Tail probabilities for M/G/∞ input processes (I): Preliminary asymptotics

Queueing Systems

Volumn 27, Issue 3-4, 1997, Pages 271-296

  Parulekar, Minothi ^a   Makowski, Armand M ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Forward recurrence times; Infinite server queue; Large deviations; Scalings; Tail probabilities

Indexed keywords

INFINITE SERVER QUEUES; LARGE DEVIATIONS; RECURRENCE TIME; SCALINGS; TAIL PROBABILITY;

NORMAL DISTRIBUTION;

EID: 0001510899     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019122400632     Document Type: Article

References (26)

1. R.G. Addie, M. Zukerman and T. Neame, Fractal traffic: Measurements, modeling and performance evaluation, in: Proceedings of INFOCOM '95, Boston, MA (April 1995) pp. 985-992.
2. J. Beran, R. Sherman, M.S. Taqqu and W. Willinger, Long-range dependence in variable bit-rate video traffic, IEEE Trans. Commun. 43 (1995) 1566-1579.
3. D.R. Cox, Long-range dependence: A review, in: Statistics: An Appraisal, eds. H.A. David and H.T. David (The Iowa State University Press, Ames, IA, 1984) pp. 55-74.
4. D.R. Cox and V. Isham, Point Processes (Chapman and Hall, New York, NY, 1980).
5. A. Dembo and O. Zeitouni, Large Deviation Techniques and Applications (Jones and Bartlett, Boston, MA, 1993).
6. N.G. Duffield and N. O'Connell, Large deviations and overflow probabilities for the general single server queue, with applications, Proceedings of the Cambridge Philosophical Society 118 (1995) 363-374.
7. A. Erramilli, O. Narayan and W. Willinger, Experimental queuing analysis with long-range dependent packet traffic, IEEE/ACM Trans. Networking 4 (1996) 209-223.
8. J.D. Esary, F. Proschan and D.W. Walkup, Association of random variables, with applications, Ann. Math. Statist. 38 (1967) 166-1474.
9. H.J. Fowler and W.E. Leland, Local area network traffic characteristics, with implications for broadband network congestion management, IEEE J. Selected Areas Commun. 9 (1991) 1139-1149.
10. M. Garrett and W. Willinger, Analysis, modeling and generation of self-similar VBR video traffic, in: Proceedings of SIGCOMM '94 (September 1994) pp. 269-280.
11. P.W. Glynn and W. Whitt, Logarithmic asymptotics for steady-state tail probabilities in a single-server queue, J. Appl. Probab. 31 (1994) 131-159.
12. F.P. Kelly, Reversibility and Stochastic Networks (Wiley, New York, 1979).
13. G. Kesidis, J. Walrand and C.S. Chang, Effective bandwidths for multiclass Markov fluids and other ATM sources, IEEE/ACM Trans. Networking (1993) 424-428.
14. W. Leland, M. Taqqu, W. Willinger and D. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Trans. Networking 2 (1994) 1-15.
15. N. Likhanov, B. Tsybakov and N.D. Georganas, Analysis of an ATM buffer with self-similar (fractal) input traffic, in: Proceedings of INFOCOM '95, Boston, MA (April 1995) pp. 985-992.
16. M. Livny, B. Melamed and A.K. Tsiolis, The impact of autocorrelation on queueing systems, Management Science 39 (1993) 322-339.
17. R.M. Loynes, The stability of a queue with non-independent inter-arrival and service times, Proceedings of the Cambridge Philosophical Society 58 (1962) 497-520.
18. I. Norros, A storage model with self-similar input, Queueing Systems 16 (1994) 387-396.
19. M. Parulekar and A.M. Makowski, Tail probabilities for a multiplexer with self-similar traffic, in: Proceedings of INFOCOM' 96, San Francisco, CA (April 1996) pp. 1452-1459.
20. M. Parulekar and A.M. Makowski, Buffer overflow probabilities for a multiplexer with self-similar traffic, Technical Report TR-95-67, Institute for Systems Research, University of Maryland, College Park, MD (1995).
21. M. Parulekar and A.M. Makowski, Tail probabilities for M/G/∞ processes (II): Buffer asymptotics, in preparation.
22. M. Parulekar and A.M. Makowski, Asymptotic tail probabilities for general single server queues: Another look, in preparation.
23. M. Parulekar and A.M. Makowski, M/G/∞ Input processes: A versatile class of models for network traffic, in: Proceedings of INFOCOM' 97, Kobe, Japan (April 1997) pp. 419-426.
24. M. Parulekar, Buffer engineering for M/G/∞ input processes, Ph.D. thesis, Electrical Engineering Department, University of Maryland, College Park, MD (expected December 1997).
25. V. Paxson and S. Floyd, Wide area traffic: The failure of Poisson modeling, IEEE/ACM Trans. Networking 3 (1993) 226-244.
26. W. Willinger, M.S. Taqqu, W.E. Leland and D.V. Wilson, Self-similarity in high-speed packet traffic: Analysis and modeling of ethernet traffic measurements, Statist. Sci. 10 (1995) 67-85.