## 4 Performance Evaluation
The ADMR of FRBP slightly increases due to the increase of signaling messages for the tree construction and fault recovery. The amount of increase however is much less than flooding. Figure 4 represents the energy consumption depending on the number of sensor nodes. We do not take beacon signaling into account since it is the same among the five protocols. Flooding consumes much more energy than comparative protocols since all sensor nodes have to transmit packets and each node has to receive packets from all neighbors even though it discards most packets. OEBP and Sprinkler consume less energy than others since they do not need to generate any signaling messages for topology construction and recovery. They are also unaffected by the density level for the same reason. FRBP consumes a little more energy than PEBP due to the recovery process for real-time failure. PEBP has a recovery process for communication failure, but \begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Value** \\ \hline Simulator & NS-3 \\ Transmission range & 30 m \\ MAC layer & IEEE 802.11 b \\ Network size & 500 m \(\times\) 500 m \\ The default number of nodes & 1000 \\ Transmitting/receiving power & 312 \(\upmu\)/2.34 \(\upmu\)J \\ Desired delivery time deadline & 10 s \\ Desired delivery speed & 70 m/s \\ Real-time requirement & (4, 5)-firm \\ The number of simulation rounds & 20 \\ The number of packets in a round & 80 \\ Packet generation rate & Constant Bit Rate (CBR), 1 packet/s \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of simulation parameters. does not recover real-time failure. The number of forwarding nodes of FRBP is unaffected by the density level since neighbors of an intermediate node become leaf nodes, which do not forward data packets. The energy consumption of FRBP however slightly increases due to the increase of signaling messages for the tree construction and fault recovery process. Figure 5 shows the average throughput depending on the number of sensor nodes. The graph pattern is similar to the opposite shape of Figure 3. The average throughput of flooding exponentially decreases as the number of sensor nodes increases because high density leads to critical packet loss by collisions and congestions in flooding. This figure shows that decrease of throughput (i.e., increase of packet loss) leads to the decrease of real-time performance. Figure 4: Average energy consumption impacted by the number of nodes. Figure 3: Deadline missed ratio impacted by the number of nodes. PEBP, Probability-based Energy-efficient Broadcast Protocol; OEBP, Opportunistic EBP; FRBP, (\(m\), \(k\))-firm-based Real-time Broadcast Protocol. Figure 6 illustrates the ADMR with respect to the average single hop delay. The increase of hop delay means the degradation of the network environment, which leads to failure of delivery within the deadline. The ADMR of OEBP, PEBP and Sprinkler increases more than the other two protocols according to the increase of average single hop delay. Since they do not consider the real-time constraint, the probability of electing time-consuming nodes increases as average single hop delay increases. The ADMR of Sprinkler is higher than that of PEBP due to the detouring paths, and the ADMR of OEBP is higher than that of PEBP due to the back-off delay for neighbor election. After the average single hop delay meets 0.5, flooding and FRBP have difficulty, and their ADMR increases rapidly. When the network environment gets worse, the furthest destinations may fail to receive packets within the time deadline at first. In the case of flooding and FRBP, the further the location from the source, the greater the number of destinations. The gradients of increase therefore grow less as the average single hop delay increases more. Figure 5: Average throughput impacted by the number of nodes. Figure 6: Deadline missed ratio impacted by single hop delay. Figure 7 represents the energy consumption depending on the average single hop delay. It is certain that flooding consumes much energy.