Analysis of a nonpreemptive priority queue with exponential timer and server vacations

We consider multi-class priority queues with nonpreemptive services controlled by an exponential timer and multiple vacations. By reducing this model to the priority model with Bernoulli schedule analyzed by Katayama (1997), we obtain the Laplace–Stieltjes transform for the sojourn time in the system for each priority class, assuming (i) constant service times or (ii) general service times with either 1-limited or exhaustive service, and provide recursive equations to evaluate its first two moments.