Extreme-value analysis of teletra'c data

An empirically veri1ed characteristic of the expanding area of Internet is the long tailness of phenomena such as cpu time to complete a job, call holding times, 1les lengths requested, inter-arrival times and so on. Extreme values of the above quantities are liable to cause problems to the e'cient operation of the network and call for e7ective design and management. Extreme-value analysis is an area of statistical analysis particularly concerned with the systematic study of extremes, providing useful insight to 1elds where extreme values are probable to occur and have detrimental e7ects, as is the case of teletra'cs. In this paper, we illustrate the main elements of this analysis and proceed to a detailed application of extreme-value analysis concepts to a speci1c teletra'c data-set. This analysis veri1es, too, the existence of long tails in the data. c 2003 Elsevier B.V. All rights reserved.

[1]  Yuguang Fang,et al.  Call Performance for a PCS Network , 1997, IEEE J. Sel. Areas Commun..

[2]  T. Mikosch.  Heavy-tailed modelling in insurance , 1997 .

[3]  A. McNeil.  Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory , 1997, ASTIN Bulletin.

[4]  Gennady Samorodnitsky,et al.  LIVING ON THE EDGE , 2005 .

[5]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[6]  Sidney Resnick,et al.  Smoothing the Moment Estimator of the Extreme Value Parameter , 1999 .

[7]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[8]  Jon Danielsson,et al.  The method of moments ratio estimator for the tail shape parameter , 1996 .

[9]  Sidney Resnick,et al.  Smoothing the Hill Estimator , 1997, Advances in Applied Probability.

[10]  Richard L. Smith.  Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone , 1989 .

[11]  A. McNeil.  Extreme Value Theory for Risk Managers , 1999 .

[12]  S. Resnick.  Heavy tail modeling and teletraffic data: special invited paper , 1997 .

[13]  Walter Willinger,et al.  Statistical analysis of CCSN/SS7 traffic data from working CCS subnetworks , 1994, IEEE J. Sel. Areas Commun..

[14]  Nader Tajvidi,et al.  Extreme value statistics and wind storm losses: a case study. , 1997 .

[15]  John Panaretos,et al.  Extreme Value Index Estimators and Smoothing Alternatives: Review and Simulation Comparison , 2001 .

[16]  Ori Rosen,et al.  Comparison of estimation methods in extreme value theory , 1996 .

[17]  Jan Beirlant,et al.  Extremes in Non-Life Insurance , 1994 .

[18]  L. Haan,et al.  A moment estimator for the index of an extreme-value distribution , 1989 .

[19]  S. Resnick,et al.  Extreme Value Theory as a Risk Management Tool , 1999 .

[20]  Jon Danielsson,et al.  Beyond the Sample: Extreme Quantile and Probability Estimation , 1998 .

[21]  L. Haan,et al.  On the Estimation of the Extreme-Value Index and Large Quantile Estimation , 1989 .

[22]  M. Naldi,et al.  Measurement-based modelling of Internet dial-up access connections , 1999, Comput. Networks.

[23]  Jonathan A. Tawn,et al.  Modelling extremes of the areal rainfall process. , 1996 .

[24]  Walter Willinger,et al.  Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level , 1997, TNET.

[25]  J. Tawn,et al.  Extremal analysis of short series with outliers: sea‐levels and athletics records , 1999 .

[26]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[27]  S. Resnick,et al.  The qq-estimator and heavy tails , 1996 .

[28]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[29]  S. Resnick,et al.  Consistency of Hill's estimator for dependent data , 1995, Journal of Applied Probability.

[30]  B. M. Hill,et al.  A Simple General Approach to Inference About the Tail of a Distribution , 1975 .

[31]  J. Teugels,et al.  Practical Analysis of Extreme Values , 1996 .