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On a property of the variance of the waiting time of a queue

Published online by Cambridge University Press:  14 July 2016

D. G. Tambouratzis
D. G. Tambouratzis*
Affiliation:
University of Manchester
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Extract

In this note, we consider a queueing system under any discipline which does not affect the distribution of the number of customers in the queue at any time. We shall show that the variance of the waiting time is a maximum when the queue discipline is “last come, first served”. This result complements that of Kingman [1] who showed that, under the same assumptions, 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 the order of their arrival.

Type
Short Communication
Information
Journal of Applied Probability , Volume 5 , Issue 3 , December 1968 , pp. 702 - 703
Copyright
Copyright © Applied Probability Trust 1968 

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References

[1] Kingman, J. F. C. (1962) The effect of queue discipline on waiting time variance. Proc. Camb. Phil. Soc. 58, 163–164.CrossRefGoogle Scholar