Xiao Liu PhD Thesis.pdf - Faculty of Information and Communication ...

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iteration times associated with the workflow path where a i belongs to. The weight of each activity with different workflow structures is illustrated through the calculation of weighted joint distribution for basic Stochastic Petri Nets based building blocks, i.e. sequence, iteration, parallelism and choice. These four building blocks consist of basic control flow patterns and are widely used in workflow modelling and structure analysis [1, 2]. Most workflow process models can be easily built by their compositions, and similarly for the weighted joint distribution of most workflow processes. Here, Stochastic Petri Nets [2] based modelling is employed to incorporate time and probability attributes with additional graphic notations, e.g. stands for the probability of the path and stands for the normal duration distribution of the associated activity. For simplicity, we illustrate with two paths for the iteration, parallelism and choice building blocks, except the sequence building block which has only one path by nature. However, the results can be effectively extended to more than two paths in a similar way. 1) Sequence building block. As depicted in Figure 5.1, the sequence building block is composed by adjacent activities from a i to a j in a sequential relationship which means the successor activity will not be executed until its predecessor activity is finished. The structure weight for each activity in the sequence building block is 1 since they only need to be executed once. Therefore, according to Formula 5.1, the j weighted joint distribution is Z = ∑ X k ~ k = i ⎛ j N⎜ ( ∑ ⎝ k = i j 2 ⎞ k ),( ∑σ k ) ⎟ k = i ⎠ µ . Figure 5.1 Sequence Building Block 2) Iteration building block. As depicted in Figure 5.2, the iteration building block contains two paths which are executed iteratively until certain end conditions are satisfied. Without the context of runtime workflow execution, it is difficult, if not impossible, to obtain the number of iteration times at workflow build time. Therefore, in practice, the number of iteration times is usually estimated with the 74
mean iteration times or with some probability distribution models such as normal, uniform or exponential distribution. In this chapter, we use the mean iteration times to calculate the weighted joint distribution in the iteration building block. The major advantage for this simplification is to avoid the complex joint distribution (if exists) of activity durations (normal distribution) and the number of iteration times (may be normal or other non-normal distribution) in order to facilitate the setting of temporal constraints at build time in an efficient fashion. Here, to be consistent with the Stochastic Petri Nets, we assume that the probability of meeting the end conditions for a single iteration is ρ (i.e. the mean iteration times is 1 ρ ) as denoted by the probability notation. Therefore, the lower path is expected to be executed for 1 ρ times and hence the upper path is executed for ( 1 ρ ) + 1 times. Accordingly, the structure weight for each activity in the iteration building block is the expected execution times of the path it belongs to. The weighted joint distribution here is ⎛ j ⎞ ⎛ l Z = ⎜ ∑ ⎟ ⎜ ∑ ⎝ p= i ⎠ ⎝q= k ⎞ q⎟ ⎠ ((1 ρ ) + 1) ⎜ X p ⎟ + ( 1 ρ) ⎜ X ⎟ ~ ⎛ j l j ⎞ ⎜ 2 l 2 2 2 N (( 1 ) + 1( ) + ( ) (( ) + ) + ( ) ⎟ ∑ µ p) 1 ρ ( ∑ µ q), 1 ρ 1 ( ∑ σ p) 1 ρ ( ∑ σq) ⎝ p= i q= k p= i q= k ⎠ ρ . Figure 5.2 Iteration Building Block 3) Parallelism building block. As depicted in Figure 5.3, the parallelism building block contains two paths which are executed in parallel. Since the activity durations are modelled by normal distributed variables, the overall duration time of the parallelism building block is equal to the distribution of the maximum duration of the two parallel paths. However, to calculate the exact distribution of the maximum of two random variables is a complex issue [67] which requires fundamental knowledge on statistics and non-trivial computation cost. Therefore, in practice, approximation is often applied instead of using the exact distribution. Since the overall completion time of the parallelism building block is dominated by the 75
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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
Page 41 and 42: successful completion. Specifically
Page 43 and 44: Chapter 4 and Chapter 5 respectivel
Page 45 and 46: etween time deficit compensation an
Page 47 and 48: service user’s requirements and t
Page 49 and 50: conducted for three times, i.e. sta
Page 51 and 52: PTDA+ACOWR as an example to introdu
Page 53 and 54: currently running. It is built on t
Page 55 and 56: workflow instance to determine whet
Page 57 and 58: framework for cost-effective delive
Page 59 and 60: pattern based forecasting strategy.
Page 61 and 62: 4.2 Related Work and Problem Analys
Page 63 and 64: 4.2.2 Problem Analysis In cloud wor
Page 65 and 66: significantly deteriorate the overa
Page 67 and 68: activity durations: characteristics
Page 69 and 70: specified with different means and
Page 71 and 72: Table 4.1 Notations Used in K-MaxSD
Page 73 and 74: 1) Duration series building As ment
Page 75 and 76: Table 4.5 Algorithm 4: Pattern Matc
Page 77 and 78: to search for those activities whic
Page 79 and 80: cycle. Here, we also trace back the
Page 81 and 82: ecognition. Sliding Window ranks in
Page 83 and 84: predicted value will be the one pre
Page 85 and 86: segmentation algorithm is capable o
Page 87 and 88: distributed soft real-time system,
Page 89 and 90: Table 5.1 Overview on the Support o
Page 91: 2 2 can be denoted as N ( µ , σ )
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
Page 101 and 102: constraints until the constraint is
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 and 126: expected time redundancy of subsequ
Page 127 and 128: the probability for self-recovery i
Page 129 and 130: skipped if self-recovery applies. A
Page 131 and 132: To evaluate the average performance
Page 133 and 134: activities and around 300 violation
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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alone does not involve any time def
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swap slower machines in the active
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TD( a p ) L{ ( ai , R j ) | i = p +
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For example, in Figure 8.2, local w
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value to sample all of the solution
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mapping task a i to resource R j fr
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have done some simulation experimen
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violations can still be recovered b
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PTDA+ACOWR for Level III Violations
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an integer from 1 to 5 where the ex
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D: Definition for Fitness Value Fit
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strategy; and End(Rescheduling) is
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(a) Optimisation Ratio on Total Cos
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makespan. In our two stage workflow
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espectively. It is clearly that ACO
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comparison results on the violation
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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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