Resource sharing for book-ahead and instantaneous-request calls using a CLT approximation

This paper extends the admission control algorithm for book-ahead and instantaneous-request calls proposed by Greenberg, Srikant and Whitt (1997) to cover multiple classes of instantaneous-request calls, each with their own traffic characteristics and their own performance requirements. As before, book-ahead calls specify their starting and finishing times, and are assumed to book far ahead relative to the holding times of the instantaneous-request calls. The book-ahead calls may be constrained by an upper-limit on the capacity that can be reserved for them. Instantaneous-request calls are admitted if the probability of interruption (or some other form of service degradation in response to the conflict) for that call is below a threshold, but now this threshold can be class-dependent, and now the interrupt probability is calculated by a normal approximation based on the central limit theorem. Simulation experiments show that the normal approximation performs as well as the previous detailed calculation in single-class examples, and that the normal approximation can be applied to multi-class examples.