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Transient behavior of coverage processes by applications to the infinite-server queue

Part of: Geometric probability and stochastic geometry Special processes

Published online by Cambridge University Press:  14 July 2016

Sid Browne  and
J. Michael Steele
Sid Browne*
Affiliation:
Columbia University
J. Michael Steele*
Affiliation:
University of Pennsylvania
*
∗ Postal address: 402 Uris Hall, Graduate School of Business, Columbia University, New York, NY 10027 USA. email: sbrowne@research.gsb.columbia.edu
∗∗ Postal address: Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA.
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Abstract

We obtain the distribution of the length of a clump in a coverage process where the first line segment of a clump has a distribution that differs from the remaining segments of the clump. This result allows us to provide the distribution of the busy period in an M/G/∞ queueing system with exceptional first service, and applications are considered. The result also provides the tool necessary to analyze the transient behavior of an ordinary coverage process, namely the depletion time of the ordinary M/G/∞ system.

Keywords

CLUMPSBUSY PERIODSDEPLETION TIMESEXCEPTIONAL FIRST SERVICE

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 589 - 601
Copyright
Copyright © Applied Probability Trust 1993 

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