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This means that it is not possible to have a single ow of data exceeding 622 Mbps While that might seem like an extremely large ow of data, when considering macro ows between two major hubs on a large service provider s network, this is not excessive Given all these downsides, you might be wondering why anyone in their right mind would choose to use ATM as a transport for IP packets There must have been some reasons why, in the mid to late 1990s, many of the largest service providers in the world relied upon ATM in their backbones There were, of course, excellent reasons, not least of which was scalability! Prior to ATM, many large ISPs had used multiple DS-3s and Frame Relay switches to create an overlay network.

Proof Step 1. Let k = 1. With no loss of generality, we assume that I = [0, 1]. De ne X(n) (t) as the dyadic polygonal approximation of X(t). As in the proof of Theorem 1.6, X(n) (t) X(t) tends uniformly to zero and is bounded by the random variable 2 supt I |X(t)|, which has nite moments of all orders, because of the results of 2. Using dominated convergence, it follows that Var(X(n) (t)) converges uniformly for t I to Var(X(t)). So for n large enough, Var(X(n) (t)) b for some b > 0 and all t [0, 1]. (The reader might show this using the more elementary arguments of Section 1.2.) For such an n, a.s. the process X(n) (t) does not take the value u at the partition points j 2 n (j = 0, 1, . . . , 2n ), since the random variable X(t) has a density

However, as the ows of data grew, it became necessary to run more and more parallel links between each pair of hubs At the time, DS-3 was the largest interface available on frame relay switches ATM was the obvious next step for the service providers in need of greater capacity on individual links since ATM switches had interfaces running at OC3 and OC12 and could be used in a familiar overlay scheme ATM also has great qualities for traf c engineering This allowed ISPs to make better use of expensive bandwidth, and ef ciently reroute traf c around failures and bottlenecks However, as networks inevitably continued growing, the SAR limitation became significant With the largest available SAR being 622 Mbps, it was necessary to connect routers to a switch with several links in order to carry suf cient traf c.

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In the late 1990s, the largest service providers started building new core networks using Packet over SONET and MPLS This combination provided many (but not all) of the bene ts of ATM without the constraint of requiring SAR..

for j, k = 1, . . . , d, with the notation = ( 1 , . . . , d )T , x = (x1 , . . . , xd )T . (c) Prove that if the eld has C 1 sample paths, 2 < . Let I be a Borel subset of Rd ; then E u (X, I ) = d (I ) (u)E ,

This refactoring introduces a session as a fa ade over another EJB component that aggregates a number of fine-grained methods into fewer, coarse-grained methods and effectively creates subsystem layering. This may be done over a specific entity to aggregate individual attribute accessors or mutators into coarse-grained bulk accessor or mutator methods, or over multiple sessions and/or entities to implement a sequenced workflow process by aggregating the various fine-grained steps into a coarser-grained process.

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