Network multiplexer with truncated heavy-tailed arrival streams

Proceedings - IEEE INFOCOM

Volumn 2, Issue , 1999, Pages 625-632

  Jelenković, Predrag R ^a  

^a Columbia University ^*  (United States)

Author keywords

GI GI 1 Queue; Long range dependence; Network multiplexer; Regular Variation; Single server queue; Truncated heavy tailed distributions

Indexed keywords

GI/GI/1 QUEUE; HEAVY-TAILED DISTRIBUTION; LONG RANGE DEPENDENCE; REGULAR VARIATIONS; SINGLE SERVER QUEUE;

ASYMPTOTIC ANALYSIS; DROPS; MULTIPLEXING; MULTIPLEXING EQUIPMENT; QUEUEING THEORY; BUFFER STORAGE; CLIENT SERVER COMPUTER SYSTEMS; CONGESTION CONTROL (COMMUNICATION); SIGNAL DETECTION; TELECOMMUNICATION TRAFFIC;

COMPUTER HARDWARE DESCRIPTION LANGUAGES; QUEUEING NETWORKS;

SINGLE SERVER QUEUE;

EID: 0032672547     PISSN: 0743166X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/INFCOM.1999.751448     Document Type: Conference Paper

References (42)

1. J. Abate, G.L. Choudhury, and W. Whitt. Waiting time tail probabilities in queues with long-tail service time tails probabilities in queues with long - tail service time distributions. Queueing systems, 16(3/4):311- 338. 1994.
2. R. Agrawal, A. M. Makowski, and P. Nain. On a reduced load equivalence for fluid queues under subexponentiality. preprint, June 1998.
3. V. Anantharam. On the sojourn time of sessions at an ATM buffer with long-range dependent input traffic. In Proceedings of the 34th IEEE Conference on Decision and Control, December 1995.
4. S. Asmussen, L. F. Henriksen, and C. Kluppelberg. Large claims approximations for risk processes in a blarkoviaii environment., Stochastic Processes and their Applications, 54:29-43, 1994.
5. S. Asmussen, H. Schmidli, and V. Schmidt. Tail probabilities for non-standard risk and queueing processes with subexponential jumps. preprint, 1997.
6. N. H. Bingham, C. M. Goldie, and J. L. Teugels. Regular variation. Cambridge University Press, Cambridge, 1987.
7. O. J. Boxma. Regular variation in a multi-source fluid queue. In ITC I5, pages 391-402, Washington, D.C., USA. June 1997.
8. O.J. Boxma and V. Dumas. Fluid queues with longtailed activity period distributions. Technical Report PNA-R9705, CWI, Amsterdam, NL, April 1997.
9. G. L. Choudhury and W. Whitt. Long-tail buffercontent distributions in broadband networks. Performance Evaluation, 30:177-190, 1997.
10. J. W. Cohen. Some results on regular variation for distributions in queueing and fluctuation theory. J. Appl. Probability, 10:343-353, 1973.
11. J. W. Cohen. On the M/G/1 model with heavy-tailed service time distributions. In 9th INFORMS Applied Probnbility Conference, Cambridge, Massachusetts, June 1997.
12. M. Crovella, The relationship between heavy-tailed file sizes and self-similar network traffic. In 9th INFORMS Applied Probability Conference, Cambridge, Massachusetts, June 1997.
13. K. Debicki, Z. Michna, and T. Rolski. On the supremum from Gaussian processes over infinite horizon. preprint, Mas 1997.
14. N. G. Duffield and N. O'Connell, Large deviations and overflow probabilities for the general single-server queue with applications. Mathematical Proceedings of tht Cambridge Philosophical Society, 118:363-374, 1995.
15. W. Feller. An Introduction to Probability Theory and its Application, Volume II. Wiley, New York, 1971.
16. D. Heath, S. Resnick, and G. Samorodnitsky. Heavy tails and long range dependence in on/off processes and associated fluid models. preprint, 1996.
17. D. P. Heyrnan and T. V. Lakshman. Source models for VBR broadcast-video traffic. IEEE/ACM Transactions on Networking, 4:40-48, February 1996.
18. P. R. Jelenković, Long-tailed loss rates in a single queue. In Proceedings of INFOCOM'98, San Francisco, California, April 1998.
19. P. R. Jelenković. GI/GI/1 queue with truncated long tailed service times. Submitted for publication, 1999.
20. P. R. Jelenković. Asymptotic results for queues with subexponential arrival processes. In K. Park and W. Willinger, editors, Self-Similar Network Traffic and Performance Evaluation. Wiley (Inter science Division), 1999, to appear.
21. P. R. Jelenković. Long-tailed loss rates in a GI/GI/1 queue with applications. Queueing Systems, 1999, to appear.
22. P. R. Jelenković and A. A. Lazar. Subexponential asymptotics of a Markov-modulated random walk with queueing applications. Journal of Applied Probability, :35(2):325-347, June 1998.
23. P. R. jelenković and A. A. Lazar. Asymptotic results for multiplexing sub exponential on-off processes. Advances in Applied Probability, 31(2), June 1999, to appear.
24. P. R. Jelenković, A. A. Lazar, and N. Semret. The effect of multiple time scales and sub exponentiality of MPEG video streams on queueing behavior. IEEE Journal on Selected Areas in Communications, 15(6):1052-1071, August 1997.
25. J. Karamata, Sur un mode de croissance réguilère des fonctions. Mathematica (Cluj), 4: 38-53, 1930.
26. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson. On the self-similar nature of Ethernet traffic. In SIGCOMM'93, pages 183-193, 1993.
27. N. Likhanov, B. Tsybakov, and N. D. Georganas. Aidpsis of an ATM buffer with self-similar ("fractal") input traffic. In INFOCOM'95, pages 985-1391 Boston, Masssachusetts, April 1995.
28. R. M. Loynes, The stability of a queue with non independent inter-arrival and service times. Proc. Cambridge Philos Soc., 58:497-520, 1968.
29. P. Nain, Z. Liu, D. Towsley, and Z.-L. Zhang. Asymptotic behavior of a multiplexer fed by a long-range dependent process. In 9th INFORMS Applied Probability Conference, Cambridge, Massachusetts, June 1997.
30. P. Newman, G. Minishall, and T. Lyon. IP switching: ATM under IP. preprint, November 1997.
31. P. Newman, G. Minishall, T. Lyon, and L. Huston. IP switching and gigabit routers. IEEE Communications Magazine, January 1997.
32. I. Norros. A storage model with self-similar input,. Queueing Systems, 16:387-396, 1994.
33. Billingsley P. Probability and Measure. John Wiley & Sons. Inc., 1986.
34. A.G. Pakes. On the tails of waiting-time distribution. J. Appl. Probab., 12:555-564, 1975.
35. M. Pamlekar and A. M. Makowski. Tail probabilities for a multiplexer with self-similar traffic. In INFOCOM' 96, San Francisco, California, March 1996.
36. M. Parulekar and A. M. Makowski. Tail probabilitites for M/G/∞ input processes (I): preliminary asymptotices. Queueing Systems, 27:271-296, 1997.
37. S. Resnick, D. Heath, and G. Samorodnitsky. Patterns of buffer overflow in a class of queues with long memory in the input stream. Annals of Applied Probability 7 : 1021 - 1057, 1997.
38. T. Rolski, S. Schlegel, and V. Schmidt. Asymptotics of palm-stationary buffer content distribution in fluid flow queues. In 9th INFORMS Applied Probability Conference, Cambridge, Massachusetts, June 1997.
39. B. K. Ryu and S. B. Lowen. Point process approaches to the modeling and analysis of self-similar traffic - part, I: Model construction. In INFOCOM'96, San Francisco, California, March 1996.
40. K. P. Tsoukatos and A. M. Makowski. Heavy traffic analysis for a multiplexer driven by M/GI/∞ input processes. In ITC 15, pages 497-506, Washington, D.C.. IJSA, June 1997.
41. N. Veraverbeke. Asymptotic behavior of Wiener-Hopf factors of a random walk. Stochastic Proc. and Appl., 5:27-37, 1977.
42. E. Willekens and J. L. Teugels. Asymptotic expansion for waiting time probabilities in an M/G/1 queue with long-tailed service time. Queueing Systems, 10:295- 312, 1992.