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In this work, we explore the so called N-model, which consists of 2 servers and 2 classes of external customers, both generated by Poisson inputs. When server 1 is occupied and there are waiting customers in queue of the first server, then class-1 customer jumps to server 2. We consider a non-preemptive service priority: a class-1 customer starts service in server 2, when a class-2 customer finishes his service. The purpose of this research is to verify the stability conditions of this model, to verify by simulation a monotonicity property: the idle stationary probability of the first server attains a minimum when the second server is saturated.