## 4 Performance Evaluation  
In this section, we compare the performance of the proposed FRBP with four other protocols: flooding [14], Sprinkler [15], the Probability-based Energy-efficient Broadcast Protocol (PEBP) [16] and the Opportunistic Energy-efficient Broadcast Protocol (OEBP) [21]. For the performance evaluation, we do not use FRUP due to the wide gap between the unicast and broadcast protocol. This implies that real-time data delivery to all sensor nodes by FRUP is still unreasonable in WSNs. Since there was no previous real-time broadcast protocol, four target protocols are chosen among the broadcast protocols. They are known as the most suitable broadcast protocols to compare with FRBP for the two goals, real-time broadcast and energy efficiency. Flooding ideally broadcasts packets more rapidly, whereas Sprinkler is a more energy-efficient broadcast protocol. PEBP and OEBP are the most recent broadcast protocols based on geographic routing and opportunistic routing, respectively. These protocols were implemented in NS-3 [25], one of the widely-used open source network simulators in the research community. We deploy 1000 sensor nodes in a 500 m \(\times\) 500 m area, and then, each sensor has several neighbors probabilistically. Sensor nodes follow the specification of MICA2 [26]. We conduct 20 rounds to obtain average result values. In each round, a source is randomly determined among sensor nodes, and the source sends data 80 turns for generating the data stream. We set a desired delivery time deadline to 10 s, and thus, a desired delivery speed is derived at 70 m/s to cover the whole network area. The experiments are conducted under the (4, 5)-firm real-timerequirement. Furthermore, average hop delay is set to 0.4 s, and the delay is randomly determined with the values range of \(\pm\) 0.2 s. The delay varies with the random value in the range mentioned earlier and the random period (from 1-10 turns). Each link and each node have failed in every turn with a low probability, 0.5%. Unlike node failures, sensor nodes recover from link failures after random turns. Summarized simulation parameters are depicted in Table 1.  
The Deadline Missed Ratio (DMR) is the ratio of the number of hitting the (\(m\), \(k\))-firm real-time requirement to the number of data packets delivered for a destination. Average DMR (ADMR) therefore means the average value of deadline missed ratios for all destinations. Energy consumption means the total energy consumed by all sensor nodes during one round of simulation. Throughput is the number of received Packets Per Second (PPS) for a destination. Average throughput means the Average value of BPS (APPS) for all destinations. Each destination starts calculating BPS when it receives the first packet. The three factors are the average values of 20 rounds of simulation. Figure 3 shows the ADMR with respect to the number of sensor nodes. The increment of the number of sensor nodes means the increment of the number of destinations in network broadcast. The number of sensor nodes also indicates the density since the area of the network is fixed. Flooding shows better performance than others, but ADMR exponentially increases as the number of sensor nodes increases. In flooding, high density leads to collisions and congestions since all sensor nodes have to transmit packets. This problem consequently causes the increase of hop delay and real-time failures. Other protocols are nearly impervious to the number of sensor nodes because they just select proper next-hop nodes in each path regardless of the number of neighbors. The ADMR of OEBP shows the highest value due to the back-off delay for neighbor contention. The ADMR of Sprinkler is a little higher than the PEBP due to the detouring paths. Note that the end-to-end delay is proportional to the physical distance the packet travels in a wireless multi-hop network. PEBP, OEBP and Sprinkler show worse performance than FRBP, the proposed protocol, since they do not consider the node's delay for electing forwarding nodes.