分散环境中的鲁棒巡逻
Robust Patrol in a Dispersed Environment
浏览论文内容
中文总结 AI 辅助
针对分散环境中需最小化攻击者未被检测时间的巡逻问题，提出两种基于常见巡逻实践的循环模式及对应算法，验证了最优策略依赖于问题结构与参数。
中文摘要 AI 辅助
我们考虑一个巡逻问题：一名巡逻人员在多个地理上分散的地点之间移动，以检测随时间到达的攻击者。一旦巡逻人员到达某个地点，他们可以花费任意时长搜索该地点的攻击者，并以与地点相关的瞬时检测率检测到该地点的攻击者，之后再移动到其他地点。巡逻人员的目标是无论攻击发生在何处、何时，都将攻击者未被检测到而停留于某个地点的期望时间降至最低。在行进时间可忽略不计的特殊情况下，我们阐明了一种最优循环策略，其中巡逻人员持续将固定比例的精力分配到每个地点。当行进时间不可忽略时，该巡逻问题会变得极具挑战性。我们分别基于 perimeter patrol（ perimeter 巡逻）和 border patrol（边界巡逻）的常见巡逻实践，引入两种循环巡逻模式，并推导了两种情况下检测攻击的期望时间公式。我们还提供了一种算法，用于寻找这两种情况下的最优搜索时间参数。我们给出了几个这些循环模式表现良好的示例，并通过数值验证表明，最优巡逻策略高度依赖于每个巡逻问题的结构和参数。
英文摘要
We consider a patrol problem in which a patroller moves among several geographically dispersed locations to detect attackers that arrive over time. Once the patroller arrives at a location, they can spend any amount of time searching for attackers at that location---and detect an attacker there with some location-dependent instantaneous detection rate---before moving to a different location. The objective of the patroller is to minimize the expected time an attacker stays undetected at a location, regardless of where and when the attack occurs. In the special case where travel times are negligible, we elucidate an optimal cyclic policy in which the patroller allocates a fixed fraction of their effort to each location continuously. The patrol problem becomes significantly more challenging when travel times cannot be ignored. We introduce two types of cyclic patrol patterns based on common patrol practice for perimeter patrol and border patrol, respectively, and derive formulae for the expected time to detect an attack in both cases. We also provide an algorithm for finding the best search time parameters in both of these cases. We give several examples where these cycle types perform well and numerically demonstrate that the optimal patrol policy depends highly on the structure and parameters of each patrol problem.
