Analysis of a Cyclic-service Tandem Queue with Multiple Server Vacations and Exhaustive Services

This paper presents an analysis of a cyclic-service tandem queue (M/C/l type queue) with exhaustive services and multiple server vacations, in which a single server takes repeated vacations until it finds at least one message in the first queue after emptying the queueing system. It is assumed that the vacation time is generally distributed, and switch-over times are zero. This paper analyzes queue-length distributions and message sojourn time distributions. By using the results of the two-stage tandem-queue analysis and the decomposition property in vacation models, some explicit formulas are derived for the mean total sojourn time in the multi-stage tandem queue and the mean waiting time in the first stage. These results are applicable to the performance analysis for message processing in packet switching systems.