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Zbl 0988.90003
Tsybakov, Boris; Georganas, Nicolas D.
Self-similar processes in communications networks. (English)
[J] IEEE Trans. Inf. Theory 44, No.5, 1713-1725 (1998). ISSN 0018-9448

From the introduction: The main objective of the present paper is to review and briefly discuss the known definitions and properties of second-order self-similar discrete-time processes, to supplement them with some more general conditions of self-similarity, to present a model for ATM cell traffic, and, finally, to find the conditions of model self-similarity. \par Section II contains definitions of exactly and asymptotically second-order self-similar processes, which we adopt. The most essential second-order properties of these processes are presented. A novelty here is the presentation of some unknown proofs and properties, as well as the presentation of all these properties in one paper. A comparison of different definitions is done, with discussion and comments. \par Section III gives a model of ATM cell traffic, the necessary and sufficient conditions for its exact self-similarity and a sufficient condition for its asymptotic self-similarity. The conditions are more general than others obtained earlier; they contain the known conditions as special cases. We reference earlier papers which are particularly relevant to the model and also discuss some other known models, which are linked, to our model. \par The proots of our results are placed in Appendices A--D. In this presentation, we need to use the concepts of the Karamata slow- and regular-variation theory. The definitions of slowly and regularly varying functions and sequences are given in Appendix E. For other known results in the theory, we refer to {\it N. H. Bingham, C. M. Goldie} and {\it J. L. Teugels} [Regular Variation. Cambridge, New York: Cambridge Univ. Press (1987; Zbl 0617.26001)]. A brief presentation of our results was given in [{\it N. Likhanov, B . Tsybakov} and {\it N. D. Georganas}, ``A model of self-similar communications-network traffic'', Proc. Int. Conf. ``Distributed Computer Communication Networks'' (DCCN'97) (Tel-Aviv, Israel, 1997), 212-217 (1997)].

MSC 2000:: *90B18 Communication networks
94A05 Communication theory
90B20 Highway traffic

Keywords: communication networks; slowly varying functions; second-order self-similar discrete-time processes; ATM cell traffic; self-similarity; Karamata slow- and regular-variation theory; regularly varying functions

Citations: Zbl 0617.26001

Cited in: Zbl 0992.68008

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