Models and algorithms for transient queueing congestion at airports
Management Science
A sample path analysis of the M_t/M_t/c queue
Queueing Systems: Theory and Applications
An Exact Solution for an M(t)/M(t)/1 Queue with Time-Dependent Arrivals and Service
Queueing Systems: Theory and Applications
Modeling Daily Arrivals to a Telephone Call Center
Management Science
The Pht/Pht/8 Queueing System: Part I--The Single Node
INFORMS Journal on Computing
A minimal representation of Markov arrival processes and a moments matching method
Performance Evaluation
Characterizing the variability of arrival processes with indexes of dispersion
IEEE Journal on Selected Areas in Communications
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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 $\widetilde{Ph_t}$ 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 $\widetilde{Ph_t}$ approximating departure process as the approximate composite arrival process to downstream nodes in a network of tandem queues.