Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis

References

• Adler R.J., Feldman R.E., Taqqu M.S.A Practical Guide to Heavy Tails—Statistical Techniques and Applications (1998) (Birkhauser, Boston, MA) Google Scholar
• Andersen A.T., Jensen A., Nielsen B.F. Modeling and performance study of packet-traffic with self-similar characteristics over several time scales with Markovian arrival processes (MAP). Twelfth Nordic Teletraffic Seminar, NTS (1995) 12:269–283Google Scholar
• Asmussen S.Applied Probability and Queues (1987) (John Wiley, New York) Google Scholar
• Brill P.H. An embedded level-crossing technique for dams and queues. Journal of Applied Probability (1979) 16:174–186Crossref, Google Scholar
• Brill P.H. Single server queues with delay-dependent arrival streams. Probability in the Engineering and Informational Sciences (1988) 2:231–247Crossref, Google Scholar
• Cohen J.W.The Single Server Queue (1982) rev. ed.(North-Holland, Amsterdam)Google Scholar
• Crovella M.E., Bestavros A. Self-similarity in the Word Wide Web traffic: evidence and possible causes. IEEE/ACM Transactions on Networking (1997) 5:835–847Crossref, Google Scholar
• Crovella M.E., Taqqu M.S., Bestavros A., Adler R., Feldman R., Taqqu M.S. Heavy-tailed probability distributions in the World Wide Web. A Practical Guide to Heavy Tails: Statistical Techniques and Applications (1998) (Birkhauser, Boston, MA) Google Scholar
• Dye L. March. Old rules do not apply in new age: experts find Erlang phone formula fails to explain digital traffic jams. Los Angeles Times (1999) Google Scholar
• Erlang A.K. Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. Post Office Electrical Engineer's Journal (1917–1918) 10:189–197Google Scholar
• Feldman A., Whitt W. Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. Performance Evaluation (1998) 31:245–279Crossref, Google Scholar
• Feller W.An Introduction to Probability Theory (1971) 2d ed.(John Wiley, New York) Google Scholar
• Fischer M.J., Harris C.M. A method for analyzing congestion in Pareto and related queues. The Telecommunication Review (1999) (Mitretek Systems, McLean, VA) 15–2810Google Scholar
• Fowler T.B. A short tutorial on fractals and Internet traffic. The Telecommunication Review (1999) (Mitretek Systems, McLean, VA) 1–1410Google Scholar
• Greiner M., Jobmann M., Lipsky L. The importance of powertail distributions for modeling queueing systems. Operations Research (1999) 47:313–326Link, Google Scholar
• Gross D., Harris C.M.Fundamentals of Queueing Theory (1998) 3d ed.(John Wiley, New York) Google Scholar
• Harris C.M., Marchal W.G. Distribution estimation using Laplace transforms. INFORMS Journal on Computing (1998) 10:448–458Link, Google Scholar
• Heyman D. Some issues in performance modeling of data teletraffic. Performance Evaluation (1998) 34:227–247Crossref, Google Scholar
• Heyman D., Lakshman T.V. To appear. Long range dependence and queueing effects for VBR video. Performance EvaluationGoogle Scholar
• Leland W., Taqqu M., Willinger W., Wilson D. On the selfsimilar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Networking (1994) 2:1–13Crossref, Google Scholar
• Lucantoni D.M. The BMAP/G/1 queue: a tutorial. Models and Techniques for Performance Evaluation of Computer and Communication Systems (1993) 2:1–15Google Scholar
• Lucantoni D.M., Choudhury G.L., Whitt W. The transient BMAP/G/1 queue. Stochastic Models (1994) 10:145–182Crossref, Google Scholar
• Mood A.M., Graybill F.A., Boes D.C.Introduction to the Theory of Statistics (1974) 3d ed.(McGraw-Hill, New York) Google Scholar
• Nuets M.Structured Stochastic Matrices of M/G/1 Type and Their Applications (1989) (Marcel Dekker, New York) Google Scholar
• Nuets M., Jensen A., Iversen V.B. Modeling data traffic streams. TETETRAFFIC and DATATRAFFIC in a period of change (1991) (Elsevier Science Publishers, B.V. North Holland, Amsterdam) Google Scholar
• Park K., Kim G., Crovella M. On the relationship between file sizes, transport protocols, and self-similar network traffic. Proceedings 1996 International Conference on Network Protocols (1996) (Columbus, OH)171–180Crossref, Google Scholar
• Park K., Kim G., Crovella M.E. On the effect of traffic selfsimilarity on network performance. Proceedings of the SPIE Conference on Performance and Control of Network Systems (1997) (Boston, MA)296–310Crossref, Google Scholar
• Paxson V., Floyd S. Wide-area traffic: the failure of Poisson modeling. IEEE/ACM Transactions on Networking (1995) 3:226–244Crossref, Google Scholar
• Pitkow J. Summary of WWW characterizations. (1999) (Xerox Palo Alto Research Center, Palo Alto, CA) Google Scholar
• Willinger W., Paxson V. Where mathematics meets the Internet. Notices of the AMS (1998) 45:961–970Google Scholar
• Willinger W., Paxson V., Taqqu M.S., Adler R., Feldman R., Taqqu M.S. Self-similarity and heavy tails: structural modeling of network traffic. A Practical Guide to Heavy Tails: Statistical Techniques and Applications (1998) (Birkhauser, Boston, MA) Google Scholar