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A Note on Convexity of the Expected Delay Cost in Single-Server Queues

Decision Sciences, London Business School, Regent’s Park, London, NW1 4SA United Kingdom
Department of Management Science and Engineering, Stanford University, Stanford, California 94305
kristin{at}london.edu
samchiu{at}stanford.edu

In this note, we show that the expected delay cost for a G/G/1 queue is not necessarily convex in the arrival rate as sometimes claimed in the literature. We can prove, however, that the total expected delay cost rate is convex in the arrival rate. This cost rate is often of interest when designing queueing systems.

Subject classifications: mathematics:convexity; queues:optimization.
History: Received January 2004; revision received April 2004; accepted April 2004.