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On the marginal benefit of adding servers to G/GI/m queues

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R.R. Weber,
*Management Science* **26**(9) 946-951, 1980.

Abstract

The mean queueing time in a $G/GI/m$ queue is shown to be a nonincreasing and
convex function of the number of servers, $m$. This means that the marginal
decrease in mean queueing time brought about by the addition of two extra
servers is always less than twice the decrease brought about by the addition of
one server. As a consequence, a method of marginal analysis is optimal for
allocating a number of servers amongst several service facilities so as to
minimize the sum of the mean queueing times at the facilities.

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