## 5 Proposed Adaptive Beaconing System
### Characterization of Node Distribution
#### 5.2.2 Rules and Inference Engine  
For simplicity, we utilized the fuzzy inference method of Mamdani's min-max, since it facilitates the process of formulating the rule base. We designed the knowledge base rules according to the understanding of VANETs' characteristics as well as utilizing a weight assignment technique for every input parameter. In this method, the fuzzy operator AND selects the minimum value of the antecedents. When adding multiple rules, the maximum value of the consequent is utilized as the fuzzy output. The fuzzy rules for Set 1 and Set 2's parameters are shown in Tables 2 and 3, respectively. Set 3 has two levels of fuzzy rules. The first level is shown in Table 4 and the second level in Table 5. In this fuzzy rule set, the output of the first level (preliminary congestion rank) is used as an input in the second level. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rule Number** & **SINR** & **Number of Neighbors** & **Mobility** & **Rank** \\ \hline
1 & Small & Small & High & Very Small \\ \hline
2 & Small & Small & Medium & Very Small \\ \hline
3 & Small & Small & Low & Small \\ \hline
4 & Small & Medium & High & Very Small \\ \hline
5 & Small & Medium & Medium & Small \\ \hline
6 & Small & Medium & Low & Small \\ \hline
7 & Small & Big & High & Small \\ \hline
8 & Small & Big & Medium & Medium \\ \hline
9 & Small & Big & Low & Medium \\ \hline
10 & Medium & Small & High & Small \\ \hline
11 & Medium & Small & Medium & Medium \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Set 1’s fuzzy rules. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rule Number** & **SINR** & **Number of Neighbors** & **Mobility** & **Rank** \\ \hline
12 & Medium & Small & Low & Medium \\ \hline
13 & Medium & Medium & High & Medium \\ \hline
14 & Medium & Medium & Medium & Medium \\ \hline
15 & Medium & Medium & Low & Big \\ \hline
16 & Medium & Big & High & Medium \\ \hline
17 & Medium & Big & Medium & Big \\ \hline
18 & Medium & Big & Low & Big \\ \hline
19 & Large & Small & High & Medium \\ \hline
20 & Large & Small & Medium & Big \\ \hline
21 & Large & Small & Low & Big \\ \hline
22 & Large & Medium & High & Big \\ \hline
23 & Large & Medium & Medium & Very Big \\ \hline
24 & Large & Medium & Low & Very Big \\ \hline
25 & Large & Big & High & Very Big \\ \hline
26 & Large & Big & Medium & Very Big \\ \hline
27 & Large & Big & Low & Very Big \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rule Number** & **CBT** & **Mobility** & **PDR** & **Rank** \\ \hline
1 & Small & High & Large & Very Small \\ \hline
2 & Small & High & Medium & Very Small \\ \hline
3 & Small & High & Small & Small \\ \hline
4 & Small & Medium & Large & Very Small \\ \hline
5 & Small & Medium & Medium & Small \\ \hline
6 & Small & Medium & Small & Small \\ \hline
7 & Small & Low & Large & Small \\ \hline
8 & Small & Low & Medium & Medium \\ \hline
9 & Small & Low & Small & Medium \\ \hline
10 & Medium & High & Large & Small \\ \hline
11 & Medium & High & Medium & Medium \\ \hline
12 & Medium & High & Small & Medium \\ \hline
13 & Medium & Medium & Large & Medium \\ \hline
14 & Medium & Medium & Medium & Medium \\ \hline
15 & Medium & Medium & Small & Big \\ \hline
16 & Medium & Low & Large & Medium \\ \hline
17 & Medium & Low & Medium & Big \\ \hline
18 & Medium & Low & Small & Big \\ \hline
19 & Large & High & Large & Medium \\ \hline
20 & Large & High & Medium & Big \\ \hline
21 & Large & High & Small & Big \\ \hline
22 & Large & Medium & Large & Big \\ \hline
23 & Large & Medium & Medium & Very Big \\ \hline
24 & Large & Medium & Small & Very Big \\ \hline
25 & Large & Low & Large & Very Big \\ \hline
26 & Large & Low & Medium & Very Big \\ \hline
27 & Large & Low & Small & Very Big \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Set 2’s fuzzy rules.