On the approximations to the single server queue

Jeyaveerasingam George Shanthikumar · John A. Buzacott

84 citations0/0 files storedInternational Journal of Production Research

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Advanced Queuing Theory Analysis Probability and Statistical Research Healthcare Operations and Scheduling Optimization

Abstract

In this article some approximations for the mean number in the single server queueing system are presented and compared. Based on numerical comparison a guide is provided to select the appropriate approximation(s) for different ranges, of the squared coefficient of variation of the inter-arrival and service time distributions. Two approximations for the distribution of the number in the system are given and the better is chosen.

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References

1952The theory of queues with a single server 1974Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions 1962Some Inequalities for the Queue GI/G/1 1968Some Inequalities in Queuing 1974Accuracy of the Diffusion Approximation for Some Queuing Systems

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1989Numerical Solutions of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI/G/1 Queue 1984On Approximations for Queues, I: Extremal Distributions 1993An approximation for the mean response time for shortest queue routing with general interarrival and service times 1988A Maximum Entropy Analysis of the G/G/1 Queue at Equilibrium 2011Coordination in a two-stage capacitated supply chain with multiple suppliers 1996A general approximation for the single product lot sizing model with queueing delays 2007Practical Extensions to Cycle Time Approximations for the $G/G/m$-Queue With Applications 1989Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues

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