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from a p+ 1 to a p + m , the probability time redundancy of subsequent activities is PTR ( U ( SW ),( a p + 1, a p + m )) which is equal to u ( SW ) −[ R( a1, a p ) + M ( a p+ 1, a p+ m) + θ ( a p+ m+ 1, an )] . Here, M ( a p + 1, a p + m ) is equal to p+ m n ∑(µ k ) and θ ( a p+ m+ 1, an ) is equal to ∑ ( µ k + λθ σ k ) . k = p+ 1 k = p+ m+ 1 The probability time deficit is for measuring the occurred time deficit at the current checkpoint. The probability time redundancy is for measuring the expected time redundancy (i.e. the time redundancy between the mean completion time and the temporal constraints) of the subsequent activities at the current checkpoint. For example, at checkpoint a p , if the temporal constraint for activity a p+ 1 to a p + m is equal to µ θ + λ σ , then the value of λ θ σ is regarded as the expected time redundancy which can be used to compensate for the occurred time deficit. Based on the probability time deficit and the probability time redundancy, the probability of self-recovery is defined as follows. Definition 7.3: (Probability of Self-Recovery). For activity point a p which is covered by U (SW ) , given the probability time deficit (denoted as PTD ( a p ) ) and the probability time redundancy (denoted as PTR ( a p ) ), the probability of self-recovery, i.e. the probability that PTD ( a p ) can be compensated for by PTR ( a p ) is defined as: −x 2 1 T P( T ) = ∫ e 2 2π −∞ , where T = PTR( a p ) − PTD( a PTD( a p ) p ) If without any prior knowledge, it is difficult to decide which probability distribution model that T fits. Therefore, in this chapter, we assume that T follows a standard normal distribution 6 , i.e. N (0,1) with the expected value of 0 and the standard deviation of 1. It is obvious that the larger the difference between PTR ( a p ) and PTD a ) ( p , the higher the probability for self-recovery. For example, according to Definition 7.3, if PTR ( a p ) is equal to PTD ( a p ) , i.e. T is equal to 0, 6 Note that we have tested our strategy with other distribution models such as exponential, uniform and a mixture of them. The results are similar. 108
the probability for self-recovery is 50%. If PTR ( a p ) is twice as large as PTD ( a p ) , i.e. T is equal to 1, the probability for self-recovery is 84.13% [87]. Note that in practice, historical data can be employed to discover and modify the actual probability distribution models. Nevertheless, the strategy proposed in this chapter can be applied in a similar manner. 7.2.2 Temporal Violation Handling Point Selection Strategy After the probability of self-recovery is defined, a probability threshold is required. The probability threshold can be regarded as the minimum confidence for skipping temporal violation handling on a selected checkpoint yet still retaining satisfactory temporal correctness. Given a probability threshold, a temporal violation handling point selection rule is defined as follows. Temporal Violation Handling Point Selection Rule: At activity a p , with the probability of self-recovery P (T ) and the probability threshold PT ( 0 < PT < 1), the rule for temporal violation handling point selection is as follows: if P ( T ) > PT , then the current checkpoint is not selected as a handling point; otherwise, the current checkpoint is selected as a handling point. The probability threshold PT is an important parameter in the temporal violation handling point selection rule and it needs to be defined to facilitate violation handling point selection at workflow runtime. However, whether selfrecovery will be successful or not can only be determined after the execution of the subsequent activities. It is difficult, if not impossible, to specify the optimal probability threshold which can select the minimal number of handling points while maintaining satisfactory temporal correctness. To address this problem, we borrow the idea from adaptive testing where the new testing cases are generated based on the knowledge of previous testing cases [24]. In our strategy, the probability threshold can start from any moderate initial values, e.g. 0.3 or 0.5, and it is then adaptively modified based on the results of previous temporal violation handling along scientific workflow execution. Therefore, the initial threshold has limited impact on the effectiveness of our strategy. The process of adaptive modification for PT is described as follows. 109
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A Novel Probabilistic Temporal Fram
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Declaration This thesis contains no
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Abstract Cloud computing is a lates
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Component 2, the state of scientifi
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http://dx.doi.org/10.1016/j.jpdc.20
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17. X. Liu, J. Chen, and Y. Yang, A
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4.2 RELATED WORK AND PROBLEM ANALYS
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STRATEGY ..........................
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FIGURE 7.4 EXPERIMENTAL RESULTS (NO
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Chapter 1 Introduction This thesis
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Clearly, if the execution time of t
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to seek all the candidates. Further
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e unnecessary. Hence, an effective
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temporal violations, viz. recoverab
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In Chapter 2, we introduce the rela
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a two-stage searching process with
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QoS requirements. Generally speakin
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handling strategies employed in a s
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activity points to conduct temporal
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compensation, is believed as a suit
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successful completion. Specifically
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Chapter 4 and Chapter 5 respectivel
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etween time deficit compensation an
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service user’s requirements and t
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conducted for three times, i.e. sta
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PTDA+ACOWR as an example to introdu
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currently running. It is built on t
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workflow instance to determine whet
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framework for cost-effective delive
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pattern based forecasting strategy.
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4.2 Related Work and Problem Analys
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4.2.2 Problem Analysis In cloud wor
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significantly deteriorate the overa
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activity durations: characteristics
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specified with different means and
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Table 4.1 Notations Used in K-MaxSD
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1) Duration series building As ment
Page 75 and 76: Table 4.5 Algorithm 4: Pattern Matc
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Page 79 and 80: cycle. Here, we also trace back the
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Page 83 and 84: predicted value will be the one pre
Page 85 and 86: segmentation algorithm is capable o
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Page 89 and 90: Table 5.1 Overview on the Support o
Page 91 and 92: 2 2 can be denoted as N ( µ , σ )
Page 93 and 94: mean iteration times or with some p
Page 95 and 96: Figure 5.4 Choice Building Block No
Page 97 and 98: activities may be omitted for the e
Page 99 and 100: 5.3.1 Calculating Weighted Joint Di
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Page 103 and 104: Therefore, it can be expressed as n
Page 105 and 106: Table 5.3 Specification of the Work
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Page 109 and 110: ease of discussion and to avoid the
Page 111 and 112: Unfortunately, conventional discret
Page 113 and 114: The probability consistency range w
Page 115 and 116: 6.2.3 Temporal Checkpoint Selection
Page 117 and 118: 100 times each. All the activity du
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Page 121 and 122: Figure 6.3 Checkpoint Selection wit
Page 123 and 124: work and problem analysis. Section
Page 125: expected time redundancy of subsequ
Page 129 and 130: skipped if self-recovery applies. A
Page 131 and 132: To evaluate the average performance
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Page 135 and 136: Figure 7.3 Experimental Results (No
Page 137 and 138: Figure 7.5 Cost Reduction Rate vs.
Page 139 and 140: 8.1 Related Work and Problem Analys
Page 141 and 142: scientific processes, human interve
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Page 145 and 146: swap slower machines in the active
Page 147 and 148: TD( a p ) L{ ( ai , R j ) | i = p +
Page 149 and 150: For example, in Figure 8.2, local w
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Page 153 and 154: mapping task a i to resource R j fr
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Page 157 and 158: violations can still be recovered b
Page 159 and 160: PTDA+ACOWR for Level III Violations
Page 161 and 162: an integer from 1 to 5 where the ex
Page 163 and 164: D: Definition for Fitness Value Fit
Page 165 and 166: strategy; and End(Rescheduling) is
Page 167 and 168: (a) Optimisation Ratio on Total Cos
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Page 171 and 172: espectively. It is clearly that ACO
Page 173 and 174: comparison results on the violation
Page 175 and 176: percentiles. The average global vio
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equivalent times of ACOWR are calcu
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Chapter 9 Conclusions and Future Wo
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the real world, simulation experime
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ased temporal consistency model. Ac
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the whole lifecycle support for hig
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which can be further investigated i
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Bibliography [1] W. M. P. van der A
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Systems", ACM Trans. on Software En
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conjunction with 23 rd Parallel and
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Elsevier, vol. 84, no. 3, pp. 354-3
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Distributed Computing Systems", Jou
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Appendix: Notation Index Symbols α
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PTR ( U ( SW ), ( a p + , a p + 1 m
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