## 4 DMRF Protocol
### Network Congestion Detection Method
This shows that no matter whether the topology of the sensor networks is uniform or not, the reachability of DMRF does not obviously change. The jumping transmission mode utilized in DMRF can confront the effect of network topology on transmission performances. In Figure 6, it also shows the network topology does not affect the successful transmission times of DMRF. Therefore, DMRF can resist the impact of network topology effectively. ### Successful Transmission Ratio in Case of VOID Region

We compare SPEED, MMSPEED, FTSPEED with DMRF in terms of the impact of void region on the successful transmission ratio in the case of uniform distribution. The simulation results are shown in Figure 7.

Since DMRF dynamically adjusts the jumping probability, the packet transmission may fail because of void region in the original transmission. But in later transmissions, the probability of the successful transmission increases greatly. In Figure 7, when the radius of void region increases to seven, only FTSPEED and DMRF can still transmit data. DMRF can achieve the successful transmission ratio up to 92%. When the radius is eight, DMRF directly transmits the data packet from the source to the destination node. Although the energy consumption of this kind of transmission is high, it is the only way to achieve successful transmission. Figure 6: The impact of network congestion on transmission. ### Average Transmission Delay in Case of Different VOID Region Radius

The average delay of data transmission with respect to void area radius change is shown in Figure 8. In Figure 7 and 8, we can see when the radius exceeds six under SPEED, SPEED-T, SPEED-S, and MMSPEED, the network transmission delay significantly increases while the times of successful transmission significantly decreases, and serious congestion occurs, which causes a large number of data packets to be discarded. In contrast, DMRF can switch to jumping transmission mode and jump the void region or congested areas, hereby the packet transmission delay has no significant change. ### The Number of Control Packets in Case of Different VOID Region Radius

In DMRF, when node failure, void area or network congestion occurs, the current node feeds back the information to its upstream node immediately. The upstream node then adjusts its jumping probability. In Figure 9, when the radius of the void region is in (0, 5], the number of control packets increases. When the radius is above five, the number of control packets declines due to the decrease of the number of working nodes. It can be seen from Figure 9, that DMRF uses more control packets than other methods when the radius of the void region is in [1, 4], because DMRF uses three kinds of feedback packets. When the radius is more than four, network congestion occurs, and SPEED, SPEED-T, SPEED-S, and MMSPEED begin to discard packets. Therefore, the number of control packets increases dramatically. In total, the number of control packets of DMRF is related to the number of nodes working in the area, instead of the global network topology. Therefore, the number of control packets is relatively stable. The number of control packets of DMRF is slightly higher than that of FTSPEED, but far less than those of SPEED, SPEED-T, and SPEED-S. That is, DMRF still has certain superiority in reducing the number of control packets. Figure 7: Influence of Void region on transmission. ## 7 Conclusions and Future Work

In this paper a dynamical jumping real-time fault-tolerant routing protocol (DMRF) has been proposed. DMRF works in two data transmission modes: hop-by-hop mode and jumping transmission mode. Once node failure, network congestion or empty region occurs, the transmission mode will switch to jumping mode, which can reduce the transmission time delay, ensuring the data packets to be sent to the sink node within the specified time limit. We theoretically prove that DMRF can meet real-time and fault tolerance requirements. The performance of DMRF is evaluated by extensive

Figure 8: Relationship between transmission delay and Void region.