Securing Gates of a Protected Area: A Hybrid Game and Queueing Theory Modeling Approach

Abstract

The prevention of malicious attacks on secured areas, such as airports and government installations, is a major concern everywhere as terror organizations increase their global reach. Typically, traffic in and out of such protected areas happens through well-defined gates. An attacker who wants to penetrate the area has to do it through one of the gates, and the defender who protects the area tries to prevent it by inspecting the incoming traffic. The trade-off faced by the defender is that increased inspections adversely affect the vast majority of innocent people passing through the gates by causing longer queues and discomfort. We combine game theory considerations with queueing theory analysis to address such situations. We formulate and analytically solve a defender–attacker game that takes place at multiple gates of a secured area. The gates are modeled as M/M/N queueing systems, where the “N”s are chosen strategically by the defender and may vary among the gates. Our analysis shows scenarios where even a limited number of guards is sufficient to deter would-be attackers and there is no need to assign additional guards even if they are available at no further cost.