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in which the positive constant k represents the smallest possible value of the random variable. In practice, random variables that follow heavy-tailed distributions are characterized as exhibiting many small observations mixed in with a few large observations. In such data sets, most of the observations are small, but most of the contribution to the sample mean or variance comes from the few large observations. This effect can be seen in Fig. 3.1, which shows 10,000 synthetically generated observations drawn from a Pareto distribution with a 1:2 and mean m 6. In Fig. 3.1(a) the scale allows all observations to be shown; in Fig. 3.1(b) the y axis is expanded to show the region from 0 to 200. These gures show the characteristic, visually striking behavior of heavy-tailed random variables. From plot (a) it is clear that a few large observations are present, some on the order of hundreds to one thousand; while from plot (b) it is clear that most observations are quite small, typically on the order of tens or less.

... Preface -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- A -- B -- C -- Refs Front -- Contents -- Help

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Each time an approach works to secure an application, it has the potential to become the pattern for the next round of applications For example, setting up identity services for the new applications potentially allows retrofitting of the legacy application to use the same service Establishing the controls inherent in a security architecture design from a priority list one application at a time is the most workable tactic Using such a methodical approach allows the patterns of the solution to emerge and be leveraged in the subsequent work 2 discusses the individual elements of data and privacy protection that must be controllable for access and accountability As you read through it, keep in mind that each of the nine elements of data or privacy protection presented there must be evaluated as to whether it should be controlled for access within the circumstances of the data use in your organization.

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Sample data from heavy-tailed distribution with a 1:2.

If the answer is yes, then the next question becomes how you can design to accomplish that required control within your architecture at all appropriate levels Any system s security architecture design will be judged, audited, and qualitatively ranked on how well it can control each of those elements..

An example of the effect of this variability on sample statistics is shown in Fig. 3.2. This gure shows the running sample mean of the data points from Fig. 3.1, as well as a level line showing the mean of the underlying distribution (6). Note that the sample mean starts out well below the distributional mean, and that even after 10,000 observations it is not close in relative terms to the distributional mean. 3.2.2 Heavy Tails in Computing Systems

In the early days of Java, life was simple, security policy was black and white, and external code was summarily untrusted. Since then, life has become more complex, security policy is now made to order, and code runs the gamut from trusted to untrusted (encompassing every state in between). Figure 1.6 in 1 illustrates the difference in trust models. It is easiest to get a grasp on the notion of trust assigned to Java classes by harkening back to ancient Java history circa 1996.

A number of recent studies have shown evidence indicating that aspects of computing and telecommunication systems can show heavy-tailed distributions. Measurements of computer network traf c have shown that autocorrelations are often related to heavy tails; this is the phenomenon of self-similarity [5, 10]. Measurements of le sizes in the Web [1, 3] and in I=O patterns [13] have shown evidence that le sizes can show heavy-tailed distributions. In addition, the CPU time demands of UNIX processes have also been shown to follow heavy-tailed distributions [7, 9]. The presence of heavy-tailed distributions in measured data can be assessed in a number of ways. The simplest is to plot the ccdf on log log axes and visually inspect the resulting curve for linearity over a wide range (several orders of magnitude). This is based on Eq. (3.1), which can be recast as d log F x a; x3I d log x lim so that for large x, the ccdf of a heavy-tailed distribution should appear to be a straight line on log log axes with slope a. An example empirical data set is shown in Fig. 3.3, which is taken from Crovella and Bestavros [3]. This gure is the ccdf of le sizes transferred through the network due to the Web, plotted on log log axes. The gure shows that the le size distribution appears to show power-law behavior over approximately three orders of magnitude. The slope of the line t to the upper tail is approximately 1:2, ^ yielding a % 1:2.

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