On the time-dependent moments of Markovian queues with reneging

Authors:
Brian H. Fralix
Affiliations:
Dept. of Math. Sciences, Clemson University, Clemson, USA 29634
Venue:
Queueing Systems: Theory and Applications
Year:
2013

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Abstract

We give an explicit representation for the time-dependent moments of a Markovian queueing system with reneging. Our expressions are comparable in form to the moment expressions for the M/M/1 queue found in Abate and Whitt (Queueing Syst. 2:41---65, 1987; Adv. Appl. Probab. 20:145---178, 1988). We also illustrate how to use these expressions to derive analogous moment expressions for a reflected Ornstein---Uhlenbeck process, with reflection at zero.