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On Finite Moments of Full Busy Periods of GI/G/c Queues

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Saeed Ghahramani  and
Ronald W. Wolff
Saeed Ghahramani*
Affiliation:
Western New England College
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
∗ Postal address: School of Arts and Sciences, Western New England College, Springfield, MA 01119-2684, USA.
∗∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: wolff@ieor.berkeley.edu
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Abstract

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For a GI/G/c queue, a full busy period is an interval that begins when an arrival finds c − 1 customers in the system, and ends when, for the first time after that, a departure leaves behind c − 1 customers in the system. We present a probabilistic proof of conditions for full busy periods to have finite moments. For queues that empty, this result may be deduced from results in the literature, but our proof is much easier. For queues that do not empty, our proof still applies, and this result is new.

Keywords

Full busy periodremaining busy periodfast single-serverequilibrium distribution

MSC classification

Secondary: 60K25: Queueing theory

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 275 - 278
Copyright
© Applied Probability Trust 2005 

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