Spatial Queueing Analysis of an Interdiction System to Protect Cities from a Nuclear Terrorist Attack

We formulate and analyze a spatial queueing model concerning a terrorist who is attempting to drive a nuclear or radiological weapon toward a target in a city center. In our model, imperfect radiation sensors form a circular wall around the periphery of the city, and vehicles setting off sensor alarms (representing a terrorist or a nuisance alarm) arrive randomly at the perimeter of a circle (representing the wall of sensors) and drive toward the center of the circle. Interdiction vehicles, one in each wedge of the circle, chase the alarm-generating vehicles. We derive an accurate mathematical expression for the mean damage inflicted by a terrorist in this system in terms of the arrival rate of alarm-generating vehicles and the number of interdiction vehicles. Our results suggest that detection-interdiction systems using current technology are capable of mitigating the damage from a nuclear weapon made of plutonium, but not one made of uranium or a radiological weapon.