Selection of circulatory loops for patrol vehicles operating in a network

Many applications exist in which a vehicle or set of vehicles have the responsibility of patrolling and providing coverage over a wide area or network for the purpose of responding quickly to service requests generated randomly at demand points in the network. One of the decisions in the operation of such patrol vehicles is that of determining the home location or circulatory loop for free or idle vehicles. A vehicle is said to be idle if it is not responding or attending to a service request. Such home location can be a point, a set of points in a network, a circulatory loop, or a set of circulatory loops in the network. The actual number of home locations is system, fleet size, and analyst dependent. Whether a point or loop strategy is implemented, the specification of the home locations or loops is usually done with the objective of improving the response time of idle vehicles to service requests originating from demand stations. In cases where circulatory loop strategy is adopted, the problem is one of determining the best overall circulatory loop or loops that would improve the overall system response time. In a typical conventional or generalized network, several loops may exist. Unless a systematic procedure is developed, non-optimal loops could be selected. In this paper, methodologies for determining the best circulatory loops for patrol vehicles for a given problem scenario in both unidirectional and bidirectional networks are presented. The problem is modelled as a mathematical programming problem. Example problems are given to illustrate the application of the approach. The criterion for optimization is the minimization of the maximum system response time.