Dynamics of the M/G/1 Vacation Model

Julian Keilson · L. D. Servi

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Advanced Queuing Theory Analysis Reliability and Maintenance Optimization Age of Information Optimization

Abstract

An M/G/1 processor schedule attends to auxiliary vacation tasks iteratively. We describe the influence of these tasks on the dynamic behavior of the system and obtain, for several cases of interest, the relaxation time of the vacation system required to validate steady-state approximations. Finally, we find the distribution of the duration of the primary busy period, the vacation busy period, and an associated cycle time.

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1963Introduction to the Theory of Queues.1983The Single Server Queue 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1986Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules 1972Queues with Periodic Service and Changeover Time 1970Queues Served in Cyclic Order: Waiting Times 1969Queues Served in Cyclic Order 1984M/G/1/N Queue with Vacation Time and Exhaustive Service Discipline

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2006Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy 1990Time-dependent analysis of M/G/1 vacation models with exhaustive service 1986Queueing models of secondary storage devices 1992Time-dependent process of M/G/1 vacation models with exhaustive service 2006A two phase batch arrival retrial queueing system with Bernoulli vacation schedule 1988The busy period of the migi1 vacation model with a bernoulli schedule

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