On optimal call admission control in a resource-sharing system

In this paper, we consider call admission control of multiple classes without waiting room. We use event-based dynamic programming for our model. We show that sometimes the customer classes can be ordered: if it is optimal to accept a class, then to accept a more profitable class is optimal too. We demonstrate submodularity of the minimum cost for the 2-classes problem and establish some properties of optimal policies. Then we formulate a fluid model that allows us to study the optimal control for the large-capacity case. We show that in the case of same service time distributions, the control problem can be reduced to a model with a one-dimensional (1-D) state space, and a trunk reservation policy is optimal. We present numerical examples that validate our results.