# 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 and 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), 642-653. 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), 337-350. [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), 1-6. [4] G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling," Series on Statistics and Applied Probability. ASA-SIAM, Philadephia, PA, American Statistical Association, Alexandria, VA, 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), 699-716. [6] S. Ramabhadran and J. Pasquale, Analysis of long-running replicated systems, Proceedings of the 25th IEEE Conference on Computer Communications, (2006), 1-9. 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, 93. Springer, New York, 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), 1-17. [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), 1585-1595. 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), 1151-1160. 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), 1-5.

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), 642-653. 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), 337-350. [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), 1-6. [4] G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling," Series on Statistics and Applied Probability. ASA-SIAM, Philadephia, PA, American Statistical Association, Alexandria, VA, 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), 699-716. [6] S. Ramabhadran and J. Pasquale, Analysis of long-running replicated systems, Proceedings of the 25th IEEE Conference on Computer Communications, (2006), 1-9. 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, 93. Springer, New York, 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), 1-17. [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), 1585-1595. 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), 1151-1160. 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), 1-5.
 [1] Magdalena Nockowska-Rosiak, Piotr Hachuła, Ewa Schmeidel. Existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with $p$-Laplacian. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 369-375. doi: 10.3934/dcdsb.2018025 [2] Vinay Aggarwal, Anja Feldmann. Locality-aware P2P query search with ISP collaboration. Networks and Heterogeneous Media, 2008, 3 (2) : 251-265. doi: 10.3934/nhm.2008.3.251 [3] Yeping Li, Jie Liao. Stability and $L^{p}$ convergence rates of planar diffusion waves for three-dimensional bipolar Euler-Poisson systems. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1281-1302. doi: 10.3934/cpaa.2019062 [4] Hao Chen, Kaitai Li, Yuchuan Chu, Zhiqiang Chen, Yiren Yang. A dimension splitting and characteristic projection method for three-dimensional incompressible flow. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 127-147. doi: 10.3934/dcdsb.2018111 [5] Madalina Petcu, Roger Temam, Djoko Wirosoetisno. Averaging method applied to the three-dimensional primitive equations. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5681-5707. doi: 10.3934/dcds.2016049 [6] Yuming Qin, Yang Wang, Xing Su, Jianlin Zhang. Global existence of solutions for the three-dimensional Boussinesq system with anisotropic data. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1563-1581. doi: 10.3934/dcds.2016.36.1563 [7] Brigita Ferčec, Valery G. Romanovski, Yilei Tang, Ling Zhang. Integrability and bifurcation of a three-dimensional circuit differential system. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021243 [8] Nouressadat Touafek, Durhasan Turgut Tollu, Youssouf Akrour. On a general homogeneous three-dimensional system of difference equations. Electronic Research Archive, 2021, 29 (5) : 2841-2876. doi: 10.3934/era.2021017 [9] Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the three-dimensional acoustic scattering problem. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 61-79. doi: 10.3934/dcdsb.2020351 [10] Arun K. Kulshreshth, Andreas Alpers, Gabor T. Herman, Erik Knudsen, Lajos Rodek, Henning F. Poulsen. A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data. Inverse Problems and Imaging, 2009, 3 (1) : 69-85. doi: 10.3934/ipi.2009.3.69 [11] Corinna Burkard, Roland Potthast. A time-domain probe method for three-dimensional rough surface reconstructions. Inverse Problems and Imaging, 2009, 3 (2) : 259-274. doi: 10.3934/ipi.2009.3.259 [12] Masaru Ikehata, Mishio Kawashita. An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method. Inverse Problems and Imaging, 2014, 8 (4) : 1073-1116. doi: 10.3934/ipi.2014.8.1073 [13] Wangtao Lu, Shingyu Leung, Jianliang Qian. An improved fast local level set method for three-dimensional inverse gravimetry. Inverse Problems and Imaging, 2015, 9 (2) : 479-509. doi: 10.3934/ipi.2015.9.479 [14] Amira Khelifa, Yacine Halim. Global behavior of P-dimensional difference equations system. Electronic Research Archive, 2021, 29 (5) : 3121-3139. doi: 10.3934/era.2021029 [15] Anderson Silva, C. Polcino Milies. Cyclic codes of length $2p^n$ over finite chain rings. Advances in Mathematics of Communications, 2020, 14 (2) : 233-245. doi: 10.3934/amc.2020017 [16] Wanli Yang, Jie Sun, Su Zhang. Analysis of optimal boundary control for a three-dimensional reaction-diffusion system. Numerical Algebra, Control and Optimization, 2017, 7 (3) : 325-344. doi: 10.3934/naco.2017021 [17] Dan Li, Chunlai Mu, Pan Zheng, Ke Lin. Boundedness in a three-dimensional Keller-Segel-Stokes system involving tensor-valued sensitivity with saturation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 831-849. doi: 10.3934/dcdsb.2018209 [18] Leo Howden, Donald Giddings, Henry Power, Michael Vloeberghs. Three-dimensional cerebrospinal fluid flow within the human central nervous system. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 957-969. doi: 10.3934/dcdsb.2011.15.957 [19] Gianluca Mola. Global attractors for a three-dimensional conserved phase-field system with memory. Communications on Pure and Applied Analysis, 2008, 7 (2) : 317-353. doi: 10.3934/cpaa.2008.7.317 [20] Ling Liu, Jiashan Zheng, Gui Bao. Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system modeling coral fertilization. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3437-3460. doi: 10.3934/dcdsb.2020068

2020 Impact Factor: 1.801

## Metrics

• HTML views (0)
• Cited by (1)

• on AIMS