Fitting the Pht/Mt/s/c Time-Dependent Departure Process for Use in Tandem Queueing Networks

This paper considers time-dependent Pht/Mt/s/c queueing nodes and small tandem networks of such nodes. We examine characteristics of the departure processes from a multiserver queueing node; in particular, we focus on solving for the first two time-dependent moments of the departure-count process. A finite set of partial moment differential equations is developed to numerically solve for the departure-count moments over specified intervals of time [ti, ti + τi). We also present a distribution fitting algorithm to match these key characteristics with a Pht process serving as the approximate departure process. A distribution fitting algorithm is presented for time-dependent point processes where a two-level balanced mixture of Erlang distribution is used to serve as the approximating process. We then use the Pht approximating departure process as the approximate composite arrival process to downstream node(s) in a network of tandem queues.