## 4 Numerical Evaluations
### Firework Parameter Study  
Finally, we analyze parameter influences by the firework method. Figures 9 and 10 show the simulation results of the improvement of reachability, the difference of delay and the difference of overhead by firework routing with different firework hop limits and firework threshold values, respectively, which are simulated for 4000 nodes under RWK at the speed of 100 m/s and with different wireless ranges for packet transmission. Here, the firework hop limit is defined as the maximum number of hops for packets to be replicated and transferred to neighboring nodes by intermediate nodes. In other words, the intermediate nodes replicate and transfer packets with a hop count up to the firework hop limit and stop broadcasting packets beyond the firework hop limit. In addition, the firework threshold is defined as the minimum temperature value at which intermediate nodes replicate and transfer packets received from neighboring nodes. Hence, intermediate nodes with the temperature of a firework threshold value or larger replicate and transfer intercepted packets, while, on the other hand, nodes with a smaller temperature than firework threshold do not replicate them and operate the same way as conventional potential-based routing.  
From Figure 9(a), a firework hop limit of five hops appears to achieve high reachability, while trying to maintain a low delay (Figure 9(b)) and overhead (Figure 9(c)) to some extent. It is observed that the best hop limit value depends on current conditions, such as node density. Increasing the hop limit too much does not yield much improvement in reachability, but increases delay and especially overhead. An interesting observation can be further made in Figure 9(c). Although it would be expected that an increased firework hop limit would lead to more overhead, for transmission ranges between 300-400 m, the overhead actually drops below that of a hop limit of three. The reason for this is that with a large wireless transmission range and hop limit, there is a large overlap of neighboring nodes, and since each  
Figure 8: Traffic overhead degradation analysis shows that the peak of overhead difference between with and without firework shifts as the number of nodes decreases.  
node only participates once in each broadcast process beyond the firework threshold, the overhead for large ranges becomes less after the first hop of the broadcast.  
In addition, from Figure 10, it is shown that the firework threshold value should be selected in a more precise manner than the hop limit value. For example, the firework thresholds between 0.5 and 0.7 might be the best parameters in the case of wireless transmission ranges 250 m, 300-350 m and 400 m or above, respectively. A firework threshold between 0.5 and 0.7 produces overall better reachability improvement, much closer to the best performance at a firework threshold of 0.3, while at the same time having a smaller traffic overhead. However, the threshold of 0.5 has a slightly higher delay difference than the other values, and all thresholds converge for large ranges to the same values. Note that a firework threshold of zero means that we have a pure broadcasting mechanism, while a threshold of one is the same as conventional potential-based routing.  
Figure 9: Evaluation of the hop limit _versus_ the transmission range shows that even a hop limit threshold = 3 yields a fair improvement, while a hop limit of five appears to produce sufficient reachability (\(N=4000\)). (**a**) Reachability difference; (**b**) delay difference; (**c**) overhead difference.