## 4 DMRF Protocol
### Network Congestion Detection Method
During the transmission, the buffer occupancy of partial nodes increases and network congestion occurs, causing some data packets to be discarded due to deadline miss. All the parameters used in the simulations are shown in Table 2.

### Times of Successful Transmission with Different Ratios of Faulty Nodes

We randomly inject a certain ratio of faulty nodes in the network, the initial buffer size is set as 0, _i.e._, there is no congestion. 100 data packets are sent from the source node to the destination node. Times of successful transmission are recorded to reflect the impact of faulty nodes on data transmission. The comparison between SPEED, SPEED-S, SPEED-T, MMSPEED, FTSPEED and DMRF is shown in Figure 5. Because the VOID region in the network only yields to faulty nodes or the change of the nodes distribution (random distribution), this experiment can also reflect the capacities to avoid the influence of the VOID region among these six protocols. In Figure 5, we can see that with the ratio of faulty nodes increasing, the times of successful transmission of most methods decline, whatever distribution the nodes conform to. In the random distribution case, an even more dramatic decline occurs, which is mainly due to the uneven distribution of nodes causing larger empty regions and leading to the transmission failure. DMRF establishes multiple non-overlapping paths, which can reduce the impact of node failure. In the interval [0.2,0.4], the number of successful transmissions increases for the DMRF protocol. The jumping transmission mode adopted in DMRF reduces the impact of node failure greatly. Moreover, the jumping probability will be adjusted according to the transmission result (success or failure). With the transmission going on, the times of successful transmission will increase. As regarding SPEED-S and SPEED-T, only the selection method of the next hop node is different from SPEED. Therefore the overall trend is similar to the results of SPEED. In MMSPEED, the transmission failure ratio is higher because nodes in the initial transmission cannot meet the reachability requirements. According to the results, we can see that DMRF exhibits higher capacity in avoiding VOID region. \begin{table}
\begin{tabular}{l l} \hline Routing Protocol & SPEED, SPEED-T, SPEED-S, \\  & MMSPEED, FTSPEED, DMRF \\ \hline MAC Layer & 802.11 \\ MAC Protocol & CSMA/CA \\ Bandwidth & 200 Kb/s \\ Buffer Size & 100 Bytes \\ Data packet Size & 32 Bytes \\ Region Size & (20 m, 20 m) \\ Node Number & 400 \\ Node Distribution & Random and Uniform \\ Maximum Transmission Distance & 30 m \\ \hline \end{tabular}
\end{table} 
Table 2: The setting of parameters used in the simulation. ### Successful Transmission Ratio under Congestion Condition

As can be seen from Figure 6, with the initialization ratio of the buffer increasing, the times of successful transmission reduce gradually. In this experiment, we just omit the effect of faulty nodes, so the probability of the faulty node is set 0. Therefore the VOID region can be treated as congested nodes or the change of the nodes distribution (random distribution). The decrease of all the methods except MMSPEED is flat. When the next hop is a congested node, FTSPEED applies a bypass way to relieve the effect of the congestion node. But this method can only achieve the local solution of reducing the effect of congestion nodes. For SPEED, it simply discards the package when congestion occurs. As depicted in Figure 6, the times of successful transmission of DMRF is obviously higher than that of the SPEED. The main reason is that DMRF can jump over the congestion node at a degree of probability. But the successful ratio is not always 100%, since the packet can be sent to another congestion node. As the data packet is sent, the jumping probabilities are adjusted, which increases the ratio of successful jumping transmission. Figure 5: The impact of faulty nodes on network transmission. ### The Effect of Network Topology on DMRF

In Figure 5, there is not much change in successful transmission times.