Effects on Differentiation

In the following trial, the workload generator always keeps 75 virtual users for each class, which are composed of 25 virtual users for three types of requests in the class. Because the empty server at the initial stage serves requests much faster then the fully loaded server, the window adjusting mechanism cannot determine correctly at the initial stage. Hence, we let the window adjusting mechanism waits for a minute after the trial starts. The virtual users of class 1 will stop sending requests at the 570^th second for 90 seconds to test if the algorithm can tolerate rapid change of traffic while keeping the proportional differentiation between classes.

4.3.1 WTP is stable in short timescales

Figure 7(a) shows that WTP is particularly suitable to apply on the MR-PSTD gateway because WTP can converge to the stable state in a few seconds even after the rapid change of traffic. After the WTP-based MR-PSTD gateway runs for 30 minutes, the averaged system time differentiation ratio in last 10 minutes between classes is 1:1.92:3.81, and it is very close to the pre-specified ratio.

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(a) Average system time among classes

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(b) Average system time of Disk I/O-intensive requests

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(c) The average system times of database-intensive requests Figure.7 Averaged system time of WTP-based MR-PSTD gateway

The experiment results shown in Figure 7(b) reveal that the system time of Disk I/O-intensive requests is the most unpredictable. Because the operation system, Linux

2.6.12, tends to accumulate the Disk I/O-intensive requests and serves the entire backlog requests at the same time, the service time of Disk I/O-intensive requests are not stable. Thus, it also results in the vibration in Figure 7(a).

In Figure 7(c), the system time of Database-intensive requests, which is much stable than that of Disk I/O-intensive requests, shows that the WTP algorithm is not influenced by the rapid change traffic because of WTP’s properties. Although Disk I/O-intensive requests cause the vibration of average system time of total requests in short timescale, the differentiation ratio between classes is kept in acceptable range.

4.3.2 PWAD is unsuitable for PSTD

Figure 8 shows that PWAD is unsuitable to be employed in the MR-PSTD gateway, because it is extremely unstable. After the PWAD-based MR-PSTD gateway runs for 30 minutes, the averaged system time differentiation ratio in the last 10 minutes between classes is 1:1.63:3.23, and it is far from the pre-specified ratio. The unstable results and pathological behavior comes from its basic properties because PWAD only considers departed requests but ignores future requests. When the system starts to work and warms up, because the server is empty at start time, the server serves requests fast, and C2 and C3 requests have short normalized system time, which is much smaller than the normalized system time of C1 requests, before the server becomes busy. Thus, the normalized average system time of departed C1 requests is longer than those of departed C2 and C3 requests, which causes PWAD sends only C1 requests to reduce the normalized average system time of C1. After the departed requests of C2 and C3 are discarded by the moving window averaging mechanism, PWAD turns to send C2 and C3 requests since they are already queued for a long time. Thus, the normalized averaged system time of C2 and C3 becomes very large and PWAD do not send C1 requests anymore until the departed requests of

algorithm decides to send only C2 and C3 requests, C1 requests experience long

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Figure 8 Averaged system time of PWAD based MR-PSTD gateway 4.3.3 MDP is stable in medium timescales

Figure 9 shows that MDP is suitable to be employed in the MR-PSTD gateway, because the reformed MDP not only keeps only w seconds information of departed requests but also considers the lower bound system time of requests currently in queue. Although MDP never causes pathological variation of system time as PWAD in long timescale, after a rapid change of traffic, MDP gets unstable for about 100 seconds. The wavelet of system time, which results from redeeming the gap of normalized mean system time, costs about 400 seconds to converge. However, in another point of view, MDP can keep the differentiation ratio in medium timescale while WTP cannot keep it, because MDP redeems the normalized averaged system time in recent p seconds, which is defined to 120 seconds in our experiments.

After the MDP based MR-PSTD gateway starts for 30 minutes, the averaged system time differentiation ratio in last 10 minutes between classes is 1:2.03:4.19, and it is very close to the pre-specified ratio.

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(b) Averaged system time of database intensive requests Figure 9 Averaged system time of MDP based MR-PSTD gateway

In Figure 9(b), the result of database intensive requests shows that the MDP algorithm wants to redeem the gap, when C1 traffic is suspended. The C3 and C2 traffic experienced higher system time right after the C1 traffic restore. However, after about 400 seconds, the wavelet of the system time of C3 finally gets smooth.

The results show that MDP is suitable for the web site that has stable traffic and need more accuracy on the effect of service differentiation, because MDP always keeps the high priority classes have better service quality which is proportion to its differentiation ratio in the specified timescale.

Comparing with MDP, WTP does not always keep the differentiation ratio in

medium timescale because WTP does not redeem the gap after rapid change of traffic, but WTP is always stable in short timescale. Thus, in the environment that the traffic changes frequently, WTP may be more suitable than MDP. Among all of the three algorithms, WTP is the most suitable algorithm to approximate PSTD model in the environment that the traffic changes frequently, and MDP is the most suitable algorithm in the environment that the traffic in stable.