Markov processes in data center networks

Abstract

A data center network is an important infrastructure in various applications of modern infor- mation 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 d -1 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 RG-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.