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

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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