Chapter 4 Experimental Results
4.1 Study of content popularity evolution
In order to evaluate the effectiveness of our caching strategies, we need to take the popularity of the videos into account. In our simulation model, the hit rate that each method performed is related to specific videos. Especially when VoD is available, which video is the choice of a client depended on video’s popularity. The Zipf-distribution is the model used for request probability and [10] is used for modeling video life cycle.
4.1.1 Zipf distribution
We assume N is the amount of videos at this time, k is the rank of the distribution, andα is the value of the exponent characterizing the distribution.
∑
==
Nn
n
N k k f
1
( 1 / ) /
) 1 ,
;
(
αα
αThe figure 18 has shown a comparison for two differentα . Figure 18 (a) and (b) have shown the Zipf PMF for α = 0.8 and α =1.6 respectively. The horizontal axis is the index k and N=400. The vertical axis is the access probability. The function is only defined at integer values of k.
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
0
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
0
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
51 1
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
101 151
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
1 201
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
251
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
301
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
351
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
22 (a) 0.8
(b) 0.6
Figure 18 (a, b) Comparison of different Zipf parameters
4.1.2 Video life cycle
In our experiments, three distinct video life cycles have been taken into account:
short-term, long-term, and up-and-down. Assuming the model has a temporal resolution of every 30 minutes, as figure 19 (a, b, c) illustrated, these three kinds of life cycle are described as following:
• Short life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses per time unit decreases suddenly.
23
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
• Long life: This content reaches the highest popularity during the first 30 minutes, and the number of accesses for every time unit decreases slowly.
• Up and down: The popularity of contents goes up and down.
(a) (b)
(c)
Figure 19 (a, b, c) Content life-cycles
As mentioned in 4.1.1, each video has distinct life-cycles; we can map the index of Zipf-distribution to the distinct videos according to the content popularity evolution model. We used both of the population models in [7] and [10].
The population model in [7] is called Range n in our simulation. The parameter n can be adjusted to a smaller value for a low variability of content popularity environment, and a larger value for high variability.
The population model in [10] is expressed by RP (t):
24
The coefficient of correlation, both of aand care set equal to 0.01, and B is a variable value. B can be adjusted to a smaller value for modeling short-term life cycle, and a larger value for long-term life.
Since our model has a temporal resolution of every 30 minutes, the t of RP (t) is 30 minutes as a unit. As figure 20 illustrated, the horizontal axis is how long a video has been produced, and the vertical axis represents the popularity of this video, which is measured in terms of access probability.
(a)
(b)
Figure 20 (a, b) Long-term life-cycles