By Prasad Yarlagadda, Yun-Hae Kim

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8%. In an extreme case, if the IaaS service is offline, regardless of the PaaS service availability, deploy availability is reduced to zero. The deploy availability relationship between AU and AS which provides service for AU can be expressed as this: = × (4) where, is standalone availability of the AU service, is the deploy availability of available = 100%, = . set AS which supports the AU deployment. Obviously, when After getting the quantitative relationship among the DA availability of each AU in AS, which depends on its underlying service, you can easily define and derive a DA availability of AS.

99999% or the like. Since in any AS, each AU is based on the same design and deployment equivalent. Therefore, they own the same standalone availability. 2) = 1 − 1 − (3) A default arbiter algorithm of an AS is to provide the most appropriate availability for the service applicants. When all the m AU of AS are unable to work simultaneously, this AS as a whole is failed [4, 5]. Obviously, the probability of m AU fails at the same time is 1 − . Thus, AS can provide . maximum availability 1 − 1 − Since 0 ≤ ≤ 1, it can be proved by mathematical induction: 1 − 1 − ≥ .

MapReduce: simplified data processing on large clusters[J]. Communications of the ACM, 2008, 51(1): 107-113. [2]Condie T, Conway N, Alvaro P, et al. MapReduce Online[C]//NSDI. 2010, 10(4): 20. [3]Li F, Ooi B C, et al. Distributed data management using mapreduce[J]. ACM Computing Survey, 2013. [4]Zaharia M, Konwinski A, Joseph A D, et al. Improving MapReduce Performance in Heterogeneous Environments[C]//OSDI. 2008, 8(4): 7. [5]ChenQ,Zhang D,et al. Samr: A self-adaptive mapreduce scheduling algorithm in heterogeneous environment[C]//Computer and Information Technology (CIT).

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Computers and Information Processing Technologies I by Prasad Yarlagadda, Yun-Hae Kim
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