## 5 Performance Analysis
### Performance Metrics  
The following performance metrics were used for analysis:  
1. Safety Period (SP): the same as in Reference [3], safety period can be defined in multiple ways: (i) the time required for an adversary to successfully back trace and capture the asset, (ii) the number of packets successfully delivered to the destination sink node before the adversary locates the source node, or, (iii) the maximum duration of time the monitored asset will be at a given location before it moves to a new location. The first definition is assumed in this study. Safety period \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network size (m\({}^{2}\)) & \(2000\times 2000\) \\ Number of nodes & 2500 \\ Number of sink nodes & 1 \\ \(dP_{in}\) (m) & 400 \\ \(dP_{out}\) (m) & 600 \\ \(T_{P}\) & 0.5 \\ \(d_{H}\) (hops) & 3 \\ \(d_{P}\) (hops) & 4 \\ \(d_{NB}\) (m) & 200 \\ \(T\) & 0.5 \\ Sensor node sensing range (m) & 30 \\ Adversary detection range (m) & 30 \\ Adversary waiting timer (source packets) & 4 \\ Adversary initial location & In the vicinity of the sink node \\ Source packet rate (packet/second) & Varied between 1 and 7 \\ Target monitoring scheme & k-nearest neighbors tracking \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Network simulation parameters. is used to measure the privacy performance of the protocols. Longer safety periods provide stronger SLP protection. To evaluate the SLP performance, the following expression was assumed \[\max(SP)=\max(\mathit{SLP}_{\mathit{Protection}}).\]
2. Attack success rate (ASR): the measure of the rate of source node traceability when an eavesdropping adversary is back tracing against a SLP routing protocol. It is computed by counting the number of successful adversary attempts [8]. ASR has an inversely proportional relationship with the safety period. When a protocol achieves a long safety period and high privacy, the ASR is low. To evaluate the ASR of the adversary, the following expression was assumed \[\max(SP)=\min(ASR).\]
3. Energy consumption: the energy consumed by the sensor nodes for transmitting and receiving packets as shown in Equations (1,2). The energy consumption model was adopted from References [3; 4; 5; 7]. To transmit an \(l\)-bit packet to a transmission distance \(d\), transmission energy, \(E_{\mathit{trans}}\), and receive energy, \(E_{\mathit{rec}}\), follow Equations (1,2), respectively. According to the model, energy consumption for packet transmission is an exponential function of \(d\). \(E_{\mathit{loss}}\) represents the transmitting circuit loss. Two loss models are applied, the free space (\(d^{2}\) power loss) and the multi-path fading (\(d^{4}\) power loss) channel models. If the transmission distance between sensor nodes is less than the threshold \(d_{0}\), the power amplifier loss is based on free-space model. Otherwise if the transmission distance is equal or greater than the threshold \(d_{0}\), the multi-path attenuation model is used. The threshold distance, \(d_{0}\), is computed according to Equation (3). \(E_{\mathit{fs}}\) and \(E_{\mathit{amp}}\) are the energy required by power amplification in the two power loss models. Table 7 shows the energy consumption model parameters as adopted from References [3; 4; 5; 7]. \[E_{\mathit{trans}}=\left\{ \begin{array}{ll}IE_{\mathit{loss}}+IE_{\mathit{fs}} d^{2},&\text{if }d\;<\;d_{0}\\ IE_{\mathit{loss}}+IE_{\mathit{amp}}d^{4},&\text{otherwise}\end{array} \right.\] (1) \[E_{\mathit{rec}}=IE_{\mathit{loss}}\] (2) \[d_{0}=\sqrt{\frac{E_{\mathit{fs}}}{E_{\mathit{amp}}}}.\] (3)
4. Packet delivery ratio (PDR): the ratio between the total numbers of packets successfully delivered to the destination sink node and the number of packets transmitted by the source nodes. To evaluate the PDR performance, Equation (4) was adopted from References [34; 35]. \[PDR=\frac{P_{\mathit{Rec}}}{\sum_{i=1}^{n}P_{\mathit{Trans}_{i}}}\] (4) where \(P_{\mathit{Rec}}\) is the total number of data packets successfully received by the destination sink node.