Two Queues with Alternating Service and Switching Times

摘要

A system of two queues, attended by a single server who alternately serves one customer of each queue (if not empty) is considered. The server experiences switching times in his transition from one queue to the other. It is shown that the joint stationary queue-length distribution, at the instants at which the server becomes available to a queue, can be determined via transformation to a Riemann boundary value problem. The latter problem can be completely solved for general service and switching-time distributions. The stationary distributions of the waiting times at both queues, and of the cycle times of the server, are also derived. The results, particularly the extensive numerical data for moments of waiting times and cycle times, yield insight into the behavior of more general cyclic-service models as used to analyze polling systems.