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We now show how to estimate the time to recover from the high-congestion event, where the high-congestion event is a large initial bandwidth x. We understand recovery to occur when the aggregate bandwidth is again less than or equal to the capacity c. In applications, we suggest examining the function of aggregate bandwidth giving both the probability of reaching that level and the recovery time from that level to assess whether or not capacity is adequate to meet demand. We assume that recovery occurs when the aggregate bandwidth drops below a level c, where x > c > m, with x being the initial level and m being the steady-state mean. Given that we know the current level of each level process, we know that the remaining holding time (and also the age) is distributed according to the levelholding-time stationary-excess distribution in Eq. (17.33). We use the LDP to approximate the conditional distribution of the level process for each source (in the steady state). The idea is to perform the appropriate change of measure (tilting) corresponding to the rare event.

17:46

There are a large and growing number of Java systems running the gamut from Java gizmos such as Java rings, through smart cards with built-in Java interpreters (the subject of this chapter), to complete Java Development Kits and Integrated Development Environments (IDEs) Java is simultaneously making inroads on many fronts In distributed systems, Java-based servers and servlets are becoming as common as Java clients As with any platform meant to interact in a networked world, there are security concerns with each flavor of Java These concerns take on a new urgency when it comes to e-commerce When electronic blips are money, the stakes change considerably It may be an inconvenience to lose a Web server that amounts to fancy brochureware; it is something else entirely if the Web server and its associated backend perform all customer transactions.

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where y* yields the supremum in Eq. (17.41). Put another way, comparing Eq. P (17.46) with Eq. (17.43) we see that y* is chosen to make the expectation of i Bi equal to x under the distribution p. In the homogeneous case, equality in Eq. (17.46) in the limit as the number of sources increases is due to the conditional limit theorem of Van Campenhout and Cover [26]. The limit can be extended to cover suitably regular heterogeneity in the bij , for example, nitely many types of source. We thus approximate the conditional bandwidth process by B t jB 0 x % E B t jB 0 x n Ji PP i I i % E Bij t jBij 0 y dGje y pj

Going with Biology Checking Out the Paracentric Approach Checking Out the Endocentric Approach Looking at Prospective New Roles for Directories

bik Pjk t ;

The security concerns raised by e-commerce are a large enough topic in their own right that there is no way we can do them justice here Of course, because Java is commonly used at all levels in e-commerce systems, the risks we identify have serious e-commerce implications This is especially true for Java cards Counterintuitively, Java is both growing and shrinking at the same time On one hand, the JDK, now up to Java 2, is doubling in size with each major release Just to complicate matters, at the same time as the explosive growth of the code base is occurring, the security architecture is undergoing major reorganization 2, "The Base Java Security Model: The Original Applet Sandbox," and 3, "Beyond the Sandbox: Signed Code and Java 2," detail the new model On the other hand, embedded Java systems like Card Java 2.

17:47

^ bik Pjk s :

x strip Java functionality down to bare bones The security model is not immune to this effect and has been deeply affected by Java's migration to smart cards These two diverse directions both have important security implications Java 2 involves fundamental changes to the Java security model as the Java sandbox metamorphoses itself into a trust-based system built on code signing Card Java 2x removes much of the sandbox, leaving smart card applets more room.

17:48

197 197 198 200

^ The Laplace transform Pjk s in Eq. (17.48) was derived in Theorem 17.6.1. We can numerically invert it to calculate the conditional mean as a function of time. We then can determine when E B t jB 0 x rst falls below c. In general, this conditional mean need not be a decreasing function, so that care is needed in the de nition, but we expect it to be decreasing for suitably small t because the initial point B 0 is unusually high.

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

Assuming that the relevant time is not too large, we might approximate the conditional mean bandwidth using a Taylor-series approximation E B t jB 0 x x tr x ; 17:49

17:50

Understanding Standard Data-Related Access Rights Exploring First-Person Access Roles and Rights Exploring Second-Person Access Roles and Rights Exploring Third-Person Access Roles Exploring Subordinate Roles Looking at Interim Steps

Copyright 1999 Gary McGraw and Edward Felten. All rights reserved. Published by John Wiley & Sons, Inc.

which has the advantage that no numerical inversion is required. Suppose the service capacity is c > E B 0 and we condition on B 0 > c. If r B 0 < 0, we can use Eq. (17.49) to approximate the rst time to return to c, the recovery time, by t x c =r x : 17:51

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