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Secondorder optimality conditions for cone constrained multiobjective optimization
Performance optimization of paralleldistributed processing with checkpointing for cloud environment
1.  Graduate School of Informatics, Kyoto University, YoshidaHommachi, Sakyoku, Kyoto 6068501, Japan 
2.  Graduate School of Information Science, Nara Institute of Science and Technology, 89165 Takayama, Ikoma, Nara 6300192, Japan 
In cloud computing, the most successful application framework is paralleldistributed processing, in which an enormous task is split into a number of subtasks and those are processed independently on a cluster of machines referred to as workers. Due to its huge system scale, worker failures occur frequently in cloud environment and failed subtasks cause a large processing delay of the task. One of schemes to alleviate the impact of failures is checkpointing method, with which the progress of a subtask is recorded as checkpoint and the failed subtask is resumed by other worker from the latest checkpoint. This method can reduce the processing delay of the task. However, frequent checkpointing is system overhead and hence the checkpoint interval must be set properly. In this paper, we consider the optimal number of checkpoints which minimizes the taskprocessing time. We construct a stochastic model of paralleldistributed processing with checkpointing and approximately derive explicit expressions for the mean taskprocessing time and the optimal number of checkpoints. Numerical experiments reveal that the proposed approximations are sufficiently accurate on typical environment of cloud computing. Furthermore, the derived optimal number of checkpoints outperforms the result of previous study for minimizing the taskprocessing time on paralleldistributed processing.
References:
[1] 
L. A. Barroso and U. Hölzle, The Datacenter as a Computer: An Introduction to the Design of WarehouseScale Machines, Morgan & Claypool Publishers, California, 2009. doi: 10.2200/S00193ED1V01Y200905CAC006. 
[2] 
T. C. Bressoud and M. A. Kozuch, Cluster faulttolerance: An experimental evaluation of checkpointing and MapReduce through simulation in Proc. the IEEE International Conference on Cluster Computing and Workshops (CLUSTER 2009), (2009). doi: 10.1109/CLUSTR.2009.5289185. 
[3] 
C. L. P. Chen and C.Y. Zhang, Dataintensive applications, challenges, techniques and technologies: A survey on big data, Information Sciences, 275 (2014), 314347. doi: 10.1016/j.ins.2014.01.015. 
[4] 
T. Condie, N. Conway, P. Alvaro, J. M. Hellerstein, K. Elmeleegy and R. Sears, MapReduce online, in Proc. the 7th USENIX Symposium on Networked Systems Design and Implementation (NSDI 2010), (2010). 
[5] 
J. T. Daly, A higher order estimate of the optimum checkpoint interval for restart dumps, Future Generation Computer Systems, 22 (2006), 303312. doi: 10.1016/j.future.2004.11.016. 
[6] 
J. Dean and S. Ghemawat, MapReduce: Simplified data processing on large clusters, Communications of the ACM, 51 (2008), 107113. doi: 10.1145/1327452.1327492. 
[7] 
J. Dean, Designs, lessons and advice from building large distributed systems, in Keynote Presentation of the 3rd ACM SIGOPS International Workshop on Large Scale Distributed Systems and Middleware (LADIS 2009), (2009). 
[8] 
J. Dean and S. Ghemawat, MapReduce: A flexible data processing tool, Communications of the ACM, 53 (2010), 7277. doi: 10.1145/1629175.1629198. 
[9] 
S. Di, Y. Robert, F. Vivien, D. Kondo, C. L. Wang and F. Cappello, Optimization of cloud task processing with checkpointrestart mechanism in Proc. the International Conference for High Performance Computing, Networking, Storage and Analysis (SC 13), (2013). doi: 10.1145/2503210.2503217. 
[10] 
L. Fialho, D. Rexachs and E. Luque, What is missing in current checkpoint interval models?, Proc. the 31st International Conference on Distributed Computing Systems (ICDCS 2011), (2011), 322332. doi: 10.1109/ICDCS.2011.12. 
[11] 
B. Javadi, D. Kondo, A. Iosup and D. Epema, The failure trace archive: Enabling the comparison of failure measurements and models of distributed systems, Journal of Parallel and Distributed Computing, 73 (2013), 12081223. doi: 10.1016/j.jpdc.2013.04.002. 
[12] 
H. Jin, Y. Chen, H. Zhu and X.H. Sun, Optimizing HPC faulttolerant environment: An analytical approach, Proc. the 39th International Conference on Parallel Processing (ICPP 2010), (2010), 525534. doi: 10.1109/ICPP.2010.80. 
[13] 
A. Martin, T. Knauth, S. Creutz, D. Becker, S. Weigert, C. Fetzer and A. Brito, Lowoverhead fault tolerance for highthroughput data processing systems, Proc. the 31st International Conference on Distributed Computing Systems (ICDCS 2011), (2011), 689699. doi: 10.1109/ICDCS.2011.29. 
[14] 
P. Mell and T. Grance, The NIST Definition of Cloud Computing, Recommendations of the National Institute of Standards and Technology, NIST Special Publication 800145,2011. doi: 10.6028/NIST.SP.800145. 
[15] 
M. Taifi, J. Y. Shi and A. Khreishah, SpotMPI: A framework for auctionbased HPC computing using Amazon spot instances, Proc. the 11th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP 2011), (2011), 109120. doi: 10.1007/9783642246692_11. 
[16] 
J. W. Young, A first order approximation to the optimum checkpoint interval, Communications of the ACM, 17 (1974), 530531. doi: 10.1145/361147.361115. 
[17] 
M. Zaharia, T. Das, H. Li, T. Hunter, S. Shenker and I. Stoica, Discretized streams: Faulttolerant streaming computation at scale, Proc. the 24th ACM Symposium on Operating Systems Principles (SOSP 2013), (2013), 423438. doi: 10.1145/2517349.2522737. 
show all references
References:
[1] 
L. A. Barroso and U. Hölzle, The Datacenter as a Computer: An Introduction to the Design of WarehouseScale Machines, Morgan & Claypool Publishers, California, 2009. doi: 10.2200/S00193ED1V01Y200905CAC006. 
[2] 
T. C. Bressoud and M. A. Kozuch, Cluster faulttolerance: An experimental evaluation of checkpointing and MapReduce through simulation in Proc. the IEEE International Conference on Cluster Computing and Workshops (CLUSTER 2009), (2009). doi: 10.1109/CLUSTR.2009.5289185. 
[3] 
C. L. P. Chen and C.Y. Zhang, Dataintensive applications, challenges, techniques and technologies: A survey on big data, Information Sciences, 275 (2014), 314347. doi: 10.1016/j.ins.2014.01.015. 
[4] 
T. Condie, N. Conway, P. Alvaro, J. M. Hellerstein, K. Elmeleegy and R. Sears, MapReduce online, in Proc. the 7th USENIX Symposium on Networked Systems Design and Implementation (NSDI 2010), (2010). 
[5] 
J. T. Daly, A higher order estimate of the optimum checkpoint interval for restart dumps, Future Generation Computer Systems, 22 (2006), 303312. doi: 10.1016/j.future.2004.11.016. 
[6] 
J. Dean and S. Ghemawat, MapReduce: Simplified data processing on large clusters, Communications of the ACM, 51 (2008), 107113. doi: 10.1145/1327452.1327492. 
[7] 
J. Dean, Designs, lessons and advice from building large distributed systems, in Keynote Presentation of the 3rd ACM SIGOPS International Workshop on Large Scale Distributed Systems and Middleware (LADIS 2009), (2009). 
[8] 
J. Dean and S. Ghemawat, MapReduce: A flexible data processing tool, Communications of the ACM, 53 (2010), 7277. doi: 10.1145/1629175.1629198. 
[9] 
S. Di, Y. Robert, F. Vivien, D. Kondo, C. L. Wang and F. Cappello, Optimization of cloud task processing with checkpointrestart mechanism in Proc. the International Conference for High Performance Computing, Networking, Storage and Analysis (SC 13), (2013). doi: 10.1145/2503210.2503217. 
[10] 
L. Fialho, D. Rexachs and E. Luque, What is missing in current checkpoint interval models?, Proc. the 31st International Conference on Distributed Computing Systems (ICDCS 2011), (2011), 322332. doi: 10.1109/ICDCS.2011.12. 
[11] 
B. Javadi, D. Kondo, A. Iosup and D. Epema, The failure trace archive: Enabling the comparison of failure measurements and models of distributed systems, Journal of Parallel and Distributed Computing, 73 (2013), 12081223. doi: 10.1016/j.jpdc.2013.04.002. 
[12] 
H. Jin, Y. Chen, H. Zhu and X.H. Sun, Optimizing HPC faulttolerant environment: An analytical approach, Proc. the 39th International Conference on Parallel Processing (ICPP 2010), (2010), 525534. doi: 10.1109/ICPP.2010.80. 
[13] 
A. Martin, T. Knauth, S. Creutz, D. Becker, S. Weigert, C. Fetzer and A. Brito, Lowoverhead fault tolerance for highthroughput data processing systems, Proc. the 31st International Conference on Distributed Computing Systems (ICDCS 2011), (2011), 689699. doi: 10.1109/ICDCS.2011.29. 
[14] 
P. Mell and T. Grance, The NIST Definition of Cloud Computing, Recommendations of the National Institute of Standards and Technology, NIST Special Publication 800145,2011. doi: 10.6028/NIST.SP.800145. 
[15] 
M. Taifi, J. Y. Shi and A. Khreishah, SpotMPI: A framework for auctionbased HPC computing using Amazon spot instances, Proc. the 11th International Conference on Algorithms and Architectures for Parallel Processing (ICA3PP 2011), (2011), 109120. doi: 10.1007/9783642246692_11. 
[16] 
J. W. Young, A first order approximation to the optimum checkpoint interval, Communications of the ACM, 17 (1974), 530531. doi: 10.1145/361147.361115. 
[17] 
M. Zaharia, T. Das, H. Li, T. Hunter, S. Shenker and I. Stoica, Discretized streams: Faulttolerant streaming computation at scale, Proc. the 24th ACM Symposium on Operating Systems Principles (SOSP 2013), (2013), 423438. doi: 10.1145/2517349.2522737. 
Parameter  Description  Value 
Number of workers  
Subtaskprocessing time  
Time to make a checkpoint  
Mean time between worker failures  
Time to resume a failed subtask  
Number of checkpoints 
Parameter  Description  Value 
Number of workers  
Subtaskprocessing time  
Time to make a checkpoint  
Mean time between worker failures  
Time to resume a failed subtask  
Number of checkpoints 
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