State Dependence in M/G/1 Server-Vacation Models

Carl M. Harris · William G. Marchal

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Advanced Queuing Theory Analysis Optimization and Search Problems Age of Information Optimization

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.

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1977Fundamentals of Queueing Theory.1984Matrix-Geometric Solutions to Stochastic Models 1986Queueing systems with vacations ? A survey 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1985Fundamentals of queueing theory (2nd ed.).1962A Waiting Line with Interrupted Service, Including Priorities 1975Utilization of Idle Time in an M / G /1 Queueing System 1986Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules

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1989Blocking Probability for M/G/1 Vacation Systems with Occupancy Level Dependent Schedules 2003Vacation models in discrete time 2004A two threshold vacation policy in multiserver queueing systems 1990Conditional and unconditional distributions forM/G/1 type queues with server vacations 2006A Quorum Queueing System with a Random Setup Time under N-policy and with Bernoulli Vacation Schedule 2003Stationary Distributions of GI/M/c Queue with PH Type Vacations

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