Sliding window size

As we have mentioned in section 3.5, each segment in buffer has a cache value to reveal its popularity. The problem is how the value of ts is decided. If the ts is adjusted too small, the segment that will be popular at future may be replaced. If the ts is adjusted too large, the replacement strategy will be insensitive. There are two goals that the cache value approached can be classified:

A. To keep the segment that will be popular at future for longer time.

B. To detect the wasted storage sensitively to replace the unpopular segments.

For the goal A, we concern that the video life cycle is up and down. In order to predict the ts, we have ranked all segments according to their popularity over time, and then we evaluated the rank of a segment over time in figure 21. Assuming the rank is from 0 to 250, the rank 0 is most popular, and rank 250 is most unpopular.

According to the figure 21 (a), assume that the top 10 ranks are popular enough, and it’s unpopular when the number of a rank is over 10. Now we discuss how to decide ts in order to keep top 10 ranks of videos in cache even though these videos may fall out of top 10 ranks for short time.

First of all, we discuss the Range n environment. The figure 21 (a) has shown that the variability of the population is higher when the value of n is 20. Taking the Range 20 situation into consideration, we scale up the figure 21 (a) curve that the Range 20 video stayed at top 10 ranks and show it in figure 21 (b). In figure 21 (b), it is observed that the popularity of a video falls below top 10 ranks in two periods. To keep this video in cache when it goes up to top 10 again, since the maximum period e

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is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

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is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

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is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

29

is long enough to cover the shorter period d, the value of the ts can be predicted as the interval of period e.

Secondary, we discuss the complex video life-cycle environment where the popularity of video may go up and down. The population models are generated by RP(t) that parameter B are 7 and 38 as figure 21 (c) and (d), respectively. For instance, a peer has requested the segment for the duration a, we hope that the peer will retain the segment in its buffer until the duration c, so that it can be accessed when it is at top 10 ranks. In this case, the value of ts is supposed to be as the duration b at least.

For the goal B, in order to improve the sensibility of our replacement strategy, we set the value of ts to be 30 minutes through our experiments except the value of ts is 60 minutes instead of 30 minutes in “Half 88-7” and “Pop 88-7” popularity environments which are having more long life segments.

(a)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

30 (b)

(c)

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(c)

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Figure 21(a, b, c, d) Popularity ranked

4.3.2 Experimented results

As the figure 23 shows the results of performance evaluation of the method 1, method 2, and method A. And the method 1, method 2, and method A indicate the

“Overwriting continuous”, “No overwriting”, and “Adaptive overwriting”

respectively. The figure 23 (a, b) are the results in all population models that have been defined in 4.1 and illustrated in table 4. The figure 23 (c, d, e) are the results in Range 50 population environment.

In figure 23 (a) and (b), we set the Zipf parameterα equal to 0.8 and 1.6, respectively, and evaluated all of three methods in all population environments that were mentioned in 4.2.2. By comparing the Zipf PMF forα = 0.8 andα =1.6 as figure 18 (a, b), we can describe the Zipf PMF for α = 0.8 has the lower difference in popularity between the segments. And the Zipf PMF for α = 1.6 has the higher difference in popularity between the segments. Due to the characteristic of Zipf PMF, we found out the method 2 can obtain higher hit-rate obviously than the hit-rate of method 1 whileα is equal to 1.6.

Figure 23 (a) shows the method 2 outperforms the method 1 in most case. And the method A outperforms the method 1 and method 2 in all cases. However, in the Full-RP and Half-RP7-88 environments, the method 2 has lower hit-rate than method 1. The possible reasons are discussed below:

• Range n/Half-RP88-7: Method 2 can obtain a higher hit-rate in Range n and Half-RP88-7 because each segment was popular when it is newly produced from the content provider. For an instance in figure 22 (a), we assume the segment 1 is a long life video, and it’s popular when it is newly produced from the content provider at t0. According to method 2, segment 1 will be stored on the peers

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arrived until the storage space is full, so other peers (including early arrived peers and lately arrived peers) can receive segment 1 from the caches of these peers. The access to segment 1 may last for a long time because it is a long life video. The peers that have the segment 1 can serve other peers for a long time as a popular duration of segment 1. Taking advantages of more long-life videos in Half-RP88-7 model, method 2 performs much better than method 1.

• Half-RP7-88: There are more short-life segments in Half-RP7-88. More peers still retained the segments that have become unpopular, because the method 2 is a No overwriting strategy. For Zipf withα =1.6, method 2 still can takes advantages of skewed access to achieve a better result than method 1. However, for Zipf withα =0.8, method 2 lost its benefits and resulted in a worse performance.

• Full-RP: We have mentioned the videos in Full-RP environment are up-and-down life cycle. For an instance of Full-RP in figure 22 (b), there is a serial requests for segment 1. The segment 1 is becoming popular at t2, but there is no peer has already stored the segment 1, because it had low request frequency before t2.

(a) (b) Figure 22 (a, b) Instance for a serial requests

Figure 23 (c) shows the method 2 can enhance the hit-rate of method 1, and the

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arrived until the storage space is full, so other peers (including early arrived peers and lately arrived peers) can receive segment 1 from the caches of these peers. The access to segment 1 may last for a long time because it is a long life video. The peers that have the segment 1 can serve other peers for a long time as a popular duration of segment 1. Taking advantages of more long-life videos in Half-RP88-7 model, method 2 performs much better than method 1.

• Half-RP7-88: There are more short-life segments in Half-RP7-88. More peers still retained the segments that have become unpopular, because the method 2 is a No overwriting strategy. For Zipf withα =1.6, method 2 still can takes advantages of skewed access to achieve a better result than method 1. However, for Zipf withα =0.8, method 2 lost its benefits and resulted in a worse performance.

• Full-RP: We have mentioned the videos in Full-RP environment are up-and-down life cycle. For an instance of Full-RP in figure 22 (b), there is a serial requests for segment 1. The segment 1 is becoming popular at t2, but there is no peer has already stored the segment 1, because it had low request frequency before t2.

(a) (b) Figure 22 (a, b) Instance for a serial requests

Figure 23 (c) shows the method 2 can enhance the hit-rate of method 1, and the

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arrived until the storage space is full, so other peers (including early arrived peers and lately arrived peers) can receive segment 1 from the caches of these peers. The access to segment 1 may last for a long time because it is a long life video. The peers that have the segment 1 can serve other peers for a long time as a popular duration of segment 1. Taking advantages of more long-life videos in Half-RP88-7 model, method 2 performs much better than method 1.

• Half-RP7-88: There are more short-life segments in Half-RP7-88. More peers still retained the segments that have become unpopular, because the method 2 is a No overwriting strategy. For Zipf withα =1.6, method 2 still can takes advantages of skewed access to achieve a better result than method 1. However, for Zipf withα =0.8, method 2 lost its benefits and resulted in a worse performance.

• Full-RP: We have mentioned the videos in Full-RP environment are up-and-down life cycle. For an instance of Full-RP in figure 22 (b), there is a serial requests for segment 1. The segment 1 is becoming popular at t2, but there is no peer has already stored the segment 1, because it had low request frequency before t2.

(a) (b) Figure 22 (a, b) Instance for a serial requests

Figure 23 (c) shows the method 2 can enhance the hit-rate of method 1, and the

32

arrived until the storage space is full, so other peers (including early arrived peers and lately arrived peers) can receive segment 1 from the caches of these peers. The access to segment 1 may last for a long time because it is a long life video. The peers that have the segment 1 can serve other peers for a long time as a popular duration of segment 1. Taking advantages of more long-life videos in Half-RP88-7 model, method 2 performs much better than method 1.

• Half-RP7-88: There are more short-life segments in Half-RP7-88. More peers still retained the segments that have become unpopular, because the method 2 is a No overwriting strategy. For Zipf withα =1.6, method 2 still can takes advantages of skewed access to achieve a better result than method 1. However, for Zipf withα =0.8, method 2 lost its benefits and resulted in a worse performance.

• Full-RP: We have mentioned the videos in Full-RP environment are up-and-down life cycle. For an instance of Full-RP in figure 22 (b), there is a serial requests for segment 1. The segment 1 is becoming popular at t2, but there is no peer has already stored the segment 1, because it had low request frequency before t2.

(a) (b) Figure 22 (a, b) Instance for a serial requests

(a) (b) Figure 22 (a, b) Instance for a serial requests