A Joint Moments Based Analysis of Networks of MAP/MAP/1 Queues

The decomposition based approximate numerical analysis of queueing networks of MAP/MAP/1 queues is considered in this paper. One of the most crucial decisions of decomposition based queueing network analysis is the description of inter-node traffic. Utilizing recent results on Markov arrival processes (MAPs), we apply a given number of joint moments of the consecutive inter-event times to describe the inter-node traffic. This traffic description is compact (uses far less parameters than the alternative methods) and flexible (allows an easy reduction of the complexity of the model, which increases in each analysis step). Numerical examples demonstrate the accuracy and the computational complexity of the proposed approximate analysis method.