Discrete-time priority queueing systems with two-state Markov modulated arrival processes

A class of discrete-time priority queueing systems with Markov modulated arrivals is considered. In these systems, N queues are served by a single server according to priorities that are preassigned to the queues. Packet arrivals are modeled as discrete-time batch processes with a distribution that depends on the state of an independent common two-state Markov chain. This allows coverage of a wide range of applications in computer and communication systems when the parameters of the arrival processes are not fixed in time but vary according to the state of the underlying Markov chain. The steady-state joint generating functions of the queue length distributions of this class of systems are derived. From these, moments of the queue lengths as well as average time delays can be obtained. A numerical example provides some insight into the behavior of such systems. Also, the effect of the transition rate between the states of the modulating Markov chain on the average time delay in the system is investigated for different patterns of loads on the queues of the system