## 4 ARP Routing Protocol Design  
### Data Transmission  
People act in different social roles and differ in their popularity. e.g., some people are more popular than others in the society. This should also be true for sensor nodes in the network. We only employ heterogeneous popularity to help designing an efficient routing strategy. In ARP, data transmission decisions are made according to two parameters. The first one the called the transmission rankings, which indicate the likelihood that sensor nodes will communicate with the sink nodes. Generally, the more likely a node is to communicate with sink nodes, the higher the transmission ranking attached to it. The second one is the communication probability that is used to identify a sensor's communication strength with sink nodes at different time periods of a day. First we look at how to define the transmission ranking value of sensor nodes. Without loss of generality, we let _Pi_ denote the transmission ranking of sensor \(i\). Due to peoples' regular movement patterns, their social relationships vary much more slowly, and thus their transmission rankings are relatively fixed. We assume each sensor node needs to maintain a table that contains a list of transmission rankings of encountered nodes and its corresponding cumulative contact duration with nodes attached to the same transmission ranking. Let _Fi_ denote the contact table for sensor node \(i\), the process of determining _Pi_ can be described as follows. * _Pi_ is initialized to be zero. * If one of the addresses associated with the agenda for sensor node \(i\) comes within the transmission range of the sink node, no matter where the node is, _Pi_ is set to \(\Delta\) (where \(\Delta\) is a large integer used to represents the highest ranking). This is because sensor node \(i\) can communicate directly with the sink nodes sooner or later in such case. * If the above case can not be held, then when a mobile node \(i\) interacts with a node \(k\), if the transmission ranking of node \(k\) is not included in _Fi_, one item will be added in _Fi_ to record the contact information: the transmission ranking of node \(k\) and their contact duration. Otherwise, the corresponding cumulative contact durations depicted in _Fi_ will be updated in a timely fashion. * If and only if the total contact duration count of node \(i\) and sensor nodes possessing higher transmission rankings than node \(i\) exceeds a certain threshold _Th_ (where _Th_ is the upgrading \begin{table}
\begin{tabular}{|l|c|c|c|c|} \hline
**Mobility Model** & **Location preference** & **Realistic** & **Group-based** & **Independent of each other** \\ \hline Random Walk Model & No & No & No & Yes \\ Random Waypoint Model & No & No & No & Yes \\ Column Mobility Model & No & No & Yes & No \\ Nomadic Community Mobility & No & No & Yes & No \\ Community-based Model & Yes & Yes & No & Yes \\ Agenda Model & Yes & Yes & No & Yes \\ \hline \end{tabular}
\end{table} 
Table 1: Node characteristics in five mobility models. threshold which we will vary in this paper to see its impact on the network performance), _Pi_ is increased. * When node \(i\) cannot contact with nodes with higher transmission rankings than itself for a certain period of time (e.g., \(\lambda\)), the transmission ranking of node \(i\) will be decreased accordingly. We define the community as formed by sensor nodes with the same transmission ranking. Thus, the social network can be partitioned into a set of communities through the aforementioned method. Figure 2 depicts a network consisting of five communities. Furthermore, for nodes with the highest transmission ranking, since they contact with sinks at different times, their communication probabilities vary with time. We let _Tp_ denote the current time and let the communication probability of node \(m\) with the sink node \(n\) be _Ymn_, when _Tm_ \(>\)_Tp_, we have:  
\[Ymn=1-\frac{(Tmn-Tp)}{24} \tag{1}\]  
where _Tmn_ denotes the encounter time between node \(m\) and the sink node \(n\) (_n_ = 1,2,3...). Otherwise, _Ymn_ = 0.