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

  • Remigijus Leipus (a1) and Donatas Surgailis (a1)

Abstract

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.

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Copyright

Corresponding author

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.

References

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Baccelli, F. and Brémaud, P. (1994). Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences. Springer, New York.
Borovkov, A. A. (1976). Stochastic Processes in Queueing Theory. Springer, New York.
Daley, D. J. and Vesilo, R. A. (1997). Long range dependence of point processes, with queueing examples. Stoch. Process. Appl. 70, 265282.
Daley, D. J. and Vesilo, R. A. (2000). Long range dependence of inputs and outputs of some classical queues. Fields Inst. Commun. 28, 179186.
Franken, P., König, D., Arndt, U. and Schmidt, V. (1981). Queues and Point Processes. Springer, Berlin.
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, 145165.
Smith, W. L. (1958). Renewal theory and its ramifications. J. R. Statist. Soc. B 20, 243302.
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, 7186.

Keywords

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

  • Remigijus Leipus (a1) and Donatas Surgailis (a1)

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