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traf cs that circulate between regional networks, in other words on the Internet, we often nd scale invariance, and almost never nd traf c obeying the traditional rules Certain types of digitized video traf c also exhibited the phenomenon (see Beran et al [BER 95]), though over a less spectacular range than for Ethernet In 1995, Willinger et al [WIL 95] returned to Ethernet data for a more re ned analysis, examining not only the traf c itself but also its components, and once again found scale invariance We will consider this example and its theoretical offshoots in section 123 Numerous discoveries followed (for a more complete list, see the bibliography in [WIL 96]) and almost always scale invariance was found, as well as heavy tails for many quantities such as the length of bursts By this quali er heavy , we understand a slow decrease in probability density at in nity, which gives rise to in nite variances or even means Despite the weight of abundant empirical evidence, resistance against this new wave in traf c was not slow in showing itself Essentially, this resistance was divided between those who preferred to believe that the evidence was in fact merely the artifact of corruptive non-stationarities, and others who thought that a continuum of scales could be effectively approximated by a suf ciently large number of discrete scales, obviating any need to talk about fractals Although it is true that, in many cases, such objections were merely a re ex against the shock of new ideas, it is nevertheless true that non-stationarities can very well be confused with the increased variability of scale invariant processes One of the rst methods used to detect scale invariance and to estimate its exponent was based on equation (123) From X (m) , we estimate v (m) using the standard variance estimator, and then plot its logarithm against log(m), the time-variance plot The slope in this plot corresponds to an estimate of This method, although simple and with a low calculation cost, suffers from many statistical defects: a notable bias, a quite large variance, and in particular a poor robustness with respect to non-stationarity This last defect is shared, at least partly, by many other methods (see [TAQ 95] for a comparison of several methods) The need to measure in a reliable way stimulated further contributions to the already sizable statistical literature In fact, the high volume of teletraf c data excluded the use of the estimators typically in use, which had good statistical performance, but very high computational costs A semi-parametric method based on wavelets, introduced into the eld by Abry and Veitch [ABR 98], solved these problems thanks to its low complexity, only O(n), without sacri cing robustness, and excellent statistical performance due to the natural match between wavelet bases and scale invariant processes Wavelet analysis operates jointly in time and scale It replaces the time signal X(t) with a set of coef cients, the details dX (j, k), j, k Z, where 2j denotes the scale, and 2j k the instant, around which the analysis is carried out In the wavelet domain, equation (123) is replaced with var[dX (j, k)] = cf C 2(1 )j , where the role of m is played by scale, of which j is the logarithm, cf is the frequency analog of c and is proportional to it, and where C is independent of j The analog of the variance-time plot, the graph of the estimates of log(var[dX (j, )]) against j, is called the logscale diagram and constitutes a spectrum estimate of the process, where low frequencies correspond to large scales (on the.

Page 63 The lines of responsibility for project development present another difficulty within the project management context Most projects are staffed with personnel borrowed (sometimes on an extended basis) from their line departments A project manager faces the unique and vexing challenge of attempting to motivate and secure the commitment of a disparate group of functional employees who often feel little personal identification with the project and preserve a profound functional loyalty This problem is further exacerbated when the project managers do not have the freedom to perform formal performance appraisals on these temporary employees When set against this unique backdrop, project control becomes increasingly problematic The irony is that most organizations, including those that have experienced terrible difficulties with their projects, will readily acknowledge the necessity of using project management in their operations What is particularly frustrating to them is that they continue (seemingly) to make the same mistakes again and again as one project after another falls further and further behind, goes increasingly over budget and then is either canceled outright or simply slides into oblivion Or, the project is finished and transferred to a customer who no longer wants it or is expecting something so different from the finished output that it is useless to them In our experience, the problems that underscore such shaky track records are usually legion; however, one common denominator shared by most troubled organizations is their unwillingness or inability to learn from past failure Project review meetings, so important as a learning tool, are either perfunctory (in the case of successes) or are ignored (in the case of failures) This is a pity and it is with this message in mind that we have developed our program of customer-based project management as detailed throughout this book We are convinced that the more we are willing to look at a project s status from the perspective of the customer, the greater the likelihood that the finished product will be both used and useful It is our hope that each of us is strong enough.

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Logscale Diagram, N=2 [ (j1,j2)= (3,15) Q= 0011384 ] Logscale Diagram, N=2 [ (j1,j2)= (3,15) Q= 0011384 ]

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clustering, which is a scheme that has been proposed for organizing nodes in a hierarchy; reputation schemes that allow good or bad reputation of nodes to be shared across the network; schemes that encourage node cooperation by providing incentives

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Figure 122 Wavelet analysis of scale invariance The Logscale diagram, an estimated wavelet spectrum (in log-log coordinates), is shown for the data Left: Ethernet pAug The slope gives an estimate of 1 with good properties, which is reliable from j = 3 We obtain 1 = 059 001 Right: the number of new TCP connections in 10 ms bins on an Internet link We see two scale ranges, from j = 1 to 8 and j = 8 to 19 Daubechies 2 wavelets were used

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