A model of two-phase priority service with interrupts in the first phase

In the two-phase service system the input is an arbitrary number of Poisson priority customer flows. The service time in the first phase is distributed by an arbitrary law and in the second phase, by an exponential law. In the first phase nonpriority customer service may be interrupted to be reserviced later. Laplace-Stieltjes transforms are obtained of the probability that the system is not busy, of the busy period distribution functions, and of the virtual queueing time.