## 4 Numerical Evaluations
### Evaluation of Traffic Overhead  
In addition, we analyze the tendency from the viewpoint of traffic overhead accompanied by the firework procedure. Figure 7 shows the simulation results of additional traffic overhead by firework with different numbers of nodes under RWK at the speed of 100 m/s and with different wireless ranges for packet transmission. Here, traffic overhead is defined as the total number of hops traveled by transmitted packets, including replicated packets, which is substituted by the total number of hops under the condition that the size of all transmitted and replicated packets is equal. In Figure 7, traffic overhead is normalized by the number of nodes and the total amount of transmitted packets.  
Figure 5: Transmission delays (hop count) show clear differences between with and without firework for larger wireless transmission ranges.  
Figure 6: The difference of end-to-end delay per packet transmission shows saturation for larger wireless transmission ranges, due to the effects of randomness.  
The normalized traffic overhead without firework is almost zero, which can be used as a criteria to evaluate our method. From Figure 7, in higher wireless transmission ranges, such as more than 350 m, it is shown that there is not much difference between without and with firework. On the other hand, in the middle wireless transmission ranges from 200 m to 350 m, additional traffic overhead by firework is observed, but remains less than 0.2 hops. In addition, in lower wireless transmission ranges, such as less than 200 m, there is no difference between without and with firework, due to poor reachability in both cases. Even though firework routing requires in the medium range cases additional traffic overhead, reachability recovery has more importance over overhead increases for the future network infrastructure, since it allows a connection to the destination compared to the case without firework. Moreover, here, in our simulation, we use a fixed firework threshold (0.5 ), and the higher the firework threshold we utilize, the less additional traffic overhead produced. We can also easily embed some additional intelligence to reduce the overhead by avoiding unwanted replicated packets, for example by not broadcasting packets to nodes that have a low expectation of recovery, due to their temperature or vehicular motion. As a consequence, the above results can be seen as the worst case scenario and indicate that firework inevitably produces an increase of traffic overhead to some extent, but the benefits of higher connectivity with MTFR outweigh this drawback to make it feasible enough for an actual system implementation.  
In addition, Figure 8 shows the simulation results of an additional traffic overhead increase by firework with different numbers of nodes under RWK at the speed of 100 m/s and with different wireless ranges for packet transmission. Here, traffic overhead is expressed as the average number of traversed hops by a packet transmission from the source node to the destination node. The difference of traffic overhead is the discrepancy in traffic overhead between the results with firework and without firework. In addition, absolute values for the traffic overhead with and without firework are given in Figure 8. As the number of nodes increases, the difference of traffic overhead increases, though the overhead per packet in Figure 7 remains almost constant irrespective of the number of nodes. In smaller and larger wireless transmission  
Figure 7: Traffic overhead analysis shows differences between with and without firework for intermediate wireless transmission ranges.  
ranges, the overhead increase is almost zero for the same reason as in the reachability improvement analysis of Section 4.1. The wireless range for each maximum overhead peak shifts similarly from a small range to a large range.