The stochastic queue core problem on a tree

In this paper, an stochastic queue core problem on a tree, which seeks to find a core in an M/G/1 operating environment is investigated. Let T = (V,E) be a tree, an stochastic queue core of T is assumed to be a path P, for which the summation of the weighted distances from all vertices to the path as well as the average response time on the path is minimized. Some general properties of the stochastic queue core problem on the tree are presented, while an algorithm with $max\{o(n^2l), o(n^2log^2(n))\}$ is provided to find the queue l-core on the tree.