Priority Queues

Customers of different priorities are arriving at a counter in accordance with a Poisson process. The customers are served by a single server in order of priority and for each priority in order of arrival. Two cases are considered: (i) service with privileged interruptions and (ii) service without interruption. It is supposed that the service times are mutually independent random variables having a prescribed distribution for each priority and independent of the arrival times. In both cases (i) and (ii) a simple method is given for finding the Laplace-Stieltjes transform and the moments of the stationary distribution of the waiting time for each priority level.