Experimental results

Figure 5.1 to Figure 5.9 show the performance results of the simulation experiments. They can be divided into three groups each containing three figures. The three groups of figures present the results under different levels of system load controlled with multiplying the original

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service time by the three different weights, 100, 300, and 500, respectively. In each group, the three figures differ in the mean inter-arrival time of consecutive requests. Each figure compares ten different approaches including six JIQ-based approaches in [1] and four our JQA-based approaches.

In [1], Lu et al. proposed two variations of JIQ approaches: JIQ_Random and JIQ_SQ(2), indicated by JIQ and JIQ_SQ(2), respectively, in the figure. With JIQ-Random, an idle server chooses a dispatcher at random, while with JIQ-SQ(2), an idle server randomly chooses 2 dispatchers first and then joins the one with the smaller queue length. In [1] the authors are also aware that JIQ might lead to a situation where a dispatcher has no servers waiting in its queue and has to dispatch the requests randomly when the system load is high and all servers are busy.

Therefore, they proposed an extension approach in which a server might join a dispatcher even though it is not idle [1]. The extension approach mainly determines the threshold value of the server load under which the server should join a dispatcher, and therefore can cooperate with JIQ_Random and JIQ_SQ(2) mechanisms.

In the following experiments, we experimented with the JIQ extension using two different threshold values: 1 and 2 which are the same as in [1]. The JIQ extension approaches with the two different threshold values are indicated by Ext(1) and Ext(2), respectively, in the figures.

For Ext(1) ,the server will join a particular dispatcher for receiving user requests once its workload has decreased to only one job in the queue and will join another dispatcher again when it becomes idle. For Ext(2) ,the server will join a particular dispatcher for receiving user requests once it has only two jobs or one job in the queue and will join the third dispatcher when it becomes idle.

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The results in Figure 5.1 to Figure 5.9 indicate that our JQA-based approaches, in general, outperform the JIQ-based approaches significantly. The three groups of figures all reveal that the performance improvement increases as the mean inter-arrival time decreases. This demonstrates the advantages of JQA-approaches which can achieve significantly better performance than JIQ-based approaches when the system load is moderate or high.

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JIQ, 154.32 JIQ_Ext(1), 154.32 JIQ_Ext(2), 154.32 JIQ_SQ(2), 154.32 JIQ_SQ(2)_Ext(1), 154.32 JIQ_SQ(2)_Ext(2), 154.32 JQA_RR, 323.82 JQA_NT, 158.22 JQA_Random, 172.13 JQA_LC, 154.32 0.00

Figure 5.1 Performance results of service time multiplied by 100 and inter-arrival time equal to 0.7

JIQ, 288.73 JIQ_Ext(1), 325.10 JIQ_Ext(2), 403.35 JIQ_SQ(2), 250.57297 JIQ_SQ(2)_Ext(1), 306.76 JIQ_SQ(2)_Ext(2), 381.45 JQA_RR, 552.04 JQA_NT, 233.35 JQA_Random, 318.46 JQA_LC, 197.14 0.00

Figure 5.2 Performance results of service time multiplied by 100 and inter-arrival time equal to 0.5

Figure 5.3 Performance results of service time multiplied by 100 and inter-arrival time equal to 0.3

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JIQ, 15462 JIQ_Ext(1), 15463 JIQ_Ext(2), 15451 JIQ_SQ(2), 15475 JIQ_SQ(2)_Ext(1), 15469 JIQ_SQ(2)_Ext(2), 15472 JQA_RR, 15945 JQA_NT, 14931 JQA_Random, 14933 JQA_LC, 14931 14400

Figure 5.4 Performance results of service time multiplied by 300 and inter-arrival time equal to 0.7

JIQ, 31207 JIQ_Ext(1), 31187 JIQ_Ext(2), 31193 JIQ_SQ(2), 31209 JIQ_SQ(2)_Ext(1), 31201 JIQ_SQ(2)_Ext(2), 31196 JQA_RR, 31025 JQA_NT, 30938 JQA_Random, 30592 JQA_LC, 30595 30200

Figure 5.5 Performance results of service time multiplied by 300 and inter-arrival time equal to 0.5

JIQ, 43113 JIQ_Ext(1), 43124 JIQ_Ext(2), 43116 JIQ_SQ(2), 43118 JIQ_SQ(2)_Ext(1), 43126 JIQ_SQ(2)_Ext(2), 43098 JQA_RR, 42602 JQA_NT, 42599 JQA_Random, 42520 JQA_LC, 42518 42200

Figure 5.6 Performance results of service time multiplied by 300 and inter-arrival time equal to 0.3

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JIQ, 46640 JIQ_Ext(1), 46618 JIQ_Ext(2), 46634 JIQ_SQ(2), 46657 JIQ_SQ(2)_Ext(1), 46629 JIQ_SQ(2)_Ext(2), 46615 JQA_RR, 46560 JQA_NT, 46337 JQA_Random, 45656 JQA_LC, 45649 45000

Figure 5.7 Performance results of service time multiplied by 500 and inter-arrival time equal to 0.7

JIQ, 62391 JIQ_Ext(1), 62369 JIQ_Ext(2), 62385 JIQ_SQ(2), 62381 JIQ_SQ(2)_Ext(1), 62373 JIQ_SQ(2)_Ext(2), 62349 JQA_RR, 61732 JQA_NT, 61675 JQA_Random, 61354 JQA_LC, 61360 60800

Figure 5.8 Performance results of service time multiplied by 500 and inter-arrival time equal to 0.5

JIQ, 74294 JIQ_Ext(1), 74278 JIQ_Ext(2), 74278 JIQ_SQ(2), 74339 JIQ_SQ(2)_Ext(1), 74305 JIQ_SQ(2)_Ext(2), 74302 JQA_RR, 73368 JQA_NT, 73355 JQA_Random, 73279 JQA_LC, 73283 72800

Figure 5.9 Performance results of service time multiplied by 500 and inter-arrival time equal to 0.3

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To make thorough performance comparison, in the following Figure 5.10 to Figure 5.18, we partition the performance results into three different groups based on the mean inter-arrival time. In each group, there are three figures which differ in the required service execution time controlled with multiplying the original service time by the three different weights, 100, 300, and 500, respectively. All the three groups of figures indicate that JQA-based approaches lead to more significant performance improvement as the multiplied weight grows. This demonstrates that JQA-approaches can achieve better load-balancing effects than JIQ-based approaches since a bigger multiplied weight means larger variation in the service execution time.

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JIQ, 11955 JIQ_Ext(1), 11949 JIQ_Ext(2), 11952 JIQ_SQ(2), 11955 JIQ_SQ(2)_Ext(1), 11955 JIQ_SQ(2)_Ext(2), 11964 JQA_RR, 11858 JQA_NT, 11845 JQA_Random, 11756 JQA_LC, 11756 11650

Figure 5.10 Performance results of service time multiplied by 100 and inter-arrival time equal to 0.3

JIQ, 43113 JIQ_Ext(1), 43124 JIQ_Ext(2), 43116 JIQ_SQ(2), 43118 JIQ_SQ(2)_Ext(1), 43126 JIQ_SQ(2)_Ext(2), 43098 JQA_RR, 42602 JQA_NT, 42599 JQA_Random, 42520 JQA_LC, 42518 42200

Figure 5.11 Performance results of service time multiplied by 300 and inter-arrival time equal to 0.3

JIQ, 74294 JIQ_Ext(1), 74278 JIQ_Ext(2), 74278 JIQ_SQ(2), 74339 JIQ_SQ(2)_Ext(1), 74305 JIQ_SQ(2)_Ext(2), 74302 JQA_RR, 73368 JQA_NT, 73355 JQA_Random, 73279 JQA_LC, 73283 72800

Figure 5.12 Performance results of service time multiplied by 500 and inter-arrival time equal to 0.3

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JIQ, 288.73 JIQ_Ext(1), 325.10 JIQ_Ext(2), 403.35 JIQ_SQ(2), 250.57297 JIQ_SQ(2)_Ext(1), 306.76 JIQ_SQ(2)_Ext(2), 381.45 JQA_RR, 552.04 JQA_NT, 233.35 JQA_Random, 318.46 JQA_LC, 197.14 0.00

Figure 5.13 Performance results of service time multiplied by 100 and inter-arrival time equal to 0.5

JIQ, 31207 JIQ_Ext(1), 31187 JIQ_Ext(2), 31193 JIQ_SQ(2), 31209 JIQ_SQ(2)_Ext(1), 31201 JIQ_SQ(2)_Ext(2), 31196 JQA_RR, 31025 JQA_NT, 30938 JQA_Random, 30592 JQA_LC, 30595 30200

Figure 5.14 Performance results of service time multiplied by 300 and inter-arrival time equal to 0.5

JIQ, 62391 JIQ_Ext(1), 62369 JIQ_Ext(2), 62385 JIQ_SQ(2), 62381 JIQ_SQ(2)_Ext(1), 62373 JIQ_SQ(2)_Ext(2), 62349 JQA_RR, 61732 JQA_NT, 61675 JQA_Random, 61354 JQA_LC, 61360 60800

Figure 5.15 Performance results of service time multiplied by 500 and inter-arrival time equal to 0.5

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JIQ, 154.32 JIQ_Ext(1), 154.32 JIQ_Ext(2), 154.32 JIQ_SQ(2), 154.32 JIQ_SQ(2)_Ext(1), 154.32 JIQ_SQ(2)_Ext(2), 154.32 JQA_RR, 323.82 JQA_NT, 158.22 JQA_Random, 172.13 JQA_LC, 154.32 0.00

Figure 5.16 Performance results of service time multiplied by 100 and inter-arrival time equal to 0.7

JIQ, 15462 JIQ_Ext(1), 15463 JIQ_Ext(2), 15451 JIQ_SQ(2), 15475 JIQ_SQ(2)_Ext(1), 15469 JIQ_SQ(2)_Ext(2), 15472 JQA_RR, 15945 JQA_NT, 14931 JQA_Random, 14933 JQA_LC, 14931 14400

Figure 5.17 Performance results of service time multiplied by 300 and inter-arrival time equal to 0.7

JIQ, 46640 JIQ_Ext(1), 46618 JIQ_Ext(2), 46634 JIQ_SQ(2), 46657 JIQ_SQ(2)_Ext(1), 46629 JIQ_SQ(2)_Ext(2), 46615 JQA_RR, 46560 JQA_NT, 46337 JQA_Random, 45656 JQA_LC, 45649 45000

Figure 5.18 Performance results of service time multiplied by 500 and inter-arrival time equal to 0.7

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In summary, the proposed JQA approach can achieve significantly better performance than JIQ, up to 31% performance improvement in terms of average request response time.

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