## 3 Efficient Multi-Parent Hierarchical Routing Protocol
### Network Implementation under the MPH Protocol  
The MPH protocol was successfully implemented in a real network under a variety of conditions of temperature, humidity and obstacles. For the purpose of validating our simulation tool, we compared the simulation results with experimental data collected from this network under the same conditions and parameters. The number of nodes forming the network was 98 plus one coordinator node, and the coverage area was 0.16 km\({}^{2}\). Nodes 1 to 39 correspond to source nodes, which are nodes that generate traffic to the coordinator node, while Nodes 40 to 99 are relay nodes that simply pass traffic to the coordinator node, but do not generate traffic. We built the MPH protocol on top of the MAC layer of the IEEE802.15.4 standard using the CC2530 chip from Texas Instruments [32]. The power transmission of each node was 4.5 dBm. Figure 2 shows the nodes running the MPH protocol. Figure 3 shows the logical connections of the real network made with nodes built by us to test the MPH protocol. This same topology was used in the simulation to carry out the comparison. Table 1  
Figure 1: Multi-parent hierarchical (MPH) link formation process. Figure 2: Wireless nodes. shows the main Physical, MAC and Network layer parameters, which were used in the simulator and in the real network. We evaluated the performance of the MPH protocol of both the real network and the simulator in order to see the similarity of the results. We analyzed the average number of hops, the delay and the number of tries that it takes the coordinator to reach a node in the topology. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline \multicolumn{2}{c}{**Physical Layer Parameters**} \\ \hline Sensitivity thresholds & \(-78\) to \(-94\) dBm \\ Transmission power & 4.5 dBm \\ \hline \multicolumn{2}{c}{**MAC Layer Parameters**} \\ \hline Waiting time for NDRACKpacket & 30 ms \\ Maximum retransmission number & 3 \\ Maximum retry number & 5 \\ Maximum number of tries to reach a node from the coordinator & 9 \\ Packet error rate & 1\% \\ Average frame length & 22 bytes \\ Maximum number of backoffs & 4 \\ MAC protocol & IEEE 802.15.4 \\ MAC layer & CSMA/CA \\ \hline \multicolumn{2}{c}{**Network Layer Parameters**} \\ \hline Number of nodes & 99 \\ Maximum number of neighbors & 16 \\ Discovery neighbor time & 30 s \\ Update time neighbors table & 30 ms \\ Maximum data rate & 250 kbps \\ Routing & Hierarchical \\ Scenario & Static nodes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation and real network parameters. CSMA/CA, carrier sense multiple access with collision avoidance. Figure 3: Real network. Figure 6: Average hops per day in source nodes. Figure 7: Average hops per day in relay nodes. Figure 8: Average number of tries per day in source nodes. Figure 9: Average number of tries per day in relay nodes. The results are generated for the average delay, number of tries and number of hops per day. We chose 10 representative nodes of the 99 nodes that simulated the network. Among the source nodes, we chose randomly Nodes 2, 12, 27 and 39, while among the relay nodes, we chose randomly Nodes 45, 53, 66, 77, 82 and 95. In this way, we can give a proper and close approach in order to measure the reliability that our simulator has against a real scenario under the same conditions. The conditions of interference, attenuation and other environmental variations can be represented in the simulator as a percentage of packet loss. Due to connections and disconnections of the nodes, we can observe time periods when the network behavior is not considered as normal, and we can assume special conditions for these periods. Considering the standard deviation of the packet loss each day, we can make an estimate of the network behavior. We analyzed the relationship between the condition of the links on the topology and the packet loss, and we empirically established intervals.