The multivariate distributions of output streams in a queueing system with preemptive repeat priority

The paper studies a single server queuing system with $r$ types of customers, preemptive repeat priority, and an infinite number of positions in the queue. The arrival stream of customers of each type is a Poisson stream. Each type has its own generally distributed service time characteristics. The main result is the Laplace–Stieltjes transform of one- and two-dimensional stationary distribution functions of the interdeparture times for each type of customers. The analysis of the output process is carried out by the method of embedded Markov chains. As embedded times, successive moments of the end of service of the same type customers are selected. From a practical perspective, an accurate characterization of the interdeparture time process is necessary when studying open networks of queues.