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14.7 Numerical Results
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To illustrate and compare performances of the rebuild algorithms we consider a system of N S = 5 active servers and one spare server. Each server has 200GB storage, so the system has a total of 1TB storage, including the redundant units. We assume a server transfer capacity of 600Mbps, e.g., using Gigabit Ethernet links. Figure 14.7 plots the data rebuild rate versus server utilization for all the rebuild algorithms. We include the data rebuild rate for reloading data from back-up for the sake of comparison. Note that this data rebuild rate is also the upper bound. We observe that for baseline rebuild, the data rebuild rate is constant at SS /(N S 1) for (1 1/(N S 1)), even if the remaining active servers are lightly loaded and have idle capacities available. As the system utilization approaches one, the rebuild rate drops quickly. Distributed rebuild performs better than baseline rebuild when the server utilization is low (e.g., 0.55), but it deteriorates earlier when the system utilization increases. This is because in distributed rebuild the active servers need to receive data transmissions from other servers in addition to sending data to other servers, and thus consume considerably more transfer capacity than baseline rebuild. Finally, as expected, the mixed distributed baseline rebuild gives the best performance in all cases.
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Algorithms for Server Rebuild
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600 Data Rebuild Rate (Mbps)
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0.4 0.6 System Utilization
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Reload from back-up Baseline rebuild Distributed rebuild Mixed distributed-baseline rebuild
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Figure 14.7 Data rebuild rate versus system utilization
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Figure 14.8 shows the time required to completely rebuild a server s worth of data (200GB). Interestingly, for system utilization 0.75 performances of the baseline rebuild algorithm and the mixed distributed baseline algorithm converge. This is because at high system utilization the remaining active servers become the bottleneck, and so it is better to switch to the baseline rebuild algorithm which consumes less transfer capacities of the active servers than distributed rebuild. In this case the mixed distributed baseline algorithm simply allocates all transfer capacity to baseline rebuild. Finally, we plot in Figure 14.9 the rebuild time versus the number of servers in the system under a system utilization of = 0.5. The key observation is that the baseline rebuild algorithm is not scalable the rebuild time increases with the number of servers in the system. This is because in baseline rebuild the maximum rebuild rate is limited by the transfer capacity of the spare server. Thus, as the number of servers increases, so will the number of data/redundant units that need to be sent to the spare server to rebuild an unavailable data unit, thereby resulting in longer rebuild time. By contrast, the rebuild times of distributed rebuild and mixed distributed baseline rebuild do not increase signi cantly with increases in the number of servers and so are much more
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Rebuild Time (hours)
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0.4 0.6 System Utilization
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Reload from back-up Baseline rebuild Distributed rebuild Mixed distributed-baseline rebuild
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Figure 14.8 Rebuild time versus system utilization
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scalable. For example, under a system utilization of = 0.5, a mixed distributed baseline rebuild can complete the rebuild process in 2.61 hours and 2.87 hours for a 16-server and 64-server system, respectively. Thus, if no new server failure occurs within this period, the system can then resume normal operation and be ready to sustain a new server failure in the future.
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14.8 Summary
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In this chapter we addressed the issue of rebuilding the data lost in a failed server to a spare server so that the system can resume normal operation. Using a model incorporating the transfer capacity of the servers, the system utilization, and other system parameters, we showed that the mixed distributed-baseline rebuild algorithm can achieve the maximum rebuild rate. Moreover, the algorithm is completely automatic, and transparent to existing streaming sessions. The numerical results showed that such a data rebuild process can be completed in a reasonably short time (a few hours) and thus can enhance the reliability of the system.
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