Start-up class models in multiple-class queues with N-policy

In this paper, we consider multiple-class queueing systems with N-policy in which the idle server starts service as soon as the number of customers in the ‘start-up class’ reaches threshold N. We consider the cases of first come first served and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behaviour of such systems.