A traffic based decomposition of two-class queueing networks with priority service

This paper presents a Markov arrival process (MAP) based methodology for the analysis of two-class queueing networks with priority service nodes. We apply the multi-class extension of MAP, referred to as Marked MAP (MMAP), for the description of the input and internal traffic in the queueing network. The MMAP traffic description allows to capture not only the dependency structure of the traffic classes themselves, but also the inter-class dependency of the high and low priority traffic. To carry out MMAP based queueing network analysis the paper presents several contributions: the departure process analysis of the MMAP/MAP/1 priority queue, an MMAP construction method based on the joint moments of two consecutive inter-departure times and some new results towards the efficient performance analysis of the MMAP/MAP/1 priority queue. Numerical examples illustrate the accuracy of the proposed traffic based decomposition method.