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On Long-Range Dependence in Regenerative Processes Based on a General ON/OFF Scheme

Part of: Special processes Design of experiments Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Remigijus Leipus  and
Donatas Surgailis
Remigijus Leipus*
Affiliation:
Vilnius University and Institute of Mathematics and Informatics, Vilnius
Donatas Surgailis*
Affiliation:
Vilnius University and Institute of Mathematics and Informatics, Vilnius
*
∗ Postal address: Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania. Email address: remigijus.leipus@mif.vu.lt
∗∗ Postal address: Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania.
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Abstract

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In this paper, we obtain a closed form for the covariance function of a general stationary regenerative process. It is used to derive exact asymptotics of the covariance function of stationary ON/OFF and workload processes, when ON and OFF periods are heavy-tailed and mutually dependent. The case of a G/G/1/0 queueing system with heavy-tailed arrival and/or service times is studied in detail.

Keywords

Regenerative processON/OFF processG/G/1/0 queuelong-range dependence

MSC classification

Primary: 60G10: Stationary processes 60K05: Renewal theory 62K25: Robust parameter designs
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 379 - 392
Copyright
Copyright © Applied Probability Trust 2007 

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