### 7.1. Comparing the Effectiveness of Different Cost-Computation Alternatives

Let us start by studying the effectiveness of Lookahead and Combinational Scheduling. Interestingly, there is no clear benefit for computing the cost over a future period of time. In some cases, as shown in Figure 7, the performance in terms of customer defection and average waiting time may be worse than those when computing the cost at the current scheduling time with MCF-P. The results of Lookahead Scheduling are shown for two different prediction window values. Only the results with future stream extensions are shown. The results without extensions are almost the same.

Although computing the cost over a time interval seems intuitively to be an excellent choice, it interferes negatively with stream merging. Later in this paper, we discuss how the interaction between stream merging and scheduling can be utilized by using the proposed ART technique, which can be used with any scheduling policy. Based on these results, we only consider next computing the cost at the current scheduling time.

### 7.2. Effectiveness of the Proposed PCS Policy

Figures 8, 9, and 10 demonstrate the effectiveness of the two implementations of PCS when applied with ERMT, Transition Patching, and Patching, respectively, in terms of the customer defection probability, average waiting time, and unfairness. The figures show that PCS outperforms MCF-P and MQL in terms of both the two most important performance metrics (defection probability and average waiting time), whereas MCF-P is fairer towards unpopular videos. The two implementations of PCS perform nearly the same and thus PCS-V is preferred because of its simplicity. From this point on, we consider only the PCS-V implementation.

### 7.3. Effectiveness of the Proposed ART Enhancement

Figure 11 shows the effectiveness of the proposed ART technique when ERMT is used. With MCF-P, ART reduces the customer defection probability and average waiting time by up to and , respectively. It also yields significant improvements when used with MQL. Unfairness, the least important metric, is a little larger with ART because of its nature in favoring videos with shorter streams, but it is still acceptable compared with MQL.

Figure 12 depicts the impact of ART on regular streams in ERMT. We observe that when ART postpones regular streams, it forces ERMT to make more merges, which, in turn, increases system utilization. We also observe that the number of regular streams does not decrease significantly despite of postponing these streams. In contrast, Figure 12(a) indicates that the average time between two successive regular streams for popular videos is even smaller with ART than that without it. This is because ERMT keeps extending streams, which eventually become regular streams. Figures 12(b) and 12(c) compare the percentage of initial regular streams (I Streams) and extended regular streams (E Streams) without and with ART, respectively. We can see that the percentage of extended regular streams with ART is much higher. This supports the fact that the number of regular streams is not reduced by postponing. In summary, we can say that ART improves ERMT by replacing many *I Streams* with *E Streams*.

Let us now discuss the impact of ART when Transition Patching and Patching are used. Transition Patching results are presented in Figure 13 and Patching results are presented in Figure 14. As with ERMT, ART reduces significantly the customer defection probability and the average waiting time when it is combined with MCF-P and MQL. Unfairness with ART is a little larger but still acceptable compared with that of MQL for medium and high server capacities.

Interestingly, ART improves Transition Patching and Patching despite that their best scheduling policy, MCF-P (RAP), depends on a conflicting principle. As discussed earlier, MCF-P (RAP) gives preference to regular streams while ART postpones them in certain situations. As illustrated in Figure 15, the main impact of ART is dynamically optimizing , which is larger than that of MCF-P (RAP) and smaller than that of MCF-P (RAF) for popular videos, and even greater than that of MCF-P (RAF) for unpopular videos. The horizontal line in the figure marks the equation-based value of [27]. (Note that the equation does not yield optimum values because it is based on important simplifying assumptions.)

### 7.4. Comparing the Effectiveness of PCS and ART

Although ART can be applied with any scheduling policy, including PCS, for the time being, we consider it as an alternative to PCS because of negative interference between the two, as will be shown in Section 7.8. In this subsection, we compare the effectiveness of PCS-V and ART in terms of customer defection probability, average waiting time, unfairness against unpopular videos, and cost per request. Figures 16, 17, and 18 show the results of ERMT, Transition Patching, and Patching respectively.

With ERMT, MCF-P when combined with ART performs better than PCS-V in terms of the customer defection probability and average waiting time. The results when Transition Patching and Patching are used exhibit different behavior than those with ERMT. MCF-P combined with ART gives almost the same results as PCS-V in terms of customer defection probability, but it reduces the average waiting time significantly. Unfairness of PCS-V is less than that with ART in all stream merging techniques because ART favors videos with shorter streams more than PCS-V. These results indicate that MCF-P when combined with ART is the best overall performer.

To further support the fact that more customers are served with only one stream when using ART, Figure 19 demonstrates the impact of ART on the cost per request. We can see that the cost per request with ART is the lowest for different server capacities.

### 7.5. Impact of Workload Parameters on the Effectiveness of PCS and ART

Figures 20, 21, 22, and 23 illustrate the impact of the request arrival rate, customer waiting tolerance, number of videos, and video length on the effectiveness of PCS-V and ART. The results for both Patching and ERMT are shown. The results demonstrate that ART always achieves smaller customer defection probability and average waiting time than PCS-V in the case of ERMT. In Patching, the same trend is observed for the average waiting time, but PCS-V and "MCF-P combined with ART" perform nearly the same in terms of customer defection probability, especially when the server is highly loaded.

Figure 24 shows that the skew in video access has significant impacts on the customer defection probability, average waiting time, and unfairness. Recall that as increases, the skew in video access decreases. Both the defection probability and average waiting time are worsen by the reduction in the skew. This is because cost-based scheduling policies favor popular videos by nature. When increases, the deference in video popularity decreases which in turns makes the scheduling decision harder to make. Unfairness decreases by increasing which is as expected. Again, "MCF-P combined with ART" is the best policy in terms of all performance metrics, except unfairness.

The results so far are for a video workload of a fixed video length. Figure 25 shows the customer defection probability, average waiting time and unfairness results for a variable-length video workload. The workload is comprised of videos with lengths in the range of 60 to 180 minutes. The length of each video is generated randomly within the specified range. The results for the workload are obtained by averaging the values of four runs. The PCS-V and ART algorithms also work well in this workload. "MCF-P combined with ART" as in most cases performs better than all other policies. Moreover, we can see that the fairness of ART and PCS-V is better than that of MCF-P with variable-length video workload.

The results so far assume a Poisson request arrival process. Let us now examine the behavior under Weibull distribution with different shape () values. Figure 26 demonstrates that the shape has a little impact, especially when the server capacity is larger than 500 channels. Figure 27 compares MCF-P, PCS-V, and MCF-P with ART under Weibull Arrival Distribution with the same shape. The results with other shape parameters have the same trend and thus are not shown. We can see clearly that PCS-V and "MCF-P combined with ART" sill perform better than MCF-P. We can see also that MCF-P with ART is the best policy.

### 7.6. Comparing Waiting-Time Predictability with PCS and ART

Figure 28 compares the predictability of MCF-P, PCS-V, and "MCF-P combined with ART" in terms of the average deviation and percentage of clients receiving expected time of service (PCRE) under waiting tolerance Model B. The results with Model are similar and thus are not shown. The results demonstrate that ART significantly improves the predictability of MCF-P. PCS-V is also more predictable than MCF-P. In particular, ART reduces the average deviation by up to and for models B and C, respectively. It also increases the number of clients receiving expected times by up to . Moreover, "MCF-P combined with ART" gives more customers expected times than PCS-V with a relatively less significant increase in the average deviation.

### 7.7. Impact of Flash Crowds on the Effectiveness of PCS and ART

Let us now discuss the impact of flash crowds on the the effectiveness of PCS-V and ART. Figure 29 demonstrates the impact of flash crowds interarrival time on MCF-P, PCS-V, and "MCF-P combined with ART." The results shows that MCF-P when combined with ART handles the flash crowds more efficiently than the other policies. In particular, it achieves the best customer defection probability and average waiting time under all flash crowds interarrival times. PCS-V achieves better results than MCF-P, but its improvement is less than that of ART. Figure 30 confirms that ART enhances the efficiency of stream handling even with flash crowds. It is clearly evident that "MCF-P combined with ART" achieves the lowest cost per request for all videos.

### 7.8. Effectiveness of Combining ART with PCS

Let us now look at the results of combining PCS-V with ART. We show the results under ERMT and Patching in Figures 31 and 32, respectively. Transition Patching has the same trend as Patching and therefore its results are not shown. These results indicate that "MCF-P combined with ART" performs the best among all variations, and that PCS-V performs better than "PCS-V with ART." From these figures, we conclude that negative interference occurs when ART is combined with PCS-V. Removing this interference by modifying these two strategies is a challenging task and left for a future study.