A Uniform Approach for Analyzing Queues with Correlated Interarrival and Service Times

Using the bivariate phase-type distribution and Markov modulated fluid flow (MMFF) process, we introduce a framework to analyze queues with correlated interarrival and service times. The queueing model of interest is quite general and versatile, which covers a number of classical cases (e.g., queues with multi-types of customers), and the solution approach is powerful enough, as compared to other applied probability approach, to obtain all the basic queueing quantities of interest. Two algorithms are developed for computing quantities such as the distributions, means, and variances of age, waiting time, sojourn time, and queue lengths. As a highlight, the impact of the correlation between the interarrival and service times on queueing performance is explored numerically.