A two priority queue with crossover feedback

This paper considers the delay distributions in a two-class non-preemptive priority queue with crossover feedback. Specifically, there are two priority classes, and the Poisson arrival process for each class can be subdivided into two groups: one group which only requires service at the priority level to which it arrives, and another group which requires subsequent service after it feeds back to the other queue. Our main result is the determination of explicit expressions for the distribution of delay until final service commences for each of the four types of customers.