# Improving Traffic Load Distribution Fairness in Mobile Social Networks
## 4 TraLDA Design
### Inherent Popularity Calculation  
The inherent popularity of a node is determined by its own sociability degree or movement pattern. In practice, this metric is defined based on a particular metric, such as the total contacts with different nodes in a time interval [21] or the neighbour change rate [38; 41]. In the literature, the former is denoted as the node degree in an aggregated encounter graph. In TraLDA, we use node degree to quantify a node's inherent popularity. Moreover, our investigation below shows that node degree in mobile social networks fluctuates significantly over time and exhibits some periodicity. Thus, it is important to take into account these features when calculating node degree at a given time. Finally, we introduce a novel calculation of node degree using the Kalman prediction [17] which consider the periodicity of human behaviour. We begin by looking into the node degree change characteristics in mobile social networks using real human movement cases. The Reality trace dataset [39] is used in this study because it consists of a large number of nodes and spans a lengthy period of time. Furthermore, an instantaneous node degree is estimated by the number of distinct nodes contacted in a given time window. In the case of Reality, we chose a time window of 6 h as the basis for node degree calculation based on a study in [21] that found that individuals' daily life is typically separated into four main periods of 6 h each: morning, afternoon,  
Figure 3: **(left)** Node degree vs. node traffic load, and (right) the buffer queue growths of illustrative hub node and non-hub node, when the hill-climbing heuristic forwarding is used in the mobile social network. This describes an imbalanced traffic load among nodes, with the highest degree nodes handling the bulk of network traffic, resulting in significant buffer occupancy throughout the simulation. evening, and night (however, for a detailed discussion of the impact of time window scale choices on the node degree calculation, see [42]). We now depict changes in node degree in the Reality scenario; for instance, in Figure 4 (left), we present the node degree variations of an illustrative hub node in Reality. We notice that the node's degree changes dramatically and rapidly over time. Subsequently, we use a periodogram analysis [43] to find the main periods (frequencies) within the node's degree data series. We display the discovered periodicities of the hub node's degree in Figure 4 (right). The figure clearly shows that the degree of the hub node firmly demonstrates a 7-days (weekly) period (moreover, our investigation on all the nodes in Reality finds that majority of the nodes possess a weekly cycle of their popularities as well). Indeed, the Reality dataset logged MIT staff and student activities on campus, which are higher during the weekdays but lower on weekends due to less interactions. Nevertheless, depending on the experimental setting, distinct human encounter datasets may have different periodicities. The structural component of the node degree data series in Figure 4 (left) is then observed using a discrete time series analysis. A discrete time series is a set of observations \(y_{t}\) logged regularly at a specific time interval. In the traditional decomposition model [44], \(y_{t}\) can be broken down into a trend component, a seasonal (periodic) component with period \(d\), and a random noise component. We apply a seasonal filter [45] to the given data series to get estimated periodic data: In Figure 5 (upper), we present the long-term seasonal data of the data series; finally, by removing the periodic data from the original data, deseasonalized data are obtained (shown in Figure 5 (lower)), consisting of a random noise element and a less obvious trend element. Based on the previous analysis, we now use the Kalman-filter theory [17] to develop an estimation model of the time series data to compute a node's inherent popularity in a time interval.