A Diffusion Approximation to the Multi-Server Queue

Exact solutions to queueing problems with customer interarrival times and customer service times drawn from arbitrary (generalized) distributions have not been found. We are, therefore, much interested in good quality approximate solutions to such problems. This paper presents a methodology for obta...

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Bibliographic Details
Published in:Management science 1978-01, Vol.24 (5), p.522-529
Main Authors: Halachmi, Baruch, Franta, W. R
Format: Article
Language:English
Subjects:
Approximation
Computer systems
Customer services
Decision making models
Estimation methods
Management science
Network servers
Point estimators
Servers
Stochastic processes
Traffic
Traffic estimation
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Summary:Exact solutions to queueing problems with customer interarrival times and customer service times drawn from arbitrary (generalized) distributions have not been found. We are, therefore, much interested in good quality approximate solutions to such problems. This paper presents a methodology for obtaining (approximately) the distribution of the number of customers in a multiserver queue for which both the customer interarnval and customer service times are drawn from arbitrary distributions. The approximation is based on the theory of diffusion, depends only on the means and variances of the interarnval and service time distributions, and as the numeric examples attest is of very good quality when the queueing system is heavily loaded. The approximate solution is obtained via a very simple computational procedure, so that good quality approximate solutions to such problems can be easily produced.
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.24.5.522