A performance analysis of a discrete-time priority queueing system with correlated arrivals

We present performance analysis of a discrete-time system with two priority queues and correlated arrivals. The arrival process to each priority queue consists of the superposition of the traffic generated by independent binary Markov sources with the arrivals to the two queues being independent of one another. The first step is the determination of the busy period of a queue with correlated arrivals. Next, the joint probability generating function of the two queue lengths is derived and the unknown boundary function is determined using the busy period of the high-priority queue. The next step is to determine closed form expressions for the mean and variance of the queue lengths. Finally, the results are extended to multiple priority queueing systems with multiple types of traffic sources. Numerical results that demonstrate the impact of the correlated arrival process in the system are presented.