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Due to the growing demand for Cloud Computing services, the need and importance of Distributed Systems cannot be underestimated. However, it is dificult to use the traditional Message Passing Interface (MPI) approach to implement synchronization, coordination, and prevent deadlocks in distributed systems. This difficulty is lessened by the use of Apache's Hadoop/MapReduce and Zookeeper to provide Fault Tolerance in a Homogeneously Distributed Hardware/Software environment. In this book, a mathematical model for the availability of the JobTracker in Hadoop/MapReduce using Zookeeper's Leader Election Service is examined. Though the availability is less than what is expected in a k Fault Tolerance system, this approach makes coordination/synchronization easy, reduces the effect of Byzantine faults, and provides scalability for distributed applications.