Delay analysis of a two-class priority queue with external arrivals and correlated arrivals from another node

Calculation of the delay distribution of (low-priority) customers in priority queues is difficult, especially when the arrival process is correlated. In this paper, we find the generating functions of the delays of high- and low-priority customers in a discrete-time queue where the arrivals are generated by a superposition of two processes, an independent one and a correlated one that can bring an extra customer in the buffer during a slot. The latter process can be seen as a simplified model for the output process of another priority queue. As a consequence, our results can be used to estimate the delay in the second stage of a tandem queueing system with an extra exogenous arrival process. A tandem priority queue is not of product-form type and its analysis is known to be a hard problem. This paper can lead to a first approximate analysis that can later be extended to incorporate the correlation in the output process of a priority queue more accurately.