On a property of the variance of the waiting time of a queue
Journal of Applied Probability1968Vol. 5(3), pp. 702–703
Citations Over TimeTop 11% of 1968 papers
Abstract
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.
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