# Smart Collaborative Caching for Information-Centric IoT in Fog Computing
## 4 Validation and Discussion
### Scenario Two: Complex Content Sharing (One Request and Multiple Responses).  
Suppose each subscriber requests 100 pieces of content from one publisher. The corresponding applications might be video surveillance, file transmission, etc. To better reflect the real situations, we consider drop events in this scenario. Set the packet loss probability of each link among clusters is \(p\) (\(0<p<0.5\)). Let us assume that the request packets, retransmitted packets and packets in last hop will not be dropped by the network.  
Figure 4: Results for scenario one: simple status inquiry.  
Before calculating the packet number and transmission latency in four candidates, a fundamental issue must be analyzed in depth: Will longer path or shorter path generate larger packet number during the transmissions? It is straightforward in previous scenario because no packet is lost. To answer such question quantitatively, we need to consider a generic case. The topology is minimized by adding one subscriber, one cluster, one rendezvous server (located inside another cluster) and one publisher. For the backward path, the number of data packets \(X\) (for the shorter path case) can be achieved based on Equation (6):  
\[X=100+100(1-p)+100(1-p) \tag{6}\]  
where each item is for each independent link. Then the topology can be enlarged by adding \(N\)-2 more intermediate clusters. For the backward path, the number of data packets \(Y\) (for the longer path case) can be recalculated based on Equation (7):  
\[Y=100+\left[100(1-p)+\cdots+100(1-p)^{N-1}\right]+100(1-p)^{N-1} \tag{7}\]  
where the items inside square brackets are for the links among clusters. If the target condition is \"larger packet number belongs to longer path\", the value of \(Y\) should be bigger than that of \(X\). Based on the geometric progression theory, such condition could be equivalently converted to Formula (8):  
\[\frac{(1-p)-(1-p)^{N-1}+p(1-p)^{N-2}}{p}>1 \tag{8}\]  
To further explore the relationship between \(p\), \(N\) and packet number, we draw two analytical figures in Matlab. Figure 4(a) illustrates the results of three representative \(N\) (5, 10 and 20 are represented with black, blue and red, respectively). With the increasing of packet loss probability (from 0 to 1), all curves are getting down. The critical value appears when \(p\) is around 0.5, i.e., the value of polynomial will approach 1. Since more values of \(N\) will lead to serious overlaps, we only reserve three curves in Figure 4(a). More details are demonstrated in Figure 4(b) from the three-dimensional perspective. It also proves that \(0<p<0.5\) is a reasonable selection for scenario two.  
Figure 5(a) illustrates the packet number statistics. Although the sequence (from top to down) of four curves are the same with Figure 3(a), the values of many points have been changed. We still select 80 and 140 as two representatives for \(N\). The increasing rates for ICN Flooding and IP Network curves are 207.8% and 9.3%, respectively. The disadvantages of the flooding scheme are also displayed. By adding new features of ICN SCC, the packet number growth is only 7.4%. Such a benefit is more obvious if the ICN SCC-E scheme is utilized.  
Figure 5: Relationship analysis for \(p\), \(N\) and packet number.  
Figure 6b illustrates the transmission latency statistics. The variations in scenario switching and experiment adjustment did not drastically influence the validation results. The performance enhancement of ICN SCC and ICN SCC-E is confirmed.