Limit Behavior of Fluid Queues and Networks

References

• Billingsley P.Convergence of Probability Measures (1968) (Wiley, New York) Google Scholar
• Campos F., Marron J., Samorodnitsky G., Smith F. Variable heavy tailed durations in Internet traffic, Part I: Understanding heavy tails. Proc. Tenth IEEE/ACM Internat. Sympos. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (IEEE/ACM MASCOTS 2002) (2002) October 12–16Fort Worth, TXCrossref, Google Scholar
• Downey A. The structural cause of file size distributions. (2000) . Wellesley College Tech. Report CSD-TR25-2000. Available at http://rocky.wellesley.edu/downey/filesizeGoogle Scholar
• Feller W.An Introduction to Probability Theory and Its Applications (1957) 13rd ed.(Wiley, New York) Google Scholar
• Feller W.An Introduction to Probability Theory and Its Applications (1971) 22nd ed.(Wiley, New York) Google Scholar
• Gaigalas R., Kaj I. Convergence of scaled renewal processes and a packet arrival model. Bernoulli (2003) 9:671–703Crossref, Google Scholar
• Gong W., Liu Y., Misra V., Towsley D. Bilinear time-scale analysis applied to local scaling exponents estimation. Proc. 39th Allerton Conf. Comm., Control, Comput. (2001) Google Scholar
• Harrison J. The diffusion approximation for tandem queues in heavy traffic. Adv. Appl. Probab. (1978) 10:886–905Crossref, Google Scholar
• Heath D., Resnick S., Samorodnitsky G. Heavy tails and long range dependence in on/off processes and associated fluid models. Math. Oper. Res. (1998) 23:145–165Link, Google Scholar
• Kella O. Makron-modulated feedforward fluid networks. Queueing Systems (2001) 37:141–161Crossref, Google Scholar
• Konstantopoulos T., Lin S.-J., Glasserman P., Sigman K., Yao D. Fractional Brownian approximations of queueing networks. Stochastic Networks (1996) 117(Springer, New York) 257–273Lecture Notes in StatisticsCrossref, Google Scholar
• Mandelbaum A., Massey W., Reiman M. Strong approximation for Markovian service networks. Queueing Systems (1998) 30:149–201Crossref, Google Scholar
• Mikosch T., Stegeman A. The interplay between heavy tails and rates in self-similar network traffic. (1999) . Technical report, Department of Mathematics, University of Groningen, Groningen, The NetherlandsGoogle Scholar
• Mikosch T., Resnick S., Rootzen H., Stegeman A. Is network traffic approximated by stable Lévy motion or fractional Brownian motion. Ann. Appl. Probab. (2002) 12:23–68Crossref, Google Scholar
• Reiman M. Queueing networks in heavy traffic. (1977) . Ph.D. thesis, Department of Operations Research, Stanford University, Stanford, CAGoogle Scholar
• Reiman M., Disney R., Ott T. The heavy traffic diffusion approximation for sojourn times in Jackson networks. Applied Probability–Computer Science, the Interface (1982) II(Birkhauser, Boston, MA) 409–422Crossref, Google Scholar
• Samorodnitsky G. Long range dependence, heavy tails and rare events. (2002) . Lecture notes, MaPhySto, Centre for Mathematical Physics and Stochastics, Aarhus, DenmarkGoogle Scholar
• Samorodnitsky G., Taqqu M.Stable Non-Gaussian Random Processes (1994) (Chapman and Hall, New York) Google Scholar
• Smith F. D., Hernandez F., Jeffay K., Ott D. What TCP/IP protocol headers can tell us about the Web. Proc. ACM SIGMETRICS 2001/Performance 2001 (2001) (Cambridge, MA)245–256Crossref, Google Scholar
• Taqqu M., Willinger W., Sherman R. Proof of a fundamental result in self-similar traffic modeling. Comput. Comm. Rev. (1997) 27:5–23Crossref, Google Scholar
• Whitt W.Stochastic-Process Limits. An Introduction to Stochastic-Process Limits and Their Applications to Queues (2002) (Springer, New York) Crossref, Google Scholar