## 4 Numerical Evaluations
### Effects of Wireless Coverage  
First, we investigate the basic tendency of the firework effect on the influence of packet reachability over the number of nodes and the wireless transmission range for both MTFR and conventional potential-based routing (PBR). In this paper, reachability probability is defined as the ratio of the number of packets successfully reaching the destination over the number of all transmitted packets. From Figure 3, we can  
\begin{table}
\begin{tabular}{c c c} \hline  & **Parameter** & **Value** \\ \hline Layout & \begin{tabular}{c} initial layout \\ area size \\ \end{tabular} & \begin{tabular}{c} uniformly random \\ \(10\,\mathrm{km}\times 10\,\mathrm{km}\) \\ \end{tabular} \\ \hline Nodes & \begin{tabular}{c} number of nodes \\ wireless range \\ node speed \\ mobility model \\ \end{tabular} & \begin{tabular}{c} 2000–4000 (**4000**) \\ 100–500 m \\ \end{tabular} \\ \hline Firework & \begin{tabular}{c} hop limit \\ threshold \\ \end{tabular} & \begin{tabular}{c} 3–7 hops (**5**) \\ 0.3–0.9 (**0.5**) \\ \end{tabular} \\ \hline Simulation & \
\begin{tabular}{c} time \\ repetitions \\ \end{tabular} &
\begin{tabular}{c} 100 s \\ 1,000 \\ \end{tabular} \\ \hline \end{tabular}
\end{table}
Table 1: Basic simulation parameters with default values marked in bold.  
conclude that packet reachability improves with a growing number of nodes and with transmission range. This is because increasing both values results in a wider wireless coverage area. MTFR is able to restore reachability almost completely to that of the theoretically maximum possible without mobility. The wireless transmission range affects the node density with an exponent of two, which produces a stronger relationship with reachability. Therefore, steeply increasing curves are observed.  
It was also observed that there are some unrecoverable conditions in certain densely populated cases, like 4000 nodes and over 400 m wireless ranges. This is because the increase of possible links with more neighbors has the side effect of increasing the hop count between the source node and the destination node. The wider the transmission range becomes, the more links one node has, which eliminates the firework effect by the hop number limit. In conclusion, there is an optimal point against the number of nodes and wireless transmission range on the reachability improvement under some specific conditions. Here, the firework improvement effect represents the difference between results obtained with and without firework.  
In addition, Figure 4 shows the simulation results of reachability improvement 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, reachability improvement is defined as the difference in reachability between the methods with firework and without firework and for which absolute values can be found in Figure 3. In smaller and larger wireless transmission ranges, reachability improvement is almost zero, due to the lack of connectivity and no room for improvement, respectively. On the other hand, in middle ranges, there is a peak for each curve in which the wireless range is increasing as the number of nodes decreases. In addition, the maximum value slightly decreases as the number of nodes decreases, and therefore, as mentioned above, the wireless range has a larger effect on producing full reachability than the number of nodes.  
In [2], we also investigated the effects of vehicular speed, the node mobility model, the temperature update interval and transmission delays against the traffic overhead. Those results are left out for the sake of brevity, and the reader is referred to [2] for further details.  
Figure 3: Reachability increases in an S-shape manner with growing transmission range and number of nodes. PBR, potential-based routing.