# Improving Traffic Load Distribution Fairness in Mobile Social Networks
## 5 Simulation and Discussion
### Simulation Results and Discussions
#### 5.2.1 BubbleRap vs. Bubble-TLDA  
BubbleRap bases its routing on both node global popularity and the community to which the destination belongs to. When either the current node or the encountered node is in the destination's community, routing decisions are performed based on local popularity, which is the popularity of the node within the given community; otherwise, global popularity is considered. In BubbleRap, the C-Window method is used to compute node global popularity. This method calculates a node's degree value in the current time window by simply taking the average of all the node's degree values in prior time windows. TraLDA, on the other hand, estimates node inherent popularity in a time window (also measured in node degree) based on the Kalman prediction which considers the periodicity of human activities. For a performance comparison between two schemes, in Figure 7 we show the time series of an illustrative hub node's degree values in Reality. In each time window, the node's degree value is determined based on real measurement (\(y_{t}\)), C-Window (\(\overline{y}_{t}\)) and Kalman prediction (\(\hat{y}_{t}\)) (we show these values in a daily basis to make them easily observed). For Kalman prediction, we assume (from Section 3.1) that the seasonality \(S_{t}\) is known with the period of 7 days. Figure 7 shows that Kalman prediction captures fluctuations in the node degree values, and thus delivers more accurate estimations of the instantaneous node's popularity compared to BubbleRap's C-Window. C-Window reacts slowly to variations in node popularity and ignores the regularity of human activity. We next discuss the delivery performance of BubbleRap compared with that of BubbleTLDA in the Reality and Sassy scenarios based on the given evaluation metrics. As we noted above, BubbleRap considers node global popularity, and the community of the destination belongs to when making forwarding decisions. To determine the community of a node, we exploit the \(k\)-clique community detection in [50]. For the parameters of the  
Figure 7: Node degree values of an illustrative Reality hub node in a certain time window, comparing the actual value, the Kalman prediction, and the C-Window estimate. [PERSON] prediction clearly outperforms C-Window when estimating the actual node’s degree level in each time window, and it captures the periodic pattern of the node degree quite well. \(k\)-clique scheme used by both BubbleRap and Bubble-TLDA, we choose \(k\) = 5 and familiar threshold \(T_{th}\) = 250 k seconds for Reality, and for Sassy \(k\) = 3 and \(T_{th}\) = 3 k seconds. Moreover, for the TraLDA's parameters in Bubble-TLDA, we use two distinct values of friendship thresholds for each mobility scenario: \(F_{th}\) = 150 k seconds and 300 k seconds for Reality, and \(F_{th}\) = 2 k seconds and 3 k seconds for Sassy. In addition, for both mobility scenarios, we use a social impact factor (\(\xi\)) of 0.8, which determines the weight of neighbours' influences on the overall node's popularity. As previously mentioned in the node social-relations popularity (Section 4.2), the neighbourhood of a node is defined in terms of a friendship set, with another node being involved in the node's friendship set if their pairwise total encounter time surpasses a given friendship threshold (\(F_{th}\)). Indeed, this threshold is critical for TraLDA's performance as it dictates the size of a node's friendship set, which in turn impacts the node's social influence in its neighbourhood. For instance, in Table 1 we show the comparison of the friendship sets of hub node and non-hub node in the Reality scenario for various values of friendship threshold (\(F_{th}\)) (in seconds). In the hub node, we notice that increasing the friendship threshold \(F_{th}\) makes the friendship set shrinking (Table 1a). This implies that as \(F_{th}\) increases, the spread of social influences of the hub node to its neighbours diminishes.