The shape of the loss curve and the impact of long-range dependence on network performance

AEU - International Journal of Electronics and Communications

Volumn 58, Issue 2, 2004, Pages 101-117

  Mandjes, Michel ^a   Boots, Nam Kyoo ^b,c  

^a CWI   (Netherlands)

^b ABN AMRO Corporate Research   (Netherlands)

^c VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Buffer overflow; Heavy tailed distributions; Large deviations asymptotics; Long range dependence; Packet networking; Queueing theory

Indexed keywords

ASYMPTOTIC STABILITY; INTERNET; MATHEMATICAL MODELS; MULTIPLEXING; PROBABILITY; QUALITY OF SERVICE; QUEUEING THEORY; TELECOMMUNICATION TRAFFIC; WEB BROWSERS;

BUFFER OVERFLOW; HEAVY TAILED DISTRIBUTIONS; LARGE DEVIATIONS ASYMPTOTICS; LONG-RANGE DEPENDENCE;

PACKET NETWORKS;

EID: 3042696754     PISSN: 14348411     EISSN: None     Source Type: Journal    
DOI: 10.1078/1434-8411-54100215     Document Type: Article

References (42)

1. Anick, D.; Mitra, D.; Sondhi, M.: Stochastic theory of a data-handling system with multiple sources. Bell System Tech. J. 61 (1982), 1871-1894.
2. Asmussen, S.; Rubinstein, R.: Steady state rare event simulation in queueing models and its complexity properties. In Dshalalow, J. (Ed.), Advances in queueing theory, theory, methods and open problems, 429-461, Boca Raton, USA: CRC Press, 1995.
3. Botvich, D.; Duffield, N.: Large deviations, the shape of the loss curve, and economies of scale in large multiplexers. Queueing Systems 20 (1995), 293-320.
4. Boxma, O.: Fluid queues and regular variation. Performance Evaluation 27-28 (1996), 699-712.
5. Boxma, O.; Dumas, V.: Fluid queues with long-tailed activity period distributions. Comput. Commun. 21 (1998), 1509-1529.
6. Choudhury, G.; Lucantoni, D.; Whitt, W.: Squeezing the most out of ATM. IEEE Trans. Commun. 44 (1996), 203-217.
7. Cohen, J.: Some results on regular variation for distributions in queueing and fluctuation theory. J. Appl. Probability 10 (1973), 343-353.
8. Courcoubetis, C.; Weber, R.: Buffer overflow asymptotics for a buffer handling many traffic sources. J. Appl. Probability 33 (1996), 886-903.
9. Crovella, M.; Bestavros, A.: Self-similarity in World Wide Web traffic: evidence and possible causes. IEEE/ACM Trans. Networking 5 (1997), 835-846.
10. Dembo, A.; Zeitouni, O.: Large Deviations Techniques and Applications. Jones and Bartlett, Boston, 1993.
11. Duffield, N.: Queueing at large resources driven by long-tailed M/G/∞-modulated processes. Queueing Systems 28 (1998), 245-266.
12. Duffield, N.; O'Connell, N.: Large deviations and overflow probabilities for the general single server queue, with applications. Proc. Cambridge Philos. Soc. 118 (1995), 363-374.
13. Duffield, N.; Whitt, W.: Large deviations of inverse processes with nonlinear scalings. Ann. Appl. Probability 8 (1998), 995-1026.
14. Dumas, V.; Simonian, A.: Asymptotic bounds for the fluid queue fed by subexponential on-off sources. Preprint.
15. Elwalid, A.; Mitra, D.; Wentworth, R.: A new approach for allocating buffers and bandwidth to heterogeneous, regulated traffic in an ATM node. IEEE J. Selected Areas Commun. 13 (1995), 1115-1127.
16. Feldmann. A.: Characteristics of TCP connection arrivals. Internal memorandum AT&T Labs, available at http://www.research.att.com/~anja/ feldmann/ papers.html#traffic
17. Grossglauser, M.; Bolot, J.-C.: On the relevance of long-range dependence in network traffic. IEEE/ACM Trans. Networking 7 (1999), 629-640.
18. Heyman, D.; Lakshman, T.: What are the implications of long-range dependence for VBR traffic engineering? IEEE/ACM Trans. Networking 4 (1996), 301-317.
19. Heyman, D.; Lakshman, T.; Liu, D.: Assessing the effects of short-range and long-range dependence on overflow probabilities. Proceedings 13th ITC specialist seminar: IP traffic measurement, modeling, and management, 19.1-19.11, 2000.
20. Jelenković, P.; Lazar, A.: Asymptotic results for multiplexing on-off sources with subexponential on-times. Advances in Applied Probability 31 (1999), 394-421.
21. Jelenković, P.; Lazar, A.; Semret, N.: The effect of multiple time scales and subexponentiality in MPEG video streams on queueing behavior. IEEE J. Selected Areas Commun. 15 (1997), 1052-1071.
22. Kosten, L.: Stochastic theory of data-handling systems with groups of multiple sources. In H. Rudin and W. Bux (Eds.), Performance of Comput.-Communication Systems, 321-331, Elsevier, Amsterdam, 1984.
23. Leland, W.; Taqqu, M.; Willinger, W.; Wilson, D.: On the self-similar nature of Ethernet traffic. IEEE/ACM Trans. Networking 2 (1994), 1-15.
24. Likhanov, N.; Mazumdar, R.: Cell loss asymptotics in buffers fed with a large number of independent stationary sources. Proc. IEEE Infocom 1998, 339-346.
25. Mandjes, M.; Borst, S.: Overflow behavior in queues with many long-tailed inputs. Adv. Appl. Probability 32 (2000), 1150-1167.
26. Mandjes, M.; Kim, J.H.: Large deviations for small buffers: an insensitivity result. Queueing Systems 33 (2001), 349-362.
27. Mandjes, M.; Mitra, D.; Scheinhardt, W.: A simple model of network access: feedback adaptation of rates and admission control. Comput. Networks 41 (2003), 489-504.
28. Mandjes, M.; Ridder, A.: Finding the conjugate of Markov fluid processes. Probability Eng. Informational Sci. 9 (1995), 297-315.
29. Massoulié, L.; Simonian, A.: Large buffer asymptotics for the queue with FBM input. J. Appl. Probability 36 (1999), 894-906.
30. Norros, I.: A storage model with self-similar input. Queueing Systems 16 (1994), 387-396.
31. Pakes, A.: On the tail of waiting time distributions. J. Appl. Probability 12 (1975), 555-564.
32. Paxson, V.; Floyd, S.: Wide area traffic: the failure of Poisson modeling. IEEE/ACM Trans. Networking 3 (1995), 226-244.
33. Rose, O.: Traffic modeling of variable bit rate MPEG video and its impact on ATM networks. Ph.D. thesis, University of Würzburg, Germany, 1997.
34. Ryu, B.; Elwalid, A.: The importance of long-range dependence of VBR video traffic in ATM traffic engineering: myths and realities. Comput. Commun. Rev. 26 (1996), 3-14.
35. Shwartz, A.; Weiss, A.: Large deviations for performance analysis, queues, communication, and computing. Chapman and Hall, New York, 1995.
36. Simonian, A.; Guibert, J.: Large deviations approximation for fluid queues fed by a large number of on/off sources. IEEE J. Selected Areas Commun. 13 (1995), 1017-1027.
37. Sriram, K.; Whitt, W.: Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Selected Areas Commun. 4 (1986), 833-846.
38. van der Wal, K.; Mandjes, M.; Bastiaansen, H.: Delay performance analysis of the new internet services with guaranteed QoS. Proceedings IEEE 85 (1997), 1947-1957.
39. Weiss, A.: A new technique of analyzing large traffic systems. Adv. Appl. Probability 18 (1986), 506-532.
40. Whitt, W.: Tail probabilities with statistical multiplexing and effective bandwidth in multi-class queues. Telecommunication Systems 2 (1994), 71-107.
41. Willinger, W.; Taqqu, M.; Sherman, R.; Wilson, D.: Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level. Comput. Commun. Rev. 25 (1995), 100-113.
42. Wischik, D.: Sample path large deviations for queues with many inputs. Ann. of Applied Probability 11 (2001), 379-404.