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On the time-dependent moments of Markovian queues with reneging

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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.

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  1. Dept. of Math. Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC, 29634, USA

    Brian H. Fralix

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  1. Brian H. Fralix
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Correspondence to Brian H. Fralix.

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Fralix, B.H. On the time-dependent moments of Markovian queues with reneging. Queueing Syst 75, 149–168 (2013). https://doi.org/10.1007/s11134-012-9281-2

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  • DOI: https://doi.org/10.1007/s11134-012-9281-2

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