State Dependence in <i>M</i>/<i>G</i>/1 Server-Vacation Models

Abstract

This paper examines a generalization of the exhaustive and one-at-a-time-discipline M/G/1 server vacation models. This alternative model is viewed as a state-dependent (nonvacation) M/G/1 queue in which the original service times are extended to include a (possibly zero length) state-dependent vacation after each service. Such a vacation policy permits greater flexibility in modeling real problems, and does, in fact, subsume most prior M/G/1 approaches. This device reveals a fundamental decomposition somewhat like that previously established for the classical vacation disciplines. In addition, necessary and sufficient conditions for system ergodicity are established for the state-dependent vacation policy, and some comments are offered on computations.