N,n-Preemptive-Priority M/G/1 Queues with Finite and Infinite Buffers

Abstract

In this paper, we analyze an M/G/1 priority queueing model with finite and infinite buffers under the $\left(N,n\right)$-preemptive priority discipline, under which preemption decisions are made based on the number of high-priority customers. This priority queueing model can be used for the performance analysis of communication systems accommodating delay- and loss-sensitive packets simultaneously. To analyze the proposed model, we extend the method of delay cycle analysis and develop a queue length version of it for finite-buffer queues. Throughout our analysis, we demonstrate that by the proposed method the analysis of the complex priority queueing model can be reduced to that of simple delay cycles, so two different preemption modes of the queueing model can be dealt with in a unified way. The numerical study reveals that adjusting the decision variables $N$ and $n$ allows us to fine-tune system performance for different classes of customers, and $N$ operates as a primary control variable, regardless of the preemption mode and service-time distributions.