The Design of a Layered Security System Using Imperfect Sensors and Response Units

This paper addresses the optimal design of a multi-layer security system for protecting borders or sensitive areas against intruders who may deploy decoys. The system comprises successive layers of imperfect sensors and a limited number of mobile response units. Intruders that evade detection or neutralization in one layer proceed to the next. Our objective is to minimize the overall probability of a threat escaping the entire system. We formulate a nonlinear integer programming model within a queuing-theoretic framework to jointly determine the optimal number of security layers and the allocation of sensors and response units across them. A simulated annealing heuristic is proposed to solve this complex optimization problem. Furthermore, we extend the model to analyze the impact of decoys—objects that trigger intentional false alarms—which strategically drain system resources and increase the evasion risk for genuine threats. Numerical experiments demonstrate that the optimized multi-layer configuration significantly reduces the final escape probability compared to a single-layer baseline, validating the efficacy of the proposed framework for enhancing security in resource-constrained environments.