On the Additional Delay in an M/G/1 Queue with Generalized Vacations and Exhaustive Service

Abstract

We analyze an M/G/1 queue with generalized vacations and exhaustive service. This system has been shown to possess a stochastic decomposition property. That is, the customer waiting time in this system is distributed as the sum of the waiting time in a regular M/G/1 queue with no vacations and the additional delay due to vacations. In this paper, a general formula for the additional delay is derived for a wide class of vacation policies. The formula is also extended to cases with multiple types of vacations. Using these new formulas, existing results for certain vacation models as well as head-of-line priority queues are easily rederived and unified. More importantly, they enable us to obtain the waiting times for many complex vacation policies, which would otherwise be difficult to analyze. These new results are also applicable to other related queueing models, if they conform with the basic model considered in this paper.