A Diffusion Model Approximation for the GI/G/1 Queue in Heavy Traffic

Daniel P. Heyman

56 citations0/0 files storedBell System Technical Journal

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

For the single-server queue with renewal input, we obtain heavy traffic approximations for the time-dependent distributions of queue length and virtual delay by constructing approximating diffusion processes. These approximations are shown to agree with known limiting cases, and a comparison is made with results from a computer simulation.

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References

1961A Proof for the Queuing Formula: L = λ W 1952The theory of queues with a single server 1970Multiple channel queues in heavy traffic. I 1970Multiple channel queues in heavy traffic. II: sequences, networks, and batches 1968Diffusion approximations and models for certain congestion problems 1974Heavy Traffic Limit Theorems for Queues: A Survey 1968Queues with time-dependent arrival rates I—the transition through saturation 1964General Stochastic Processes in the Theory of Queues

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2012Interpolation approximations for queues in series 1982Refining diffusion approximations for queues 1981Optimal control of an M/G/1 queuing system with removable server via diffusion approximation 1978A Diffusion Approximation to the Multi-Server Queue 2013Classification of queueing models for a workstation with interruptions: a review 1995Diffusion approximation to a queueing system with time-dependent arrival and service rates

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