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One potential problem with the concurrent-push architecture, and any parallel server architectures in general, is reliability. As the system distributes video data over multiple servers, failure of a single server will cripple the entire system. Worst still, as the system is scaled up to more users, more servers will be needed and consequently the system-wide reliability will decrease accordingly. Drawing similar principles from disk array researches, we present in this chapter fault-tolerant algorithms to improve the system reliability. In particular, we address three key problems pertaining to supporting fault tolerance in the concurrent-push architecture, namely, redundancy management, redundant data transmission protocol, and real-time fault masking. First, redundant data based on erasure codes are introduced to video data stored in the servers, which are then delivered to the clients to support fault tolerance. Despite the success of distributed redundancy striping schemes such as RAID-5 in disk array implementations, we discover that similar schemes extended to the server context do not scale well. Instead, we develop a redundant server scheme that is both scalable and consumes less server buffer. Second, two protocols are introduced to control the transmission of redundant data to the clients, namely, forward erasure correction (FEC) and progressive redundancy transmission (PRT). These two protocols achieve different tradeoffs between bandwidth overhead, implementation complexity, and client buffer requirement. Finally, we derive the amount of client buffers required so that non-stop, continuous video playback can be maintained during server failure.

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To support server-level fault tolerance, we need redundant data so that a client can re-compute the unavailable video data after server failures. The problem of correcting data errors has been studied extensively in the literature. According to coding theory [1], one can encode a set of symbols with redundancies so that errors occurring within the set can be corrected later. However, server failure is slightly different in the sense that there is really no error in the coding sense. Instead, a server failure introduces erasures the absence of data.

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where 2h is a small class-interval width For a given Monte Carlo sample (x[1], x[2], , x[n]) of x-values, we again estimate p by the sample average <u(x X)> of an indicator function u(x X) equal to 1 if X h < x < X + h and 0 otherwise Specifically, u(x X) rect((x X)/h), where rect(x) is the library function defined in Fig 2-5c For small window widths 2h we thus estimate the probability density x(X) p/2h by

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Errors and erasures are different, because, for errors, data are still being received but the content may be corrupted. In case of erasure, the expected data are simply missing and hence no erroneous data will be received. Here we have implicitly assumed that the server is fail-stop, i.e., it stops sending out data upon failure. This type of failure could be caused by disk subsystem failure, network failure, power loss, or even software crashes. In any case, erasures are introduced into the video stream because data stored in the failed server will become unavailable. According to coding theory, to recover an erased symbol (a unit of data) in a codeword (also called a parity group, or a stripe), one needs to encode the data with at least one redundant symbol per codeword. One well-known coding algorithm called Reed-Solomon Erasure correction (RSE) code [2, 3] can encode data with any codeword size and level of redundancies. If one needs to protect the system from only single-server failure, then an even simpler code parity can be used instead. For simplicity, we assume in this chapter a generic code where each additional redundant symbol can recover one erasure. Drawing related principles from RAID [4], Figures 11.1 and 11.2 depict the proposed redundant striping policies for block striping and sub-schedule striping. The basic idea is the same introduces one or more redundant stripe units in every stripe. The redundant units are

f(X) (1/2h) <rect [(x X)/h]> (1/2hn)

Q bytes (Transaction/Striping Size)

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rect ((x[k] X)/h) (4-13)

to it:

Q bytes (Transaction Size)

For random samples of size n, 2hn f(X) has a binomial distribution with success probability p, [4] so that

U bytes (Striping Size)

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