The Limit Distribution of the Queue Length in a Priority System with Autoregressive Arrivals Under the Heavy Traffic Condition

In this paper a one-line queueing system with two priority classes, relative priority, Poissonian input flow with random intensity and infinite number of places in queue for waiting is considered. The current intensity value is taken at the beginning of the time reckoned for the arrival of the next requirement. Successive values of the flow intensity form a Markov chain of a special kind. This input flow structure allows to take in consideration not only mathematical expectation and variance, but also correlation between interval of two next arrivals. The main result is the limit distribution of the queue length for the least priority class, it is obtained in an explicit form. Also, analytical expressions for the density function, mathematical expectation and variance are given. Numerical examples, which show difference among limit distributions (for different parameters) for studied cases are provided.