# Improving Traffic Load Distribution Fairness in Mobile Social Networks
## 5 Simulation and Discussion
### Simulation Results and Discussions
#### 5.2.1 BubbleRap vs. Bubble-TLDA
Since a hub node, in general, is the most active node in the network, it consequently has weaker ties with its neighbours. Furthermore, [PERSON] [53] underlined the relevance of weak relationships in information dissemination in social networks. A non-hub node, on the other hand, has stronger relationships to its direct neighbours, and as indicated in Table 1b the friendship threshold (\(F_{th}\)) in this case has a small influence on the node's friendship set size. Finally, we depict the delivery performances of BubbleRap and Bubble-TLDA in Reality and Sassy in Figures 8 and 9, respectively, based on the four performance metrics mentioned before. For Bubble-TLDA, we consider two distinct friendship thresholds for each scenario: for Reality \(F_{th}\) = 150 ks and 300 ks, and for Sassy \(F_{th}\) = 2 ks and 3 ks. Since the primary purpose of TraLDA is to enhance fairness in forwarding across network nodes, we notice in these figures that this is achieved: Bubble-TLDA can improve the traffic distribution fairness in both scenarios, indicated by the reduced of GINI index. The improved traffic fairness of Bubble-TLDA has a little impact on the delivery rate, i.e., Bubble-TLDA keeps the delivery success rate as high as that of BubbleRap. In addition, Bubble-TLDA with a lower friendship threshold (\(F_{th}\)) can give a more significant impact on reducing the GINI index. As mentioned in Table 1, the lower friendship threshold (\(F_{th}\)) means the wider influences of hub nodes on their neighbourhoods, resulting in more non-hub nodes that can increase their popularity and, in turn, may become better relays. For example, in Figure 10 we show the distribution of traffic load among nodes in Reality for BubbleRap and Bubble-TLDA (\(\xi\) = 0.8, \(F_{th}\) = 150 ks). Bubble-TLDA is clearly capable of significantly reducing the relay traffic managed by the most popular nodes (hub nodes), while, on the other hand, simultaneously increasing the total relay traffic on a large number of non-hub nodes, and thereby improving traffic load balancing across network nodes. The reduction in load in the most popular nodes in the case of Bubble-TLDA, on the other hand, negatively impacts on the delivery latency. In both Reality and Sassy, as illustrated in Figures 8 and 9 (upper-right), Bubble-TLDA increases delivery time beyond  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**(a) Node 80 (Hub Node)** & **(b) Node 3 (Non-Hub Node)** \\ \hline \(F_{th}\) **(s)** & **Friendship Set (Node ID)** & \(F_{th}\) **(s)** & **Friendship Set (Node ID)** \\ \hline
150 k & [5, 7, 13, 15, 17, 20, 22, 32, 82, 84, 85, 95] & 150 k & [45, 63, 82, 95, 96] \\
200 k & [5, 7, 13, 17, 20, 22, 32, 82, 84, 95] & 200 k & [45, 63, 82, 95, 96] \\
250 k & [5, 7, 13, 17, 20, 22, 82, 84, 95]that of BubbleRap. Reducing traffic on the hub nodes implies that most of the network traffic is diverted away from the shortest-paths through these nodes, and now traverses on the suboptimal-paths via non-hub nodes which is typically longer than the shortest-paths, resulting in a longer delivery time. Figure 8: Performance evaluation of BubbleRap and Bubble-TLDA (\(\xi=0.8\)) for the Reality mobility scenario, comparing the delivery performances of BubbleRap and its improved version, BubbleTLDA. Bubble-TLDA significantly decreases of the GINI index of BubbleRap in this case, without negatively impacting other delivery performances. Figure 9: Performance evaluation of BubbleRap and Bubble-TLDA (\(\xi=0.8\)) for the Sassy mobility scenario. In this case, Bubble-TLDA slightly improves the traffic distribution (indicated by a reduced GINI index), while keeping other delivery performances as high as those of BubbleRap. Subsequently, we investigate the effect of a social impact factor (\(\xi\)) on Bubble-TLDA' performance, particularly delivery latency and GINI index. In TraLDA, a social impact factor (\(\xi\)) determines the weight of neighbours' influences on the node's global popularity.