Technical Note—A Convexity Result for a Class of GI/G/1 Queueing Systems

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Abstract
This note gives a sufficient condition under which the expected number of customers in a GI/G/1/FCFS queueing system will be a convex function of the service rate. Although the result is intuitively appealing and is usually accepted without proof as a “folk theorem” of queueing theory, there are systems for which it does not hold.