Weitere Kapitel dieses Buchs durch Wischen aufrufen
Heavy tails in work loads (file sizes, flow lengths, service times, etc.) have significant negative impact on the performance of queues and networks. In the context of the famous Internet file size data of Crovella and some very recent data sets from a wireless mobility network, we examine the new class of LogPH distributions introduced by Ramaswami for modeling heavy-tailed random variables. The fits obtained are validated using separate training and test data sets and also in terms of the ability of the model to predict performance measures accurately as compared with a trace-driven simulation using NS-2 of a bottleneck Internet link running a TCP protocol. The use of the LogPH class is motivated by the fact that these distributions have a power law tail and can approximate any distribution arbitrarily closely not just in the tail but in its entire range. In many practical contexts, although the tail exerts significant effect on performance measures, the bulk of the data is in the head of the distribution. Our results based on a comparison of the LogPH fit with other classical model fits such as Pareto, Weibull, LogNormal, and Log-t demonstrate the greater accuracy achievable by the use of LogPH distributions and also confirm the importance of modeling the distribution in its entire range and not just in the tail.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
S. Ahn, Joseph H. T. Kim, and V. Ramaswami. A New Class of Models for Heavy Tailed Distributions in Finance and Insurance Risk. In Insurance: Mathematics and Economics, volume 51, pages 43-52, 2012.
S. Ahn and V. Ramaswami. Bilateral phase type distributions. Stochastic Models, pages 239-259, 2005.
S. Asmussen, O. Nerman, and M. Olsson. Fitting Phase-Type Distributions via the EM Algorithm. Scandinavian Journal of Statistics, 1996.
M. E. Crovella and A. Bestavros. Self-similarity in world wide web traffic: Evidence and possible causes. Performance Evaluation Review, 1996.
Chlebus E. and Divgi G. A Novel Probability Distribution for Modeling Internet Traffic and its Parameter Estimation. In IEEE Global Telecommunications Conference - GLOBECOM, 2007.
A. Ghosh, R. Jana, V. Ramaswami, J. Rowland, and N. K. Shankaranarayanan. Modeling and characterization of large-scale Wi-Fi traffic in public hot-spots. In INFOCOM, 2011.
G. Latouche and V. Ramaswami. Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM Series on Statistics and Applied Probability, 1999.
Mitzenmacher M. and Tworetzky B. New models and methods for file size distributions. In Allerton Conference on Communications, Control and Computing, 2003.
M. F. Neuts. Probability distributions of phase type. Liber Amicorum Prof. Emeritus H. Florin, pages 173-206, 1975.
M. F. Neuts. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, 1981.
Ward Whitt. Stochastic- Process Limits. Springer, 2002.
- Modeling Heavy Tails in Traffic Sources for Network Performance Evaluation
- Springer India
Neuer Inhalt/© ITandMEDIA, Product Lifecycle Management/© Eisenhans | vege | Fotolia