Abstract
We identify structured collections of multi-class queueing systems whose optimal return (a minimised cost) is a supermodular function of the set of customer classes allowed external access to the system. Our results extend considerably the range of systems for which such a claim can be made. The returns from such systems also exhibit a form of directional convexity when viewed as functions of a vector of arrival rates. Applications to load balancing problems are indicated.
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Dacre, M., Glazebrook, K. The Dependence of Optimal Returns from Multi-class Queueing Systems on Their Customer Base. Queueing Systems 40, 93–115 (2002). https://doi.org/10.1023/A:1017948530608
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DOI: https://doi.org/10.1023/A:1017948530608