Performance analysis and optimization of a cyclic-service tandem queueing system with multi-class customers

Abstract

This paper analyzes a special single-server tandem queueing system with feedback, which appears in call processing for multi-class calls (tasks) in telecommunication systems. Explicit expressions are derived for joint queue-length generating functions and the mean total sojourn time spent by a call (task) in the tandem queueing system. Using the interchange argument and the extended Kleinrock's conservation law, an optimal task scheduling strategy (called as the K/ h rule) is obtained to minimize a cost function defined by the individual mean total sojourn times of multi-class tasks.