Abstract

We consider the so-called N -model which contains two pools of servers and two classes of external customers following independent Poisson inputs. Service times are class-depend and, in each pool, are i.i.d. Pool 1 consists of N1 servers and pool 2 consists of one server. When all servers of pool 1 are occupied, and there are waiting customers in the queue of pool 1, then a class-1 customer jumps to server of pool 2, becoming a class-(1,2) customer. We consider a non-preemptive service priority: a class-(1,2) customer starts service in the server of pool 2, when an ongoing customer service, if any, is completed. The purpose of the research is to deduce explicit stationary distribution of number of customers at the 1st pool, and to verify stability conditions of the model. Moreover, we simulate a model with one server in the 1st pool, N1 = 1, in which class-1 customers jump to pool 2 provided the queue at pool 1 exceeds a positive threshold C. In this setting we verify by simulation that (i) for each fixed C, the stationary idle probability P0 of server 1 attains minimum when the 2nd server is always busy with class-2 customers (saturated regime) and (ii) P0 decreases as the threshold C increases.