An approximation for the busy period of the M/G/1 queue using a diffusion model

Daniel P. Heyman

24 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

A diffusion model for the M/G/1 queue due to D. P. Gaver is used to obtain an approximation for the density function of the busy period. The approximation has the same mean and variance as the exact density function, and can be given explicitly when the service time is constant, or has a negative exponential or gamma distribution, or is a mixture of these types.

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1968Diffusion approximations and models for certain congestion problems

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1996An operational calculus for probability distributions via Laplace transforms 1975On-Line and Adaptive Optimum Advertising Control by a Diffusion Approximation 2011Diffusion Approximation as a Modelling Tool 1979Approximation techniques in the solution of queueing problems 2001Busy Periods of Poisson Arrival Queues with Loss 1995Limits and Approximations for the Busy-Period Distribution in Single-Server Queues 2000A new approach to the busy period of the M/M/1 queue

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