# American Institute of Mathematical Sciences

January  2014, 10(1): 151-166. doi: 10.3934/jimo.2014.10.151

## Performance analysis of a P2P storage system with a lazy replica repair policy

 1 College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China, China 2 Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501

Received  September 2012 Revised  June 2013 Published  October 2013

Peer-to-Peer (P2P) storage systems are a prevalent and important mode for implementing cost-efficient, large-scale distributed storage. Considering the random departure feature of the peers and the diverse popularity of the data objects, a proper number of replicas needs to be maintained, and a reasonable trigger threshold of replica repair needs to be set for high data availability and low system overhead. In this paper, based on the working principle of the lazy replica repair policy in a P2P storage system, a three-dimensional Markov chain model is constructed, and the model is analyzed in steady-state by using a matrix-geometric method. Then, the performance measures in terms of the availability of one data object, the average access latency, and the replication rate are given. Moreover, numerical results with analysis are provided to demonstrate how system parameters such as the replica number and the replica repair instant influence the system performance. Finally, we develop benefit functions to optimize the replica number and the repair trigger threshold.
Citation: Shunfu Jin, Yuan Zhao, Wuyi Yue, Lingling Chen. Performance analysis of a P2P storage system with a lazy replica repair policy. Journal of Industrial & Management Optimization, 2014, 10 (1) : 151-166. doi: 10.3934/jimo.2014.10.151
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