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where the multipliers M k re ect the ``state of the network'' and determine the amount of workload that the connection can send across the link at any given point in time. Small multipliers suggest heavy competition for the link, while large multipliers indicate that the connection can temporarily transmit at close to full speed. As we have seen earlier, the idea of successively fragmenting the total work-load into parts leads naturally to a multiplicative process or cascade. While the networking application justi es our choice of considering conservative cascades, our focus on an underlying binomial structure for the cascades is for simplicity. On mild independence assumptions on the multipliers (they should form a certain martingale) we are assured that we can talk about the limit of in nitely ne scales n 3 I and that this limit has interesting statistical properties. In fact, by experimenting with turning a constant bit-rate connection into a highly bursty one via an appropriately chosen conservative binomial cascade construction [14], we nd that the latter can closely match the way networking mechanisms operating on small time scales determine the actual ow of packets=bytes over the duration of a TCP connection. Moreover, when the traf c rate over a small time interval is described in terms of a conservative binomial cascade, it is explicitly multiplicative in nature (Eq. (20.32)); and as a result, the marginals of the traf c rate process over small time scales will automatically be approximately lognormal (e.g., apply CLT to the random variables log M k ). 20.4 TOWARD COMPLETE DESCRIPTIONS OF NETWORK TRAFFIC



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One of the most critical design rules for networked, highly available systems is to distinguish a host s network identity from the name used for a host supplying a network service. If that sentence seems like it was written by political spinmeisters, but you still understood it, skip the following list of requirements. Otherwise, here s what makes Internet protocol addressing interesting when designing for availability:





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The empirical nding that measured WAN traf c contains an additive component as well as a multiplicative component provides new motivation for and insights into developing a more complex description of the dynamic nature of actual network traf c. In the following, we discuss a simple workload model that exhibits selfsimilar as well as multifractal scaling but is not consistent with measured network traf c. Then we illustrate the changes that are required to turn this simple model into one that is consistent with actual traf c, not only with respect to the large-time and small-time scaling behavior of measured aggregate traf c rate processes, but also at the different layers in the IP protocol hierarchy. 20.4.1 A Simple Multifractal Workload Model

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Every host on a network must have at least one IP address. That IP address matches some hostname. We ve referred to these IP/hostname pairs as private or administrative addresses in previous discussions of failover mechanics. Private addresses are useful for things like telnet, rlogin, and rdist, where you need to ensure that you end up at a precise physical destination. Any network client looking for a service uses a hostname-to-IP-address mapping to find the required server. From the client s point of view, the IP address could correspond to a single physical location, a collection of machines, or a proxy service that forwards the request on to another server behind a firewall or redirector farm. The client doesn t really care; it only sees a logical location on the network. The converse is also true, though, in that clients want to find services at the same IP address over time. Reconfiguring clients to wander through the network looking for available servers isn t fast, easy, or reliable; clients should be able to rest assured that the IP addresses they use correspond to something that will be highly available. Services that are static or hosts that don t participate in any kind of redundancy scheme can use the same physical (private) name and logical (public) name. Your desktop machine is a good example; there s no need to give it multiple logical names. Services that move between hosts in an HA pair or services that correspond to one of several machines in a server farm use logical addresses that map to one or more physical addresses. Enter the concept of the virtual IP address.

To start, we consider the workload model discussed in Section 20.2.3, where userinitiated sessions (1) arrive in accordance with a Poisson process, (2) bring with

them a workload (eg, number of bytes, packets, ows, or TCP connections, session duration) that is heavy tailed with in nite variance, and (3) distribute the workload over the lifetime of the session at a constant rate A result by Kurtz [19] states that, over large enough time scales, the uctuations of the aggregate traf c rate around its mean value are well described by FGN, for a very general class of within-session traf c rate processes that includes the special case of constant bit-rate sessions Recall that the self-similar scaling property over large time scales (or equivalently, long-range dependence) is essentially due to the fact that the session sizes exhibit in nite variance, and that approximate Gaussianity follows from an application of the CLT, that is, from aggregating over a large number of independent sessions whose individual traf c rates are suf ciently ``tame.

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Apr 17, 2018 · You may be able to use third-party OCR software to retain more of the text format styles that are present in the source document image. Note As ...

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