Discrete-time Priority Queues with Two-state Markov Modulated Arrivals

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 to cover a wide range of applications in computer and communication systems when the parameters of the arrival processes are not xed in time, but vary according to the state of the underlying Markov chain. We derive the steady-state joint generating functions of the queue lengths distributions of this class of systems. From the latter, 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 eeect of the transition rate between the states of the modulating Markov chain on the average time delays in the system is investigated for diierent patterns of loads on the queues of the system.