Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models

References

• Anantharam V. On the sojourn time of sessions at an ATM buffer with long-range dependent input traffic. Proc. 34th IEEE Conf. Decision and Control (1995) 1New Orleans, LA:859–864Dec. 13–15Crossref, Google Scholar
• Asmussen S. Applied Probability and Queues. (1987) (J. Wiley and Sons, New York) Google Scholar
• Bingham N., Goldie C., Teugels J. Regular variation. Encyclopedia of Mathematics and Its Applications(Cambridge University Press, Cambridge, UK) Google Scholar
• Brichet F., Roberts J., Simonian A., Veitch D. Heavy traffic analysis of a storage model with long range dependent on/off sources. Queueing Systems (1996) 23:197–215Crossref, Google Scholar
• Choudhury G. F., Whitt W. Long-tail buffer-content distributions in broadband networks. Performance Evaluation (1997) 30:177–190Crossref, Google Scholar
• Cohen J. W. On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue. Ann. Inst. H. Poincare B (1972) 8:255–263Google Scholar
• Crovella M., Bestavros A. Self-similarity in World Wide Web traffic-evidence and possible causes. Proc. of ACM Sigmetrics '96 (1996) Philadelphia, PA:160–169Crossref, Google Scholar
• Cunha C., Bestavros A., Crovella M. Characteristics of www client-bases traces. . (preprint). Available as BU-CS-95-010 from [email protected] or [email protected]Google Scholar
• Erramilli A., Narayan O., Willinger W. Experimental queuing analysis with long-range dependent packet traffic. IEEE/ACM Trans. on Networking (1996) 4:209–223Crossref, Google Scholar
• Feller W.An Introduction to Probability Theory and Its Applications (1971) II2nd ed.(Wiley, New York) Google Scholar
• Frenk J. B. G.On Banach algebras, renewal measures and regenerative processes (1987) (Centre for Mathematics and Computer Science, CWI, Amsterdam, The Netherlands) . CWI Tract 38Google Scholar
• Heyman D., Lakshman T. What are the implications of long-range dependence for VBR-video traffic engineering? IEEE/ACM Trans. on Networking (1996) 4:301–317Crossref, Google Scholar
• Jelenkovic P., Lazar A. Subexponential asymptotics of a Markov modulatedG/G/1 queue. (1995) . PreprintGoogle Scholar
• Leland W., Taqqu M., Willinger W., Wilson D. On the self-similar nature of ethernet traffic. Proc. of the ACM/SIGCOMM '93 (1993) 23(San Francisco, CA)183–193Comput. Comm. Rev.Crossref, Google Scholar
• Leland W., Taqqu M., Willinger W., Wilson D. On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Trans. on Networking (1994) 2:1–15Crossref, Google Scholar
• Likhanov N., Tsybakov B., Georganas N. D. Analysis of an ATM buffer with self-similar (“fractal”) input traffic. Proc. of the 14th Annual IEEE INFOCOMM (1995) 985–992Crossref, Google Scholar
• Livny M., Melamed B., Tsiolis A. K. The impact of autocorrelations on queuing systems. Management Sci. (1993) 39:322–339Link, Google Scholar
• Pakes A. J. On the tails of waiting time distributions. J. Appl. Probab. (1975) 12:555–564Crossref, Google Scholar
• Parulekar M., Makowski A. M. Tail probabilities for a multiplexer with a self-similar traffic. Proc. of the IEEE INFOCOMM '96 (1996) San Francisco, CA:1452–1459Crossref, Google Scholar
• Resnick S.Adventures in Stochastic Processes (1992) (Birkhäuser, Boston) Google Scholar
• Resnick S., Samorodnitsky G. Performance decay in a single server exponential queuing model with long range dependence. Oper. Res. (1997) 45:235–243Link, Google Scholar
• Willinger W., Taqqu M., Leland W., Wilson D. Self-similarity in high-speed packet traffic: Analysis and modeling of ethernet traffic measurements. Statist. Sci. (1995) 10:67–85Crossref, Google Scholar
• Willinger W., Taqqu M., Sherman R., Wilson D. Self-similarity through high variability: Statistical analysis of ethernet LAN traffic at the source level. Proc. of the ACM/SIGCOMM '95 (1995) 25(Cambridge, MA)100–113Comput. Comm. Rev.Crossref, Google Scholar
• Willinger W., Taqqu M., Sherman R., Wilson D. Self-similarity through high variability: Statistical analysis of ethernet LAN traffic at the source level (extended version). IEEE/ACM Trans. on Networking (1997) 5:71–96(to appear 1997)Crossref, Google Scholar