A dynamic priority queue model for simultaneous service of two traffic types

We consider a priority queue with a dynamic, queue-length-threshold scheduling policy. Customers are classed into two types (type-1 and type-2), and the service order of the two classes depends on the queue length of the type-1 queue. The high priority ( type-2) class ( e. g., voice) is served until the low priority ( e. g., data) queue exceeds the threshold L, at which time service is given to the low priority class until its queue length decreases to L. The arrivals of the two classes follow independent Poisson processes, and the service time of each customer has an exponential distribution with parameter mu. We derive the balance equations in the steady state, and explicitly obtain the joint probability generating function for the queue lengths of the two customer classes. This gives the joint queue length distribution as an integral. We then obtain detailed asymptotic results for the joint distribution. In particular, we study the tail behavior. We also discuss heavy traffic diffusion approximations for this model.