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 $\widetilde{{\mathrm{Ph}}_t}$ 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 $\widetilde{{\mathrm{Ph}}_t}$ approximating departure process as the approximate composite arrival process to downstream node(s) in a network of tandem queues.