Patterns of buffer overflow in a class of queues with long memory in the input stream

Annals of Applied Probability

Volumn 7, Issue 4, 1997, Pages 1021-1057

  Heath, David ^a   Resnick, Sidney ^a   Samorodnitsky, Gennady ^a  

^a School of Chemical and Molecular Engineering   (United States)

Author keywords

Buffer overflow; Fluid models; G G 1 queue; Heavy tailed distribution; Heavy tails; Long memory; Long range dependence; Maximum work load; On off models; Regular variation; Time to hit a level; Weak convergence

Indexed keywords

EID: 0031260682     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1043862423     Document Type: Article

References (30)

1. ABATE, J., CHOUDHURY, G. and WHITT, W. (1994). Waiting-time tail probabilities in queues with long-tail service-time distributions. Queueing Systems Theory Appl. 16 311-338.
2. ANICK, D., MITRA, D. and SONDHI, M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell System Technical Journal 61 1871-1894.
3. ASMUSSEN, S. (1987). Applied Probability and Queues. Wiley, New York.
4. ASMUSSEN, S. (1998). Subexponential asymptotics for stochastic processes: extremal behavior, stationary distributions and first passage probabilities. Ann. Appl. Probab. To appear.
5. ASMUSSEN, S. and PERRY, D. (1992). On cycle maxima, first passage problems and extreme value theory for queues. Stochastic Models 8 421-458.
6. AVRAM, F. and TAQQU, M. S. (1986). Weak convergence of moving averages with infinite variance. In Dependence in Probability and Statistics (E. Eberlein and M. Taqqu, eds.) 399-415. Birkhäuser, Boston.
7. AVRAM, F. and TAQQU, M. S. (1989). Probability bounds for M-Skorohod oscillations. Stochastic Process. Appl. 33 63-72.
8. AVRAM, F. and TAQQU, M. S. (1992). Weak convergence of sums of moving averages in the α-stable domain of attraction. Ann. Probab. 20 483-503.
9. BERGER, A. and WHITT, W. (1995). Maximum values in queueing processes. Probab. Engrg. Inform. Sci. 9 375-409.
10. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
11. BINGHAM, N., GOLDIE, C. and TEUGELS, J. (1987). Regular variation. In Encyclopedia of Mathematics and Its Applications 27. Cambridge Univ. Press.
12. BRICHET, F., ROBERTS, J., SIMONIAN, A. and VEITCH, D. (1996). Heavy traffic analysis of a storage model with long range dependent On/Off sources. Queueing Systems Theory Appl. 23 197-215.
13. CHOUDHURY, G. and WHITT, W. (1995). Long-tail buffer-content distributions in broadband networks. Preprint, AT&T Bell Laboratories, Murray Hill, NJ.
14. CROVELLA, M. and BESTAVROS, A. (1995). Explaining World Wide Web traffic self-similarity. Preprint. (Available as TR-95-015 from {crovella,best}@cs.bu.edu.)
15. CUNHA, C., BESTAVROS, A. and CROVELLA, M. (1995). Characteristics of www client-based traces. Preprint. (Available as BU-CS-95-010 from {crovella,best}@cs.bu.edu.)
16. EMBRECHTS, P. and VERAVERBEKE, N. (1982). Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance: Mathematics and Economics 1 55-72.
17. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications 2, 2nd ed. Wiley, New York.
18. HEATH, D., RESNICK, S. and SAMORODNITSKY, G. (1996). Heavy tails and long range dependence in on/off processes and associated fluid models. Math. Oper. Res. To appear. (Available as TR1144.ps.Z at http://www.orie.cornell.edu/trlist/trlist.html.)
19. IGLEHART, D. (1972). Extreme values in the GI/G/1 queue. Ann. Math. Statist. 43 627-635.
20. KELLA, O. and WHITT, W. (1992). A storage model with a two-state random environment. Oper. Res. 40 257-262.
21. LELAND, W., TAQQU, M., WILLINGER, W. and WILSON, D. (1993). On the self-similar nature of ethernet traffic. ACM/SIGCOMM Computer Communications Review 23 183-193.
22. LELAND, W., TAQQU, M., WILLINGER, W. and WILSON, D. (1994). On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on Networking 2 1-15.
23. PACHECO, A. and PRABHU, N. U. (1996). A Markovian storage model. Ann. Appl. Probab. 6 76-91.
24. PRABHU, N. U. and PACHECO, A. (1995). A storage model for data communication systems. Queueing Systems Theory Appl. 19 1-40.
25. PRATT, J. (1960). On interchanging limits and integrals. Ann. Math. Statist. 31 74-77.
26. RESNICK, S. (1986). Point processes, regular variation and weak convergence. Adv. in Appl. Prob. 18 66-138.
27. RESNICK, S. (1987). Extreme Values, Regular Variation, and Point Processes. Springer, New York.
28. RESNICK, S. (1992). Adventures in Stochastic Processes. Birkhäuser, Boston.
29. WILLINGER, W., TAQQU, M., LELAND, W. and WILSON, D. (1995). Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements. Statist. Sci. 10 67-85.
30. WILLINGER, W., TAQQU, M., SHERMAN, R. and WILSON, D. (1995). Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level. Preprint.