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Performance optimization of parallel-distributed processing with checkpointing for cloud environment

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  • In cloud computing, the most successful application framework is parallel-distributed 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 task-processing time. We construct a stochastic model of parallel-distributed processing with checkpointing and approximately derive explicit expressions for the mean task-processing 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 task-processing time on parallel-distributed processing.

    Mathematics Subject Classification: Primary: 68M20, 90B22; Secondary: 60K30.

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  • Figure 1.  Processing of a subtask with checkpointing method

    Figure 2.  Mean task-processing time with respect to the number of checkpoints for various $M$ ($b = 24$ [hour], $c = 300$ [sec], $f = 30$ [day], $r = 300$ [sec]): Comparison between the results of analysis and simulation

    Figure 3.  Mean task-processing time with respect to the number of checkpoints for various $b$ ($M = 100$, $c = 300$ [sec], $f = 30$ [day], $r = 300$ [sec]): Comparison between the results of analysis and simulation

    Figure 4.  Mean task-processing time with respect to the number of checkpoints for various $c$ ($M = 100$, $b = 24$ [hour], $f = 30$ [day], $r = 300$ [sec]): Comparison between the results of analysis and simulation

    Figure 5.  Mean task-processing time with respect to the number of checkpoints for various $f$ ($M = 100$, $b = 24$ [hour], $c = 300$ [sec], $r = 300$ [sec]): Comparison between the results of analysis and simulation

    Figure 6.  Mean task-processing time with respect to the number of checkpoints for various $r$ ($M = 100$, $b = 24$ [hour], $f = 30$ [day], $c = 300$ [sec]): Comparison between the results of analysis and simulation

    Figure 7.  Mean task-processing time with respect to $M$ for the optimal number of checkpoints ($b = 24$ [hour], $c = 300$ [sec], $f = 30$ [day], $r = 300$ [sec]): Comparison between the results of previous and proposal analyses and simulation

    Figure 8.  Mean task-processing time with respect to $b$ for the optimal number of checkpoints ($M = 100$, $c = 300$ [sec], $f = 30$ [day], $r = 300$ [sec]): Comparison between the results of previous and proposal analyses and simulation

    Figure 9.  Mean task-processing time with respect to $c$ for the optimal number of checkpoints ($M = 100$, $b = 24$ [hour], $f = 30$ [day], $r = 300$ [sec]): Comparison between the results of previous and proposal analyses and simulation

    Figure 10.  Mean task-processing time with respect to $f$ for the optimal number of checkpoints ($M = 100$, $b = 24$ [hour], $c = 300$ [sec], $r = 300$ [sec]): Comparison between the results of previous and proposal analyses and simulation

    Figure 11.  Mean task-processing time with respect to $r$ for the optimal number of checkpoints ($M = 100$, $c = 300$ [sec], $b = 24$ [hour], $f = 30$ [day]): Comparison between the results of previous and proposal analyses and simulation

    Figure 12.  Mean task-processing time with respect to $M$ for the optimal number of checkpoints ($b = 24$ [hour], $c = 300$ [sec], $f = 30$ [day], $r = 300$ [sec]): Comparison among three distributions for the time intervals between consecutive worker failures

    Figure 13.  Mean task-processing time with respect to $b$ for the optimal number of checkpoints ($M = 100$, $c = 300$ [sec], $f = 30$ [day], $r = 300$ [sec]): Comparison among three distributions for the time intervals between consecutive worker failures

    Figure 14.  Mean task-processing time with respect to $c$ for the optimal number of checkpoints ($M = 100$, $b = 24$ [hour], $f = 30$ [day], $r = 300$ [sec]): Comparison among three distributions for the time intervals between consecutive worker failures

    Figure 15.  Mean task-processing time with respect to $f$ for the optimal number of checkpoints ($M = 100$, $b = 24$ [hour], $c = 300$ [sec], $r = 300$ [sec]): Comparison among three distributions for the time intervals between consecutive worker failures

    Figure 16.  Mean task-processing time with respect to $r$ for the optimal number of checkpoints ($M = 100$, $c = 300$ [sec], $b = 24$ [hour], $f = 30$ [day]): Comparison among three distributions for the time intervals between consecutive worker failures

    Figure 17.  Mean task-processing time with respect to small $f$ for the optimal number of checkpoints ($M = 100$, $b = 24$ [hour], $c = 300$ [sec], $f = 1$ to $7$ [day], $r = 300$ [sec]): Comparison among three distributions for the time intervals between consecutive worker failures

    Table 1.  Parameter set.

    ParameterDescriptionValue
    $M$Number of workers$10$ to $1,000$
    $b$Subtask-processing time$6$ to $120$ [hour]
    $c$Time to make a checkpoint$30$ to $3,000$ [sec]
    $f$Mean time between worker failures$7$ to $180$ [day]
    $r$Time to resume a failed subtask$30$ to $3,000$ [sec]
    $K$Number of checkpoints$0$ to $30$
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