A. Erramilli and R. P. Singh, "Application of deterministic chaotic maps to characterize broadband traffic," in Proc. 7th ITC Specialists Seminar, Morristown, NJ, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....an initial state as well as a set of dynamical laws. The method of using chaotic deterministic maps approach to modeling packet traffic was first suggested by Erramilli and Singh in 1990, when they demonstrated that it is possible to generate complex traffic behavior with low order chaotic systems [14]. Such systems exhibit a chaotic behavior that arises from a property known as Sensitive dependence on Initial Conditions (SIC) If one considers a chaotic map defined as X n 1 = f (X n ) and two trajectories with nearly identical initial conditions X 0 and X 0 e, then SIC can be stated ....

Erramilli A. and Singh R.P., Application of Deterministic Chaotic Maps to Characterize Broadband Traffic, Proceedings of the 7th ITC Specialists Seminar, Morristown, USA, 1990.

....types which will be important in future multiservice networks. These considerations motivate the present study of alternative arrival processes. The need for alternative models has been appreciated before. Apart from the authors of the measurement studies described below, Erramilli and Singh [8] have considered the possibility of employing chaotic deterministic maps with intermittency properties, to generate arrival streams with long range dependence and inter burst gaps of all sizes. The present models have not yet been refined to the point where one would expect good quantitative ....

A. Erramilli and R. P. Singh, "The Application of Deterministic Chaotic Maps to Characterize Traffic in Broadband Packet Networks," Proceedings, ITC Specialist Seminar, 1990.

....provided by the performance analysis. Only with a thorough understanding of the traffic and with appropriate models, is the study of network performance and effective design of networks possible. Many different approaches to traffic modeling have been proposed in the literature [1] 7] 9] 11] 16][19][24] Since the majority of real traffic possesses correlated interarrival sequences which have a major effect on queue performance, the focus has been to build up models which best capture the correlation characteristics of different traffic. General traffic modeling involves the following ....

....by the real traffic, or,itresults in the similar performance as the real traffic does. Lu, Petr,Frost Survey of Source Modeling for ATM Networks September 1993 7. Chaotic Map Approach While the self similar phenomena reveals contradictions with conventional models, Erramilli and Singh [19] state that the conventional models in the literature, though they have been used with some degree of success, they do not capture all the relevant statistical characteristics of the process. They address the problem of packet traffic modeling from a fundamentally different perspective by using ....

A. Erramilli and R.P.Singh, "The Application of Deterministic Chaotic Maps to Characterize Traffic in Broadband Packet Networks," 7th ITC Seminar,Session 8, Oct 1990

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A. Erramilli and R. P. Singh, "Application of deterministic chaotic maps to characterize broadband traffic," in Proc. 7th ITC Specialists Seminar, Morristown, NJ, 1990.

....to model such ON OFF behavior. We are motivated in part by experiences in a number of other disciplines in which chaotic maps have been used as efficient generators of fractal processes. Our approach is based on earlier work on the application of deterministic chaotic maps to model traffic flows [5][6] 7] 8] Specifically, we consider the simplest class of chaotic systems, known as one dimensional (1 D) chaotic maps, in which the evolution of a state variable x over discrete time n is described by a deterministic nonlinear transformation . We can model packet traffic sources using such maps ....

A. Erramilli and R.P. Singh, "Application of Deterministic Chaotic Maps to Characterize Broadband Traffic", 7th ITC Specialists Seminar, Morristown, 1990.

.... [165] aggregation of simple short range dependent models) and [135, 294, 414, 416] wavelet analysis) Further models are considered in [16,19,176,313,379,386,403,417] A radically different approach to modeling self similar phenomena relies on ideas from the theories of chaos and fractals [73,97,118 120,124,125,171,250,287,337,344,345,377]; for a general discussion on chaos, probability and statistics, see [29, 46, 47] An overview of statistical inference methods for self similar models and random processes with long range dependence can be found in [22, 24] the papers [392 394] listing additional techniques. More specifically, ....

A. Erramilli and R. P. Singh. Application of deterministic chaotic maps to characterize broadband traffic. In Proceedings of the ITC 7th Specialist Seminar, Livingston, NJ, 1990.

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A. Erramilli and R.P. Singh , "Application of Deterministic Chaotic Maps to Characterize Broadband Traffic", 7th ITC Specialists Seminar, Morristown, 1990.

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A. Erramilli and R.P. Singh, "The Application of Deterministic Chaotic Maps to Characterize Traffic in Broadband Packet Networks," 7th ITC Seminar, Session 8, Oct 1990

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A. Erramilli and R.P. Singh, "The Application of Deterministic Chaotic Maps to Characterize Traffic in Broadband Packet Networks," 7th ITC Seminar, Session 8, Oct 1990

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A. Erramilli, R. P. Singh, "An Application of Deterministic Chaotic Maps to Characterize Packet Traffic", preprint, 1992.

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