Approximating Performance and Traffic Flow in Nonstationary Tandem Networks of Markovian Queues

In this paper we examine a tandem network of queueing nodes where a nonstationary external Markovian arrival process feeds the initial upstream node. We develop methods for modeling the departure flow from any upstream node in its role as the arrival process to the immediate downstream node, and employ various techniques to match the interarrival moments to the downstream node to the moments of the departure count from the upstream node, thereby decoupling the network. We apply these matching techniques at variable time-steps, updating the parameters of the fit at each step and holding them constant until the next update. We test the accuracy of this approach by comparing the moments of the queue size of the downstream node against the corresponding true moments of queue size: first moments of queue size are consistently accurate, while the variance of queue size is sometimes less accurate but still useful.