A. Erramilli, D. Gosby, W.Willinger, "Engineering for Realistic Traffic: A Fractal Analysis of Burstiness", Proc of Special ITC Seminar, Bangalore, India, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the design and operation of telephone networks. In contrast, traffic arrival processes in packet based networks are much more bursty and intermittent. A number of recent measurement studies from the full range of packet based networks and services (ISDN packet, Ethernet, SS7, VBR Video) 2][4][9] 11] 12] 13] indicate that packet traffic is characterized by interarrival times that decay with heavy tails, by variances that decay as a fractional power of the sample size, by a power spectrum that is divergent near the origin, and by correlations that are long range dependent. A number of ....

....heavy tails, by variances that decay as a fractional power of the sample size, by a power spectrum that is divergent near the origin, and by correlations that are long range dependent. A number of analytical and experimental studies have established the performance significance of these features [4][8] 14] More recent measurement work has focused on the physical basis of the self similarity observed in the full range of packet based networks. Based on a preliminary analysis of individual sources on an Ethernet, Willinger [17] observes that individual sources can be represented by the ....

A. Erramilli, D. Gosby, W.Willinger, "Engineering for Realistic Traffic: A Fractal Analysis of Burstiness", Proc of Special ITC Seminar, Bangalore, India, 1993.

.... in [23, 310] Other stochastic approaches to modeling self similar features are considered in [28, 156, 160, 274, 275, 369, 371] based on shot noise processes) 373] linear models with long range dependence) 30,261, 262, 276, 284, 411, 412] renewal reward processes and their superposition) [116, 283,401] (renewal processes or zero rate processes) 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 ....

A. Erramilli, D. D. Gosby, and W. Willinger. Engineering for realistic traffic: A fractal analysis of burstiness. In Proceedings of the Bangalore Regional ITC Seminar, Bangalore, India, 1993.

....likely cause of the 1 f noise illustrated in Figure 3. 3.2.3. Fractal Dimensions Fractal dimension can be used as an indicator of the burstiness of a traffic stream. Smooth processes have a dimension of 1, with decreasing dimension corresponding to increasing burstiness. It is demonstrated in [11] that over time scales of engineering interest, actual traffic is characterized by dimensions less than 1. The correlation measure for an arrival process at a time scale is equal to the expected number of arrivals in an interval of length 2 centered on an arrival point. It is estimated by counting ....

....generated by the intermittency map using the parameters d = 0.7 and = 10 4 . The iteration interval is taken to be 1 ms long. Actual data sets show strikingly similar behavior, with correlation dimensions less than 1, and well defined lower and upper cut offs of the power law scaling behavior [11]. A companion paper [12] examines the engineering significance of such behavior in more detail. Thus a simple two parameter map can capture several of the fractal properties observed in actual traffic. We next examine the feasibility of performance analysis with chaotic maps. 4. PERFORMANCE ....

A. Erramilli, D. Gosby and W. Willinger, "Engineering for Realistic Traffic: A Fractal Analysis of Burstiness," Proc of ITC Special Congress, Bangalore, India, 1993.

....times is that moments above a certain order may not exist. In particular, Meier Hellstern et al. observed that the best fit for the tail behavior of some data sets was obtained using interarrival densities with an infinite mean. The implications of this in queueing analysis are considered in [16] and by Veitch 92 [18] Slowly Decaying Variances: In conventional traffic processes, the variance of the arithmetic mean of a traffic sample (consisting of the time series of packet counts) decays inversely as the sample size, asymptotically. Erramilli and Willinger 93 6 Modeling Packet ....

....a set or an object, by some measure, fills the space in which it is embedded. It is well known that fractal dimensions quantify how nonuniformly the mass (for our purposes, the number of arrivals) is distributed within a set (the time line) and as such they are natural measures of burstiness [16]. Smooth processes have a dimension of 1, with decreasing dimension corresponding to increasing burstiness. It is shown in [16] that over time scales of engineering interest, actual traffic is characterized by dimensions less than 1. Central to the estimation of dimensions of practical data sets ....

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A. Erramilli, D. Gosby, W.Willinger, "Engineering for Realistic Traffic: A Fractal Analysis of Burstiness", preprint , to appear in Proc of Special ITC Seminar, Bangalore, India, 1993.

....impacts of self similarity by means of trace driven simulations; analysis of self similar traffic models; fast generation and simulation with self similar traffic. Early models of fractal traffic processes include Fractional Brownian Motion (FBM) Norros [34] zero rate renewal process models [11] [43] and deterministic chaotic maps [12] We will first summarize these approaches. The motivation for zero rate processes, based on renewal processes characterized by infinite mean inter arrival times, comes directly from Mandelbrot s early work on modeling bursty transmission errors [11] 43] ....

....models [11] 43] and deterministic chaotic maps [12] We will first summarize these approaches. The motivation for zero rate processes, based on renewal processes characterized by infinite mean inter arrival times, comes directly from Mandelbrot s early work on modeling bursty transmission errors [11] [43] In these approaches, the burstiness of packet traffic is captured by the power law exponent that characterizes the decay of the inter arrival time distribution (which is related to the notion of a fractal dimension) While zero rate processes may be appropriate models for quality of service ....

A. Erramilli, D. Gosby and W. Willinger, "Engineering for Realistic Traffic: A Fractal Analysis of Burstiness," Proc of ITC Special Congress, Bangalore, India, 1993.

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