## 4 Evaluation
### Evaluation Methodology
#### 4.1.2 Performance Evaluation Metrics  
This section presents the metrics, namely throughput, transmission overhead, average delivery delay, routing fairness and energy distribution, for the performance evaluation. Throughput. As shown in Equation (4), throughput is the ratio between \(d\), the total number of messages successfully delivered at their respective destinations, and \(g\), the total number of messages generated. This signifies the message delivery efficiency of a forwarding algorithm, within assigned TTL  
\[Throughput=d/g \tag{4}\]  
Transmission overhead. As shown in Equation (5), the transmission overhead represents the average number of transmissions required to deliver a message copy, where \(T\) is the total number of message transmissions, and \(V\) is the number of times messages were delivered. This is equivalent to the cost of delivering messages with a forwarding algorithm, since every transmission consumes energy on user devices. \[Transmission\;overhead=(T-V)/V \tag{5}\]  
Average delivery delay. Delivery delay is the time elapsed (in seconds) between message generation and delivery. As shown in Equation (6), the average delivery delay is the mean delivery delay in the network, where \(G_{i}\) and \(D_{i}\) are the generation time and the delivery time of Message \(i\), respectively. This gives an insight on how long it takes to deliver a message. \[Average\;delivery\;delay=\sum_{i=1}^{d}(D_{i}-G_{i})/d \tag{6}\]  
Routing fairness. Here, we elaborate the fairness metric [70] employed to measure routing fairness in this paper. The metric uses the distribution of node burden as a measure for fairness. Hence, a small variation between nodes' burden results in more fairness than a large variation. To illustrate this, consider a scenario of six fictitious routing techniques, denoted by A to F. As shown in Table 3, four nodes, identified by n1 to n4, are subjected to different amounts of burden under each forwarding  
Figure 7: The Skudai simulation area (map data provided by OpenStreetMap, 2015). algorithm. The standard deviation from the mean burden on the nodes under a routing technique, \(p\), is then given as:  
\[\gamma_{p}=\sqrt{\sum_{i=1}^{n}\bigl{(}r_{p,i}-R_{p}\bigr{)}^{2}/n} \tag{7}\]  
where \(n\) is the total number of nodes, \(r_{p,i}\) is the burden \(p\) subjects on node \(i\), and \(R_{p}\) is the mean burden for a node running on \(p\). Assuming that every node runs on the same routing technique, then \(\gamma_{p,max}\), the maximum possible standard deviation for \(p\) (i.e., the standard deviation from the mean burden if \(p\) subjects only one node to all the burden--which is also the least fair scenario, such as algorithm F in Table 3) becomes:  
\[\gamma_{p,max}=\sqrt{\left[\left(r_{p,total}-R_{p}\right)^{2}+{R_{p}}^{2}(n-1) \right]/n} \tag{8}\]  
where \(r_{p,total}\) is the sum of the burden on every node. We then define the \"unfairness\" of \(p\) as the ratio between \(\gamma_{p}\) and \(\gamma_{p,max}\) (cf., Equation (9)). \[U_{p}=\frac{\gamma_{p}}{\gamma_{p,max}}\times 100 \tag{9}\]  
\[F_{p}=100-U_{p} \tag{10}\]  
If \(p\) subjects the same amount of burden on every node, \(F_{p}\) in Equation (10) will be 100% (e.g., A in Table 3). Likewise, if only one node is subjected to all the burden in the network, \(F_{p}\) will be 0% (e.g., F in Table 3). \(F_{p}\) also decreases accordingly, the less evenly the total number of transmissions is distributed among the nodes (e.g., B to E in Table 3). Therefore, we use \(F_{p}\) as a measure of the fairness of a routing technique in terms of the burden subjected on nodes. Average energy consumption. Energy consumption (in Joules) is the amount of initial energy expended at the end of the simulation. As shown in Equation (11), the average energy consumption is the mean energy consumed by nodes in the network; where \(n\) is the total number of nodes, and \(E_{i}\) and \(e_{i}\) is the initial energy and the remaining energy of Node \(i\), respectively. This gives an insight on how routing impacts on resource consumption.