Asymptotic independence and a network traffic model

Journal of Applied Probability

Volumn 39, Issue 4, 2002, Pages 671-699

  Maulik, Krishanu ^a   Resnick, Sidney ^b   Rootzén, Holger ^c  

^a EURANDOM   (Netherlands)

^b Cornell University   (United States)

^c CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Asymptotic independence; Heavy tails; Infinite source Poisson model; Long range dependence; M G queue; Network modeling; Poisson input; Random rates

Indexed keywords

EID: 0037003085     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1037816012     Document Type: Article

References (32)

1. BASRAK, B. (2000). The sample autocorrelation function of non-linear time series. Doctoral Thesis, Rijksuniversiteit Groningen.
2. BILLINOSLEY, P. (1999). Convergence of Probability Measures. 2nd edn. John Wiley, New York.
3. BREIMAN, L. (1965). On some limit theorems similar to the arc-sin law. Theory Prob. Appl. 10, 323-331.
4. CUNHA, C. A., BESTAVROS, A. AND CROVELLA, M. E. (1995). Characteristics of WWW client-based traces. Tech. Rep. TR-95-010, Computer Science Department, Boston University. Available at http://www.cs.bu.edu/techreports/.
5. DE HAAN, L. AND DE RONDE, J. (1998). Sea and wind: multivariate extremes at work. Extremes 1, 7-45.
6. ERRAMILLI, A., NARAYAN, O. AND WILLINGER, W. (1996). Experimental queueing analysis with long-range dependent packet traffic. IEEE/ACM Trans. Network Comput. 4, 209-223.
7. GUERIN, C. A. et al. (1999). Empirical testing of the infinite source Poisson data traffic model. Tech. Rep. 1257, School of ORIE, Cornell University. Available at http://www.orie.cornell.edu/trlist/.
8. HEATH, D., RESNICK, S. AND SAMORODNITSKY, G. (1999). How system performance is affected by the interplay of averages in a fluid queue with long range dependence induced by heavy tails. Ann. Appl. Prob. 9, 352-375.
9. JELENKOVIĆ, P. R. AND LAZAR, A. A. (1996). A network multiplexer with multiple time scale and subexponential arrivals. In Stochastic Networks: Stability and Rare Events (Lecture Notes Statist. 117), eds P. Glasserman, K. Sigman and D. D. Yao, Springer, New York, pp. 215-235.
10. JELENKOVIĆ, P. R. AND LAZAR, A. A. (1999). Asymptotic results for multiplexing subexponential on-off processes. Adv. Appl. Prob. 31, 394-421.
11. KONSTANTOPOULOS, T. AND LIN, S.-J. (1998). Macroscopic models for long-range dependent network traffic. Queueing Systems 28, 215-243.
12. LEVY, J. B. AND TAQQU, M. S. (2000). Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli 6, 23-44.
13. MAULIK, K., RESNICK, S. AND ROOTZÉN, H. (2000). A network traffic model with random transmission rate. Tech. Rep. 1278, School of ORIE, Cornell University. Available at http://www.orie.cornell.edu/trlist/.
14. MIKOSCH, T., RESNICK, S., ROOTZÉN, H. AND STEGEMAN, A. W. (2002). Is network traffic approximated by stable Lévy motion or fractional Brownian motion? Ann. Appl. Prob. 12, 23-68.
15. PIPIRAS, V. AND TAQQU, M. S. (2000). The limit of a renewal reward process with heavy-tailed rewards is not a linear fractional stable motion. Bernoulli 6, 607-614.
16. PIPIRAS, V., TAQQU, M. S. AND LEVY, J. B. (2000). Slow and fast growth conditions for renewal reward processes with heavy tailed renewals and either finite-variance or heavy tailed rewards. Preprint.
17. RESNICK. S. I. (1987). Extreme Values, Regular Variation, and Point Processes. Springer, New York.
18. RESNICK, S. (1997). Heavy tail modeling and teletraffic data. Ann. Statist. 25, 1805-1869.
19. RESNICK, S. AND ROOTZÉN, H. (2000). Self-similar communication models and very heavy tails. Ann. Appl. Prob. 10, 753-778.
20. RESNICK, S. AND SAMORODNITSKY, G. (2000). A heavy traffic approximation for workload processes with heavy tailed service requirements. Manag. Sci. 46, 1236-1248.
21. RESNICK, S. AND STǍRICǍ, C. (1997). Smoothing the Hill estimator. Adv. Appl. Prob. 29, 271-293.
22. RESNICK, S. AND VAN DEN BERG, E. (2000). Weak convergence of high-speed network traffic models. J. Appl. Prob. 37, 575-597.
23. SKOROHOD, A. V. (1956). Limit theorems for stochastic processes. Theory Prob. Appl. 1, 261-290.
24. STǍRICǍ, C. (1999). Multivariate extremes for models with constant conditional correlations. J. Empirical Finance 6, 515-553.
25. WHITT, W. (1980). Some useful functions for functional limit theorems. Math. Operat. Res. 5, 67-85.
26. WHITT, W. (1999a). On the Skorohod M-topologies. Preprint, AT&T Labs, Florham Park, NJ.
27. WHITT, W. (1999b). The reflection map is Lipschitz with appropriate Skorohod M-metrics. Preprint, AT&T Labs, Florham Park, NJ.
28. WHITT, W. (2000). Limits for cumulative input processes to queues. Prob. Eng. Inf. Sci. 14, 123-150.
29. WHITT, W. (2002). Stochastic-Process Limits. Springer, New York.
30. WILLINGER, W. AND PAXSON, V. (1998). Where mathematics meets the internet. Notices Amer. Math. Soc. 45, 961-970.
31. WILLINGER, W., TAQQU, M. S., LELAND, M. AND WILSON, D. (1995). Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements. Statist. Sci. 10, 67-85.
32. WILLINGER, W., TAQQU, M.S., SHERMAN, R. AND WILSON, D. (1997). Self-similarity through high variability: statistical analysis of Ethernet LAN traffic at the source level (extended version). IEEE/ACM Trans. Networking 5, 71-86.