Preemption control of multi-class loss networks

This thesis addresses the analysis and optimization of preemption in multi-class loss networks. Preemption, admission control and rate adaptation, are control mechanisms that enable loss network operators to provide quality of service (QoS) guarantees for admitted calls. This research includes two parts: i) performance characterization of a two parallel link loss network servicing multiple classes of calls under a speci c preemption and admission policy, and ii) preemption and admission control policy analysis for a single loss link servicing two classes of calls.In Part I, we consider a two parallel link multi-class loss network, where a call may preempt, if necessary, any calls with lower priorities and may in turn be preempted by any calls with higher priorities. The preemption policy permits both preemption from a preferred link to a backup link if possible, and eviction from either link if necessary. Our contributions in this part include: i) characterizing the rates of each class causing preemption of active lower priority calls, and therates of each class being preempted by an arriving higher priority call in Erlang-B functions when all classes share a common service rate; ii) simple expressions of these preemption rates through uniform asymptotic approximation; and iii) asymptotic approximation of these preemption rates using nearly completely decomposable (NCD) Markov chain techniques when classes have individual service rates.After analyzing the performance of a typical policy, we would also like to study various policies. In Part II, we analyze di erent preemption and admission control policies for a two-class loss link where per-class revenue is earned per unit time for each active call, and an instantaneous preemption cost is incurred whenever the preemption mechanism is employed. Our contributions in this part include: i) showing that under reasonable reward models, if we always preempt when the link is full, then it is better not to preempt at non-full states; ii) a su cient condition under which the average revenue of optimal preemption policy without admission control exceeds that of optimal admission control policy without preemption, which are established via policy improvement theorems fromstochastic dynamic programming.