Models of sensor operations for border surveillance

Abstract

This paper is motivated by the diverse array of border threats, ranging from terrorists to arms dealers and human traffickers. We consider a moving sensor that patrols a certain section of a border with the objective to detect infiltrators who attempt to penetrate that section. Infiltrators arrive according to a Poisson process along the border with a specified distribution of arrival location, and disappear a random amount of time after their arrival. The measures of effectiveness are the target (infiltrator) detection rate and the time elapsed from target arrival to target detection. We study two types of sensor trajectories that have constant endpoints, are periodic, and maintain constant speed: (1) a sensor that jumps instantaneously from the endpoint back to the starting-point, and (2) a sensor that moves continuously back and forth. The controlled parameters (decision variables) are the starting and end points of the patrolled sector and the velocity of the sensor. General properties of these trajectories are investigated.

Optimizing periodic patrols against short attacks on the line and other networks

“…The case of a thick infiltrator has been considered by Baston and Kikuta (2009). If there are many infiltrators and they arrive in a Poisson manner, the analysis is given by Szechtman et al (2008). Multiple infiltrators are also considered by Zoroa et al (2012) where the infiltration is through a circular rather than a linear boundary.…”

Timely exposure of a secret project: Which activities to monitor?

“…Atkinson and Wein (2010) examine how a government should allocate its resources over the inspection of terror and criminal networks to exploit the finding of Smith, Damphousse, and Roberts (2006) that, prior to an attack, terrorists frequently participate in crimes such as theft or procuring explosives. Other articles address problems such as predicting the number of undetected terror threats (Kaplan, 2010), estimating the duration of a terrorist plot (Kaplan, 2012a), locating terrorists (Alpern & Lidbetter, 2013;Atkinson, Kress, & Lange, 2016), processing intelligence (Dimitrov, Kress, & Nevo, 2016;Lin, Kress, & Szechtman, 2009), patrolling an area (Lin, Atkinson, & Glazebrook, 2014;Papadaki, Alpern, Lidbetter, & Morton, 2016;Szechtman, Kress, Lin, & Cfir, 2008), and predicting the goal of a suspected terrorist (Tsitsiklis & Xu, 2018). In particular, Atkinson et al (2016) consider a searcher who, based on a stream of unreliable intelligence about a target's location, needs to decide whether to engage or to wait for more information.…”

Optimal Configurations in Coverage Control with Polynomial Costs

“…Applications of this work are envisioned in border patrol wherein unmanned vehicles are placed to optimally intercept moving targets that cross a region under surveillance (cf. Girard et al [2004], Szechtman et al [2008]).…”