Analysis of a queueing system with autoregressive arrivals and nonpreemptive priority

The paper studies a single server queueing system with infinite capacity and with two arrival streams, one of which is Poisson and the other is batch Poisson. The customers from the first stream have nonpreemptive priority over the customers from the second. A feature of the system under study is autoregressive dependence of the sizes of the batches from the second arrival stream: the size of the $n$th batch is equal to the size of the $(n-1)$st batch with a fixed probability and is an independent random variable with complementary probability. Service times of the customers from each stream are supposed to be independent random variables with specified distributions. The main object of the study is the number of the customers from each stream in the system at an arbitrary moment. The relations derived make it possible to find Laplace transorm in time of probability generating function of the transient queue length and also a number of additional characteristics.