Stability of a two-pool N-model with preemptive-resume priority

Abstract

The regenerative methodology is applied to find stability conditions of the so-called N-model which consists of two pools of the interacting servers with two classes of external customers following a renewal input. Service times are assumed to be pool-dependent and, in each pool, are i.i.d. with a general distribution. If the queue size in pool 1 exceeds a given threshold, then a class-1 customer jumps to pool 2 and becomes class-(1,2) customer with the preemptive-resume priority. The stability analysis of this model has been developed in [5] by a modified fluid approach. In addition to the results obtained in work [5], we find the conditions when the 1st pool is stable solely, and when the 1st pool is stable, while the 2nd pool is unstable.