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The general N server finite queue

Published online by Cambridge University Press:  14 July 2016

Asha Seth Kapadia
Asha Seth Kapadia*
Affiliation:
Quantitative Management Science, University of Houston
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Extract

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold:

  1. (a) no server sits idle while there are customers waiting to be served;

  2. (b) the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one);

he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 828 - 834
Copyright
Copyright © Applied Probability Trust 1971 

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References

Godini, G. (1965) A queueing problem with heterogeneous service. Stud. Cerc. Mat. 17, 765–775.Google Scholar
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Moder, J. J. (1962) Queueing with fixed and variable channels. Operat. Res. 10, 218–231.Google Scholar
Tambouratzis, D. G. (1968) On a property of the variance of the waiting time of a queue. J. Appl. Prob. 5, 702–703.Google Scholar