## 5 Performance Evaluation  
We evaluate our scheme in terms of energy efficiency and recovery latency. Table 3 describes the parameters used for the evaluation. The value of the parameters are based on [15] and [19], studies that researched energy consumption and communication latency in WSNs. To compare energy consumption between clustering routing protocols without checkpointing and with checkpointing, the number of backup nodes needs to be determined. Figure 6 shows the steady-state availability (\(A_{steady}\)) of our scheme, the number of backup nodes, and the ratio \(\rho\) (_i.e._, \(\lambda/\mu\)) obtained by plotting Equation (4). When the failure rate (\(\lambda\)) is higher than the repair rate (\(\mu\)) of the watchdog timer (\(\rho>1\)), ant system availability is dramatically decreased because the value of Equation (4) exponentially increases and decreases by \(\rho\). To improve availability, the watchdog timer interval must be appropriately decreased. If watchdog timer rate is higher than the failure rate, resulting in \(\rho<1\), the reliability of the system is more than 80% when using three backup nodes. In case of the repair rate is the same to the failure rate (\(\rho=1\)), and our system provides reasonable availability (more than 73%) when using just three backup nodes. We have assumed \(\rho\) is smaller than 1 in order to satisfy user expected reliability (\(R_{user}\)) requirements. Under those conditions, three backup nodes are sufficient to satisfy the system availability requirements. The energy consumption between clustering routing protocols without checkpointing (\(E_{pre}\)) and with checkpointing (\(E_{cpt}\)) is compared via Equation (5) with the results shown in Figure 7. In this comparison, three backup nodes request the checkpoint packet from the cluster head whenever member nodes send sensing data to the cluster head, with \(I_{ckpt}=17\) ms. The energy consumption of the non-checkpointing scheme is higher than that of our scheme and the difference of two schemes steadily increases with increases in the number of nodes in a cluster. By using this extra energy, our scheme can reduce the check pointing interval and increase the reliability of sensor network. In this \begin{table}
\begin{tabular}{l|l} \hline
**Parameters** & **Value** \\ \hline Field size & 500 m \(\times\)500 m \\ N & 10, 20, 50, 100 \\ n & 3 \\ \(\lambda\) & \(10^{-4}\) (\(0<\lambda<1.0\)) \\ \(\mu\) & \(2*10^{-4}\), \(2*10^{-6}\) (\(0<\mu<1.0\)) \\ \(\rho\) & 0.5 (\(\lambda/\mu\) ) \\ R\({}_{user}\) & 0.8 (80\%) \\ MSG\({}_{\rm s}\) & 128 Bytes \\ E\({}_{init}\) & 0.5 J \\ E\({}_{tf}\) & 80 nJ \\ I\({}_{cpt}\) & 17 ms \(\geq\) I\({}_{\rm kept}\geq 0\) ms \\ D\({}_{\rm schd}\) & 17 ms \\ T & (N\(-1\)) * D\({}_{\rm schd}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Parameters for simulation. We tested our checkpointing scheme on the aforementioned testbed to evaluate recovery latency. Figures 10 and 11 show the recovery latency comparison between our checkpointing scheme applied to LEACH and that from the original LEACH with the results obtained via GloMoSim and a real-world testbed respectively. Simulation result shows the recovery latency of the original LEACH increases exponentially while that from LEACH with our checkpointing scheme applied increased more slowly and steadily (Figure 10). Recovery latency is affected by the amount of messages sent during the recovery process. In the original LEACH, \(O(n^{2})\) messages are generated during the re-election process as the number of nodes increases in a cluster. However, LEACH with our checkpointing scheme applied generates only \(O(n)\) messages via the a backup node; thus, recovery latency with checkpointing increases linearly. During implementation testing, we uniformly deployed sensor nodes in a 10 m \(\times\)10 m test field and created failure conditions by turning off the cluster head, or blocking wireless communication by using obstacles.