- There has been extensive work focused on modeling discrete-time queueing systems with correlated arrivals. Specific attention has been drawn to queueing models with application to data switching, where bursty arrival streams represent more accurately real-life network traffic. To that end, the Markov modulated ON-OFF model has been frequently incorporated as a building block for constructing more complex traffic scenarios. In order to better evaluate the performance of a given switching system under bursty traffic, many packet-scheduling algorithms are examined under traffic obeying Markov modulated arrival processes. In some cases, significant degradation in performance metrics, such as the mean queueing latency, is observed under such bursty scenarios. Typically, performance metrics for switching systems under bursty traffic loads are attained by means of simulations. In this paper, we present an analytical tool that exploits the probability generating function of the interarrival times for obtaining steady-state queueing information from which performance metrics are analytically derived.