We consider general queueing models dealing with multiple classes of customers and address the question under what conditions and in what (stochastic) sense the marginal increase in various performance measures, resulting from the addition of a new class of customers to an existing system, is larger than if the same class were added to a system dealing with only a subset of its current customer base.
Our results enhance our understanding of the dependence of various performance measures with respect to the composition of the customer base. In addition they translate readily into convexity results in an (appropriately defined) arrival rate.
Federgruen, Awi, and H. Groenevelt. "The impact of the composition of the customer base in general queueing models." Journal of Applied Probability 24, no. 3 (September 1987): 709-724.
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