## 4 Performance Analysis
### Evaluation Metric  
From several results obtained from our simulation experiments, we made use of the following performance metrics for evaluation purposes.  
Energy consumption: The energy consumption is the sum of used energy of all the sensor nodes in the network during the period of the experiment in Joules (J). We estimate the node energy consumption considering the energy model proposed in [3].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Dimension of topology & 1000 \(m^{2}\) & Number of nodes & _100–500_ \\ Nodes placement & _Random_ & Mobility & _Static_ \\ Traffic & Constant Bit Rate (\(CBR\)) & Simulation time & _300 s_ \\ MAC layer & _IEEE 802.11_ & Initial energy & _1000 J_ \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Energy efficiency: This denotes the ratio of the total packets delivered at the sink node to the total energy consumed by the sensor nodes (Kbits/J).  
Energy standard deviation. This gives the average variance between energy consumed on all nodes. It describes the energy consumption distribution of the networks. A low standard deviation indicates that the data points tend to be close to the expected value of the set, while a high standard deviation indicates that the data point is spread out over a wider range of values. The motivation behind this definition is that the algorithms should result in a low energy consumption standard deviation, which implies an even consumption distribution and good load-balance.  
Network lifetime prediction. This is defined as the difference of the total initial energy of the network and the summation of the average used energy of nodes and the standard deviation of their energy levels.  
\[Lifetime\ Prediction=E-(\bar{\mu}+\sigma) \tag{11}\]  
where \(E\) is the total initial energy, \(\bar{\mu}\) is the average used energy, \(\sigma^{2}=(\mu_{i}-\bar{\mu})^{2}/N\), \(N\) is the total number of nodes in network and \(\mu_{i}\) denotes the residual energy of node \(i\). The basic motivation behind this definition is that an algorithm should try to maximise average remaining energy levels of nodes, but with a minimal standard deviation.  
Route setup time: This represents the time spent by a protocol to discover routes from the source node to the sink node. It is used to measure the time that the first effective route is discovered. We design a series of dynamic networks of different sizes to analyse this metric and evaluate the performance of the route discovery scheme and local heuristic update strategy in our proposed routing algorithm.  
Convergence time: We define the convergence time as the optimised route setup time. It is complex and non-trivial to detect if the optimal route is established. Nonetheless, for an ACO algorithm used in simulated routing algorithms, convergence has been proven [42], which means these routing algorithms will discover an optimal route in a finite time. Here, we arrive at the convergence time by measuring the interval between the detection of the stable optimal route and route discovery initialisation.  
Throughout: The number of messages per second received at thedestination. The throughput of the network is the sum of the throughput from all destinations.