensors (i.e.…”