Traffic with an fBm limit: Convergence of the stationary workload process

Queueing Systems

Volumn 46, Issue 1-2, 2004, Pages 113-127

  Dębicki, Krzysztof ^a,b   Mandjes, Michel ^a,c  

^a CWI   (Netherlands)

^b UNIVERSITY OF WROC AW   (Poland)

^c UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Fractional Brownian motion; Gaussian processes; Heavy traffic environment; On off sources; Weak convergence

Indexed keywords

FRACTIONAL BROWNIAN MOTION; GAUSSIAN PROCESSES; HEAVY TRAFFICS; ON OFF SOURCES; WEAK CONVERGENCE;

BROWNIAN MOVEMENT;

EID: 3543069330     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/b:ques.0000021144.61749.aa     Document Type: Conference Paper

References (19)

1. S. Berman, An asymptotic formula for the distribution of the maximum of a Gaussian process with stationary increments, J. Appl. Probab. 22 (1985) 454-460.
2. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
3. N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation (Cambridge Univ. Press, Cambridge, 1987).
4. A.A. Borovkov, Stochastic Processes in Queueing Theory (Springer, New York, 1976).
5. J. Cao and K. Ramanan, A Poisson limit for buffer overflow probabilities, in: Proceedings of INFOCOM 2002, 2002.
6. K. Dȩbicki and Z. Palmowski, Heavy traffic asymptotics of on-off fluid model, Queueing Systems 33 (1999) 327-338.
7. D. Heath, S. Resnick and G. Samorodnitsky, Heavy tails and long range dependence in ON/OFF processes and associated fluid models, Math. Oper. Res. 23 (1998) 145-165.
8. K. Konstantopoulos and S. Lin, Macroscopic models for long-range dependent network traffic, Queueing Systems 28 (1998) 215-243.
9. V. Kulkarni, Fluid models for single buffer systems, in: Frontiers in Queueing: Models and Applications in Science and Engineering, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997) pp. 321-338.
10. V. Kulkarni and T. Rolski, Fluid model driven by an Ornstein-Uhlenbeck process, Probab. Engrg. Inform. Sci. 8 (1994) 403-417.
11. T. Lindvall, Weak convergence of probability measures and random functions in the function space D[0, 8), J. Appl. Probab. 10 (1973) 109-121.
12. M. Mandjes and S. Borst, Overflow behavior in queues with many long-tailed inputs, Adv. in Appl. Probab. 32 (2000) 1150-1167.
13. T. Mikosch, S. Resnick, H. Rootzén and A. Stegeman, Is network traffic approximated by stable Lévy motion or fractional Brownian motion, Ann. Appl. Probab. 12 (2002) 23-68.
14. I. Norros, A storage model with self-similar input, Queueing Systems 16 (1994) 387-396.
15. V.I. Piterbarg, Asymptotic Methods in the Theory of Gaussian Processes and Fields, Translations of Mathematical Monographs, Vol. 148 (Amer. Mah. Soc., Providence, RI, 1996).
16. W. Szczotka, Central limit theorem in D[0, 8) for breakdown processes, Probab. Math. Statist. 1 (1980) 49-57.
17. M.S. Taqqu, W. Willinger and R. Sherman, Proof of a fundamental result in self-similar traffic modeling, Comput. Commun. Rev. 27 (1997) 5-23.
18. W. Whitt, Stochastic-Process Limits (Springer, New York, 2002).
19. B. Zwart, S. Borst and M. Mandjes, Exact queueing asymptotics for multiple heavy-tailed on-off flows, in: Proc. of IEEE INFOCOM, 2001, pp. 279-288.