Hierarchical Space Merging Algorithm for the Analysis of Open Tandem Queueing Networks

Abstract

The Markov model of a two-stage queueing network with feedback is proposed. Poisson flows arrive to both stages from outside. A part of already serviced calls at the first node instantaneously enter the second node (if there is free space here) while the other calls leave the network. After the service is completed at the second node, there are three possibilities: (i) the call leaves the network; (ii) it instantaneously feeds back to the first node (if there is free space here); (iii) it feeds back to the first node after some delay in orbit. All feedbacks are determined by known probabilities. Both nodes have finite capacities. The mathematical model of the investigated network is a three-dimensional Markov chain, and a hierarchical space merging algorithm is developed to calculate its steady-state probabilities. The results of numerical experiments are demonstrated.