Analysis: If there are m jobs to be scheduled in n machines, the time complexity of QoS guided
4. Rescheduling Optimization
5.3 Experimental Results of ROR
Table 3 analyzes the effectiveness of the ROR technique under different circumstances.
Table 3: Comparison of Resource Used
(a) (NR=100, QR=30%, QT=20%, HT=1, HQ=1)
Task Number (NT) 200 300 400 500 600
QOS Guided Min-Min 100 100 100 100 100 ROR 39.81 44.18 46.97 49.59 51.17 Improved Ratio 60.19% 55.82% 53.03% 50.41% 48.83%
(b) (NT=500, QR=30%, QT=20%, HT=1, HQ=1)
Resource Number (NR) 50 70 90 110 130
QOS Guided Min-Min 50 70 90 110 130 ROR 26.04 35.21 43.65 50.79 58.15 Improved Ratio 47.92% 49.70% 51.50% 53.83% 55.27%
(c) (NT=500, NR=50, QT=20%, HT=1, HQ=1)
QR% 15% 30% 45% 60% 75%
QOS Guided Min-Min 50 50 50 50 50 ROR 14.61 25.94 35.12 40.18 46.5 Improved Ratio 70.78% 48.12% 29.76% 19.64% 7.00%
(d) (NT=500, NR=100, QR=40%, HT=1, HQ=1)
QT% 15% 30% 45% 60% 75%
QOS Guided Min-Min 100 100 100 100 100
ROR 57.74 52.9 48.54 44.71 41.49 Improved Ratio 42.26% 47.10% 51.46% 55.29% 58.51%
(e) (NT=500, NR=100, QR=30%, QT=20%, HQ=1)
HT 1 3 5 7 9
QOS Guided Min-Min 100 100 100 100 100 ROR 47.86 47.51 47.62 47.61 47.28 Improved Ratio 52.14% 52.49% 52.38% 52.39% 52.72%
(f) (NT=500, NR=100, QR=30%, QT=20%, HT=1)
HQ 3 5 7 9 11
QOS Guided Min-Min 100 100 100 100 100
Similar to those of Table 2, Table (a) changes the number of tasks to verify the reduction of resource that needs to be achieved by the ROR technique. We noticed that the ROR has significant improvement in minimizing grid resources. Comparing with the QoS guided Min-Min scheduling algorithm, the ROR achieves 50% ~ 60% improvements without increasing overall makespan of a chunk of grid tasks. Table (b) changes the number of machines. The ROR retains 50% improvement ratio.
Table (c) adjusts percentages of QoS machine. Because this test has 20% QoS tasks, the ROR performs best at 15% QoS machines. This observation implies that the ROR has significant improvement when QoS tasks and QoS machines are with the same percentage. Table (d) sets 40% QoS machine and changes the percentages of QoS tasks. Following the above analysis, the ROR technique achieves more than 50% improvements when QoS tasks are with 45%, 60% and 75%. Tables (e) and (f) change the heterogeneity of tasks. Similar to the results of section 5.2, the heterogeneity of tasks is not critical to the improvement rate of the ROR technique.
Overall speaking, the ROR technique presents 50%
improvements in minimizing total resource need compare with the QoS guided Min-Min scheduling algorithm.
6. Conclusions
In this paper we have presented two optimization schemes aiming to reduce the overall completion time (makespan) of a chunk of grid tasks and minimize the total resource cost. The proposed techniques are based on the QoS guided Min-Min scheduling algorithm. The optimization achieved by this work is twofold; firstly, without increasing resource costs, the overall task execution time could be reduced by the MOR scheme with 7%~15% improvements. Second, without increasing task completion time, the overall resource cost could be reduced by the ROR scheme with 50% reduction on average, which is a significant improvement to the state of the art scheduling technique. The proposed MOR and ROR techniques have characteristics of low complexity, high effectiveness in large-scale grid systems with QoS services.
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行政院國家科學委員會補助專題研究計畫 █ 成 果 報 告
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