## 4 Performance Evaluation
Four protocols except FRBP are nearly impervious to the hop delay since they do not perform any operation against real-time failure. The energy consumption of FRBP however slightly increases as hop delay increases especially after 0.5 due to the fault avoidance and recovery process. Figure 8 shows the ADMR with respect to the node failure ratio. In simulation, each node has failed in every turn with a low probability and does not recover since node failure is primarily caused by exhaustion of energy and physical destruction. After a node has failed, the DMR of the node is not included in ADMR. As the node failure ratio increases, the ADMR of Sprinkler increases exponentially. The failures of non-forwarding nodes do not affect ADMR, but the failure of a forwarding node leads to consecutive real-time failures of downstream nodes. The consecutive failures moreover do not recover. PEBP has same problems, but could probabilistically recover the situation. PEBP therefore shows better performance than Sprinkler. FRBP recovers the failures of intermediate nodes, as well as downstream nodes by local real-time failure avoidance. FRBP recognizes a failed node as a node that does not satisfy the real-time constraint. Therefore, the ADMR of FRBP marginally increases, but is not critically affected by the node failures. Flooding is nearly impervious to the node failure ratio since it does not elect forwarding nodes, and every node forwards packets. Even when a node has failed, its neighbors can receive packets from other nodes. OEBP is also unaffected by the node failure since forwarding nodes are elected among neighbors that actually receive the packet. A failed node has no chance of being elected. However, OEBP still shows worse performance than the others due to the election process. Figure 9 represents the energy consumption depending on the node failure ratio. Flooding, Sprinkler and OEBP are almost unaffected by the node failure ratio since Sprinkler does not have any recovery process, and flooding and OEBP do not need it. The energy consumption of Sprinkler rather decreases slightly since downstream nodes of a failed node stop forwarding packets. Against node failures, PEBP and FRBP perform local failure recovery processes that cause energy consumption for signaling. The energy consumption of PEBP and FRBP therefore increases according to the increase of the node failure ratio, but signaling cost is much lower compared with data delivery cost. PEBP consumes a little more energy than PEBP since it performs the recovery process against not only node failures, but also real-time failures. Figure 7: Energy consumption impacted by single hop delay. Figures 10 and 11 show ADMR and energy consumption with respect to the link failure ratio, respectively. Unlike node failures, link failures are recovered since they are caused by temporary troubles. The two graphs show a similar pattern as shown in Figures 8 and 9. The increase of ADMR in Sprinkler however is a little more gradual than Figure 8 due to the recoveries of link failures. Figure 8 also shows that FRBP can handle the link failures, as well as node failures in an efficient way. According to the performance evaluation, our main observations are as follows. Flooding is generally efficient for real-time broadcasting except dense networks, but uses too much energy. Broadcast storming is also a well-known problem of flooding. The proposed protocol, FRBP, has better performance for real-time broadcasting than the other three protocols in various situations. FRBP consumes a little more energy than the three protocols, but we consider that this is reasonable; because the other protocols do not consider the real-time constraint and do not have any avoidance or recovery processes for real-time failures. Figure 8: Deadline missed ratio impacted by the node failure ratio. Figure 9: Average energy consumption impacted by the node failure ratio.