Heavy traffic analysis of a multi-class loss link with preemption

Preemption policies are widely used in many contexts to provide higher quality of service (QoS) to high priority traffic during congestion by preempting low priority traffic. Although there is extensive work in the queueing literature on the performance of multi-class loss systems, there is little work on the performance of preemption models. In this paper we employ heavy traffic results from queueing theory for the blocking probability on a single-class loss link to obtain expressions for preemption probabilities in a multi-class loss link. In particular, we consider the case of L classes where class l may preempt if necessary any calls of classes l+1, L, and may in turn be preempted by any calls of class 1, l-1. We characterize the probabilities of a class l call causing preemption of an admitted lower priority call upon its arrival, and of a class l call being preempted by a higher priority call.