Mathematical routing model based on nodes constraints in a distributed service network

In Distributed Service Network, the main concern of the user is mostly focused on the immediate response time of a call for service. The user evaluates the efficiency of a service network in terms of how long he or she has been waiting until a service unit arrives at the scene of a call. In same manner after dispatching, routing is another important problem, the objective of which is how to select an optimal path for the server so that resource could meet the demand as soon as possible. In this paper the mathematical model is proposed to minimize the expected response time.