Result Analysis

Job Scheduling vs. Project Scheduling

In this experiment, we compare the performance of three algorithms: Two-tier Strict Backfilling (2TSB), Two-tier Flexible Backfilling with SF = 0 (2TFB), and Two-tier Flexible Backfilling with SF > 0 (2TFB-SF). For 2TFB-SF, we use the parameters => = 0.5 and C = ∞. 2TSB algorithm is used as the baseline for the performance comparison purposes. In addition to the mean project turn-around time 34, the mean job turn-around time 34 , which is defined as

34 = _|6|⁵ ∑ _|†⁵

‚|∑^|†₈₅^‚| ( _, − )

|6|85 (8)

is another performance metric to investigate.

(a) (b)

Figure 8: Job scheduling vs. Project scheduling

As shown in Figure 8(a), it is not surprising that the mean job turn-around time is reduced considerably by 2TFB-SF algorithm because the effectiveness of the concept of slack factor has already been confirmed in several existing one-tier scheduling works [20, 21, 22]. Furthermore, the reduction in the mean job turn-around time greatly depends on the system load. For example, for the case where the mean

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project inter-arrival time is set to 10, the performance difference between 2TSB and 2TFB-SF is about 4000 time units, which means a 7.5% improvement in the mean job turn-around time. On the other hand, in the case of the mean project inter-arrival time being set to 160, the difference is merely 700 time units but an improvement of 15.5%.

Figure 8(a) also demonstrates that 2TSB and 2TFB have almost identical performance for all the values of the mean project inter-arrival time used in this experiment. This can be explained by the fact that the opportunities of carrying out the flexible backfilling mechanism are rare in 2TFB because of => = 0.

Figure 8(b) clearly indicates that the performance of 2TSB, 2TFB, and 2TFB-SF in terms of the mean project turn-around time is roughly the same. This observed phenomenon can be explained by Figure 9 where 2TFB and 2TFB-SF can reduce neither the mean project waiting time nor the mean project running time. Take 2TFB-SF for example; on the average, the mean project waiting time is decreased by 5% to 33% when the mean project inter-arrival time is changed from 10 to 160, but meanwhile, the mean project running time is increased by 0.7% to 7%. These results indicate that 2TFB-SF can decrease the waiting time of the first job of a project but lead to an increase in the waiting time of other remaining jobs of the project. Overall, adopting 2TFB-SF does not lead to a significant improvement on the mean project turn-around time.

(a) (b)

Figure 9: Mean project waiting time vs. Mean project running time

0

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In order to understand more about the relationship between two metrics 34 and 34, we conduct another experiment whose results are shown in Figure 10. In this experiment, we measure and observe the performance of 2TFB-SF while varying the

=> parameter. The experiment results show that using larger slack factors improves the mean job turn-around time significantly. However, this causes a modest increase in the mean project turn-around time. Based on our observation, the decrease of

34 does not lead to the decrease of 34.

(a) (b)

Figure 10: The impact of slack factor SF on 2TFB-SF

To sum up, although 2TFB and 2TFB-SF can reduce the mean job turn-around time notably in comparison with 2TSB, the improvement on the mean project turn-around time is negligible. One can suggest that 2TSB might be a good choice for two-tier cloud scheduling since it achieves the same performance as 2TFB and 2TFB-SF in terms of the mean project turn-around time, but its complexity is comparatively light weight.

The Impact of Priority Scheduling

In order to test how well Two-tier Priority Backfilling algorithm (2TPB) schedules high-priority projects, we devise the following two scenarios for the experiments. In the first scenario, all the submitted projects are scheduled by 2TSB.

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influenced by the slack factor => and the preemption limit C , we conduct the following two experiments to observe the effect of these parameters.

Figure 11: Improvement on the mean project turn-around time by 2TPB algorithm with differential values of slack factor SF

In the first experiment, we study the performance of 2TPB with C = ∞ by observing the mean project inter-arrival time and slack factor =>. Figure 11 shows the improvement on the mean turn-around time of all the high-priority and low-priority projects in comparison with the 2TSB’s performance. As expected, 2TPB decreases the mean turn-around time of the high-priority projects by 6% to 27% but increases the turn-around time of others by 1% to 26% when the value of ( , =>) is increased from (10,0.2) to (160,1.0). Surprisingly, the mean turn-around time of all project inter-arrival time and preemption limit C. The results are similar to those in the first experiment. The mean turn-around time of all the projects stays stable except for the case with the lowest loading of project arrivals. As the value of ( , C) increases from (10,1) to (160,∞), the mean turn-around of the high-priority projects is

-30.00%

Improvement of project turn-around time [%]

Project inter-arrival time, Slack factor Improvement of entire project turn-around time

Improvement of High-priority project turn-around time Improvement of Low-priority project turn-around time

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reduced remarkably from 1.5% to 20%. On the other hand, this also leads to an increase around 0.01% to 10.7% in the mean turn-around time of the low-priority projects.

Figure 12: Improvement of project turn-around time of 2TPB with differential limits on the number of allowable delayed projects PL

The above experimental results indicate that 2TPB works well with priority scheduling where some projects are preferred over the others. Besides, 2TPB does not lead to a general degradation in system service in most cases. Since two system parameters => and C have a strong impact on the mean turn-around time of both types of projects, the system behavior can be controlled by adjusting these parameters.

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

10,1 20,5 40,10 80,20 160,infinte

Improvement of project turn-around time [%]

Project inter-arrival time, Preemption limit Improvement of entire project turn-around time

Improvement of High-priority project turn-around time Improvement of Low-priority project turn-around time

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