# 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
##### References:
 [1] S. Alouf, A. Dandoush and P. Nain, Performance analysis of peer-to-peer storage systems,, Managing Traffic Performance in Converged Networks Lecture Notes in Computer Science, 4516 (2007), 642. doi: 10.1007/978-3-540-72990-7_57. [2] R. Bhagwan, K. Tati, Y. Cheng, S. Savage and G. Voelker, Total recall: System support for automated availability management,, Proceedings of the 1st Symposium on Networked Systems Design and Implementation, (2004), 337. [3] C. Blake and R. Rodrigues, High availability, scalable storage, dynamic peer network: Pick two,, Proceedings of the 9th Workshop on Hot Topics in Operating Systems, (2003), 1. [4] G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", Series on Statistics and Applied Probability. ASA-SIAM, (1999). doi: 10.1137/1.9780898719734. [5] S. Nanao, H. Masuyama, S. Kasahara and Y. Takahashi, Queueing analysis of data block synchronization mechanism in peer-to-peer based video streaming system,, Journal of Industrial and Management Optimization, 7 (2011), 699. [6] S. Ramabhadran and J. Pasquale, Analysis of long-running replicated systems,, Proceedings of the 25th IEEE Conference on Computer Communications, (2006), 1. doi: 10.1109/INFOCOM.2006.130. [7] N. Tian and G. Zhang, "Vacation Queueing Models-Theory and Applications,", International Series in Operations Research & Management Science, (2006). [8] C. H. Wu, K. H. Wang, J. C. Ke and J. B. Ke, A heuristic algorithm for the optimization of M/M/s queue with multiple working vacations,, Journal of Industrial and Management Optimization, 8 (2012), 1. [9] Y. Wu, Z. Yang, Z. Qu, Z. Xiao and Y. Dai, User-experience-based availability analysis model and its application in P2P storage systems,, Science China: Information Sciences, 54 (2011), 1585. doi: 10.1007/s11432-011-4313-9. [10] Z. Yang and Y. Dai, Autoproc: An automatic proactive replication scheme for P2P storage,, Science China: Information Sciences, 54 (2011), 1151. doi: 10.1007/s11432-011-4260-5. [11] Z. Yang, B. Zhao, Y. Xing, S. Ding, F. Xiao and Y. Dai, AmazingStore: Available, low-cost online storage service using cloudlets,, Proceedings of the 9th International Workshop on Peer-to-Peer Systems, (2010), 1.

show all references

##### References:
 [1] S. Alouf, A. Dandoush and P. Nain, Performance analysis of peer-to-peer storage systems,, Managing Traffic Performance in Converged Networks Lecture Notes in Computer Science, 4516 (2007), 642. doi: 10.1007/978-3-540-72990-7_57. [2] R. Bhagwan, K. Tati, Y. Cheng, S. Savage and G. Voelker, Total recall: System support for automated availability management,, Proceedings of the 1st Symposium on Networked Systems Design and Implementation, (2004), 337. [3] C. Blake and R. Rodrigues, High availability, scalable storage, dynamic peer network: Pick two,, Proceedings of the 9th Workshop on Hot Topics in Operating Systems, (2003), 1. [4] G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", Series on Statistics and Applied Probability. ASA-SIAM, (1999). doi: 10.1137/1.9780898719734. [5] S. Nanao, H. Masuyama, S. Kasahara and Y. Takahashi, Queueing analysis of data block synchronization mechanism in peer-to-peer based video streaming system,, Journal of Industrial and Management Optimization, 7 (2011), 699. [6] S. Ramabhadran and J. Pasquale, Analysis of long-running replicated systems,, Proceedings of the 25th IEEE Conference on Computer Communications, (2006), 1. doi: 10.1109/INFOCOM.2006.130. [7] N. Tian and G. Zhang, "Vacation Queueing Models-Theory and Applications,", International Series in Operations Research & Management Science, (2006). [8] C. H. Wu, K. H. Wang, J. C. Ke and J. B. Ke, A heuristic algorithm for the optimization of M/M/s queue with multiple working vacations,, Journal of Industrial and Management Optimization, 8 (2012), 1. [9] Y. Wu, Z. Yang, Z. Qu, Z. Xiao and Y. Dai, User-experience-based availability analysis model and its application in P2P storage systems,, Science China: Information Sciences, 54 (2011), 1585. doi: 10.1007/s11432-011-4313-9. [10] Z. Yang and Y. Dai, Autoproc: An automatic proactive replication scheme for P2P storage,, Science China: Information Sciences, 54 (2011), 1151. doi: 10.1007/s11432-011-4260-5. [11] Z. Yang, B. Zhao, Y. Xing, S. Ding, F. Xiao and Y. Dai, AmazingStore: Available, low-cost online storage service using cloudlets,, Proceedings of the 9th International Workshop on Peer-to-Peer Systems, (2010), 1.
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