Preemption rates for a parallel link loss network

We consider a two parallel link network supporting KK call classes, where a class kk call may preempt if necessary any calls of classes k+1,…,Kk+1,…,K, and may in turn be preempted by any calls of class 1,…,k−11,…,k−1. The two links are a (preferred) primary link (PL) and a backup link (BL). The preemption policy permits both preemption from the PL to the BL (a transfer) if possible, and eviction from either link if necessary. We characterize the rates of an arriving class kk call causing preemption of an active lower priority call, and of an active class kk call being preempted by an arriving higher priority call. When all classes share a common service rate, we express the preemption rates for each class in terms of the Erlang-B blocking probability equation. Simple expressions for the preemption rates are obtained in the heavy traffic limit. When classes have individual service rates, we approximate the preemption rates for each class using nearly completely decomposable (NCD) Markov chain techniques. The accuracy of the approximation improves with increasing timescale separation between classes.