Departure process analysis of the multi-type MMAP[K]/PH[K]/1 FCFS queue

The analysis of the departure process of queues is important in several aspects, for instance, it plays a prominent role in the decomposition based analysis of open queueing networks. While there are several results available for the departure process analysis of MAP driven single-class (or, single-type) queues, there are very few results available for the multi-type variants of these queues.In this paper we consider the departure process of the multi-type MMAP[K]/PH[K]/1 FCFS queue. We derive the joint Laplace–Stieltjes transform of the lag-nn inter-departure times, and provide efficient algorithms to compute the lag-11 joint moments, the lag-nn joint means and cross correlations of the inter-departure times.While the analysis of the departure process is typically performed via the queue length distribution at departure instants, we rely on the age process to derive various properties of the departure process.