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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: [email protected]
∗∗ 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 

References

Baccelli, F. and Brémaud, P. (1994). Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences. Springer, New York.Google Scholar
Borovkov, A. A. (1976). Stochastic Processes in Queueing Theory. Springer, New York.CrossRefGoogle Scholar
Daley, D. J. and Vesilo, R. A. (1997). Long range dependence of point processes, with queueing examples. Stoch. Process. Appl. 70, 265–282.CrossRefGoogle Scholar
Daley, D. J. and Vesilo, R. A. (2000). Long range dependence of inputs and outputs of some classical queues. Fields Inst. Commun. 28, 179–186.Google Scholar
Franken, P., König, D., Arndt, U. and Schmidt, V. (1981). Queues and Point Processes. Springer, Berlin.Google Scholar
Heath, D., Resnick, S. and Samorodnitsky, G. (1998). Heavy tails and long range dependence in ON/OFF processes and associated fluid models. Math. Operat. Res. 23, 145–165.CrossRefGoogle Scholar
Smith, W. L. (1958). Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243–302.Google Scholar
Willinger, W., Taqqu, M. S., Sherman, R. and Wilson, D. V. (1997). Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level. IEEE/ACM Trans. Networking 5, 71–86.CrossRefGoogle Scholar