Page 144 - ITU Kaleidoscope 2016

2016 ITU Kaleidoscope Academic Conference

5. ANALYSIS
To know the accuracy of the system model and the simulation,
the simulations are performed in SocialCCNSim [43] - ICN
caching simulator, according to the parameters presented in
Table 1, while the analysis is done in Maple 18 for cache
hit according to the parameters presented in Tables 2 and 3.
For the analysis of cache hit, we consider a real Facebook
topology [40–42] which consists of 4,039 nodes. We assume
that each node in the network is placed at a constant distance:
in our assumption, this distance is 25 meters. Each time when
a content is downloaded, the hop decrement increases 100 Figure 3. CPCE analysis vs. simulation
hops. This assumption is made on the basis of our ordinary
topology in Figure 1, where initially a subscriber is 4 hops
Table 2. Cache Hit: Analysis vs. Simulation with α =0.7
away (on any path) from the node (i.e., Server) having the and Chunk Size 10MB.
desired content. As hit occurs and the content popularity
Cache Size Chunk Anal Sim Difference
reaches the threshold value (i.e., 10), it is cached at all on-
2
1 1(10 ) 0.10 0.10 0.00
path routers. However, according to our proposed strategy, 2
the content may be evicted from all routers (UR 1 to UR n )but 2 2(10 ) 0.12 0.11 0.01
2
it will stay at the router having maximum outgoing interfaces 3 3(10 ) 0.14 0.12 0.02
2
(Router R1 in the given figure), which is 3 hops away from 4 4(10 ) 0.15 0.13 0.02
2
the user(s). 5 5(10 ) 0.16 0.14 0.02
2
6 6(10 ) 0.17 0.15 0.02
When 0 <α< 1, the asymptotic cache hit ratio, H c ,is 2
calculated as [45,46]: 7 7(10 ) 0.18 0.16 0.02
2
8 8(10 ) 0.19 0.17 0.02
2
H c = C 1−α (9) 9 9(10 ) 0.19 0.17 0.02
2
10 10(10 ) 0.20 0.18 0.02
where C is the cache size that caches chunks (each chunk
is of 10MB size) and α=0.7. Looking at the analysis and
simulation results, presented in Table 2, the average result of Table 3. Cache Hit: Analysis vs. Simulation with α =1.0
and Chunk Size 10MB.
analysis is 16% while it is 14.3% for simulation. The average
difference is 1.7% and hence the accuracy is 98.3% . The Cache Size Chunk Anal Sim Difference
2
resultant graph is shown in Figure 3(a). The same variables, 1 1(10 ) 0.23 0.22 0.01
2
i.e., cache size and chunk size, are used for the scenario when 2 2(10 ) 0.29 0.27 0.02
2
α=1.0. Now, if α=1.0, the asymptotic cache hit ratio, H c ,is 3 3(10 ) 0.34 0.32 0.02
2
calculated as [45,46]: 4 4(10 ) 0.36 0.34 0.02
2
5 5(10 ) 0.39 0.37 0.02
2
H c = lnC. (10) 6 6(10 ) 0.40 0.39 0.01
2
7 7(10 ) 0.42 0.40 0.02
The analysis and simulation results are presented in Figure 2
8 8(10 ) 0.43 0.42 0.01
3(b) and Table 3. The average analysis and simulation results 9 9(10 ) 0.44 0.43 0.01
2
are 37.6% and 36.1% , respectively. The average difference is 2
10 10(10 ) 0.46 0.45 0.01
1.5% and therefore the accuracy is 98.5% . It is observed that
when the cache size is small then the difference of analysis
and simulation results (with α=1.0) is high, however, with the
increase of cache size this difference approaches 0.
Similarly, for the analysis of stretch results, we consider the
αn
same scenario with a real Facebook topology [40–42]. The S = − (D + h) (12)
numerical results can be calculated as [47]: 2γ
αn where n is the number of total network nodes, γ is the distance
S = (11)
2γ between two hops, D is the hop decrement, and h is a constant.
We assume that D=γ and the value of h=4. This assumption is
where S represents the stretch, n is the total number of network based on our ordinary proposed topology, shown in Figure 1.
nodes, γ is the distance between two hops, and α is the Zipf The achieved analysis results are presented in Figure 3(c) and
probability parameter, such that 0<α< 1. Table 4 for α=0.7, and Figure 3(d) and Table 5 for α=1.0. The
In addition, the numerical results for α=1.0 can be calculated average difference in α=0.7 is 2.2% while it is 4.8% when
as: α=1.0.
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