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In baseline rebuild, the transfer capacity of the spare server can become the bottleneck even if the remaining servers have abundant idle capacities available An alternative approach is to rebuild the unavailable data units before transferring them to the spare server In this way, only the rebuilt data are sent to the spare server and hence the limited transfer capacity of the spare server can be better utilized To achieve this, we can employ a distributed rebuild scheme to distribute the rebuild computations over all the remaining servers We rst divide the unavailable data into (N S 1) equalsize subsets, with each subset then rebuilt by one of the remaining (N S 1) servers, as shown in Figure 146.

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Instead, one may want to watch a runtime time-history display and save corresponding values of r and ISE in two n-dimensional arrays declared with

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The server responsible for a subset will receive the required data/redundant units from the other (N S 2) servers, rebuild the unavailable units, and then send the rebuilt units to the spare server for storage To derive the rebuild rate of the distributed rebuild algorithm, we rst note that the sum of transfer rates in and out of the remaining (N S 1) servers is equal to SS (1 )(N S 1) Second, to rebuild each data unit we need 2(N S 2) transfers (half for transmission and the other half for reception) of data/redundant units from the other (N S 2) servers to the rebuild server the server responsible for rebuilding the unavailable data unit.

ARRAY rr[n], ise[n]

Note that we need only (N S 2) transmissions instead of (N S 1) because the rebuild server already has one of the data/redundant units stored locally, and so no transfer over the network is needed Therefore, we can compute the rebuild rate Rdistributed from Rdistributed = SS (1 )(N S 1) SS (1 )(N S 1) = 2(N S 2) + 1 2N S 3 (145).

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Interestingly, being the bottleneck in baseline rebuild the spare server is no longer the limiting factor in distributed rebuild. The following theorem shows that the rebuild data rate Rdistributed is always smaller than the transfer capacity of the spare server, regardless of the system utilization . Theorem 14.2. In distributed rebuild, the rate of data transfer from the active servers to the spare server will never exceed the capacity of the spare server. Proof. We note that (N S 1) 2(N S 3) for all N S 2 in (14.5) thus Rdistributed SS (1 ) SS . The corresponding rebuild time in distributed rebuild is thus given by U Rdistributed U (2N S 3) SS (1 )(N S 1)

One can then plot, cross-list, and analyze corresponding ise[i] and r[i] values later on 2 A replicated-model (vectorized) study (Section 4-2b) inherently implies declaration of an n-dimensional parameter array (vector) r and an n-dimensional state vector ISE The experiment-protocol script fills the r array and makes a single simulation run:

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(14.6)

ARRAY r[n], | STATE x[n], , ISE[n] for i = 1 to n | -set parameter values r = r0 + (i 1) * DELr next ------------------------drun

In distributed rebuild, the spare server is never fully utilized. This is due to the fact that for every data unit rebuilt, a total of (2N S 3) data/redundant units will need to be transferred among the remaining active servers. By contrast, the ratio is only (N S 1) in baseline rebuild, albeit at the cost of (N S 1) times more capacity required at the spare server. In other words, in baseline rebuild the remaining servers are underutilized while in distributed rebuild the spare server is underutilized. This suggests a mixed algorithm to rebuild part of the data using distributed rebuild and the rest by baseline rebuild to maximize the server utilizations to reduce the rebuild time.

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