The dependence of optimal returns from multi-class queueing systems on their customer base

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.