| Summary: | A data center network is an important infrastructure in various applications of modern information technologies. Data centers store files with useful information, but the lifetime of these data centers is limited. Once a data center suffers from natural disasters and man-made damages, all the information stored in the files will be lost. Therefore, replicating important files in other data centers is necessary to increase the lifetime of these files in a data center network. In this study, we develop a more general framework for Markov processes in data center networks, that can provide an analysis of file replication processes. A file replication strategy duplicates each important file in at most <inline-formula> <tex-math notation="LaTeX">$d-1$ </tex-math></inline-formula> other data centers such that these files can remain in a data center network under a given data security level in the long term. In this regard, we achieve a sufficient stable condition of data center networks by using a matrix-geometric solution. Then, we provide an expression for the stationary average number of normally operating data center networks. We also develop a computational technique for file lifetime via phase type distribution and the <inline-formula> <tex-math notation="LaTeX">$RG$ </tex-math></inline-formula>-factorizations. Lastly, we hope that the methodology and results presented in this study are applicable to research on file lifetime and data security for more general data center networks with a replication mechanism.
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