Waiting Times for M/G/1 Queues with Service-Time-Dependent Server Vacations

摘要

This paper shows how to determine the stationary distribution of the virtual wait in M/G/1 queues with either one at-a-time or exhaustive server vacations. Each vacation time may depend on the immediately preceding service time or on whether the server finds the system empty after returning from vacation. In this way, it is possible to model situations such as long service times followed by short vacations, and vice versa. The method of analysis employs level-crossing theory. Detailed examples are given for various cases of service and vacation-time distributions. Keywords: Applied probability; Computational analysis; Computational probability; Markov chains; Numerical methods; Probability; Queues; Stochastic models; Waiting times. (jhd)