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

This paper considers time-dependent Ph_t/M_t/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 [t_i, t_i + τ_i). We also present a distribution fitting algorithm to match these key characteristics with a $\widetilde{P{h}_t}$ 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 $\widetilde{P{h}_t}$ approximating departure process as the approximate composite arrival process to downstream node(s) in a network of tandem queues.