The stochastic queue core problem on a tree

TL;DR

This paper investigates a stochastic queue core problem on trees, aiming to find a path minimizing weighted distances and response times in an M/G/1 environment, and provides an efficient algorithm for this optimization.

Contribution

It introduces the stochastic queue core problem on trees, analyzes its properties, and develops a computationally efficient algorithm to identify the optimal core path.

Findings

Properties of the stochastic queue core problem are established.

An algorithm with complexity $maxig\{o(n^2l), o(n^2log^2(n))ig\}$ is proposed.

The algorithm effectively finds the queue l-core on a tree.

Abstract

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.