Stochastic queue core problem with an efficient length on a tree network

In this paper, we consider a stochastic queue core (SQC) problem on a tree network, aiming to identify a path P , called the core, in an M/G/1 environment system.Let T be a tree network, the SQC problem on T involves finding a core P , with an optimal length, that minimizes the total weighted travel time from all vertices to the core as well as the average response time to the customer demands.We assume that a mobile server traverses the core to provide services to customers, while customers move to their nearest vertex on the core to receive service.Some general properties of the SQC problem on the tree network are represented.Then a polynomial time algorithm is proposed to solve this problem.