# Efficient Position Change Algorithms for Prolonging Driving Range of a Truck Platoon
## 4 Performance Analysis and Simulation Results
Since \(g(j)\) is larger for a larger \(j\), the average reduction rate increases as \(n\) increases. Therefore, we have longer driving ranges. Compared to [PERSON] et al. 's work, since there are no position changes, the maximum fuel consumption reduction rate remains steady with the first truck position at 4.3% no regards the number of trucks in the platoon. Meanwhile, our proposed algorithm can obtain a higher fuel consumption reduction rate. For example, \(\frac{4.3\%+10\%}{2}=7.15\%\) for two-truck platooning. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline \(n\): number of trucks in the platoon & 2,..., 6 & - \\ \hline \(s\): velocity & 85 & km/h \\ \hline \(r\): consumption rate & 0.326 & L/km \\ \hline \(F_{i}(0)\): initial fuel at position \(i\) & 1135.62 & L \\ \hline \(g(i)\): fuel consumption reduction rate at truck position i & 4.3\%; \(i=1\) & \\ \(10\%\); \(i=2\) & - \\ \(14\%\); \(i\geq 3\) & \\ \hline \(c_{1}\): threshold of “Full Rate” & 32.6 & L \\ \hline \(c_{2}\): threshold of “Half Rate” & 16.3 & L \\ \hline \(\delta_{1}\): time slot size of “1 Hour” & 1 & h \\ \hline \(\delta_{2}\): time slot size of “2 Hours” & 2 & h \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation Parameters. For the same simulation, Figure 2 shows the number of position changes in the platoon. Before analyzing the result, we first compute the driving range and driving hour without platooning. The driving range without platooning is \(F_{i}(0)/r=1135.62\) L/(32.6 L/100 km) = 3483 km. Since the speed of the trucks is \(s=85\) km/h, the driving time is about 41 h. Due to the effect of position changes, the driving range and time become longer than those values. In Figure 2, FAH shows very few numbers of position changes, and TTH shows a high position change count. The reason is quite clear. In FAH, the position change occurs when the difference of the fuels of two consecutive trucks becomes larger than the fuel amount of 100 km driving, i.e., 32.6 L. For a simple calculation, we consider \(g(1)\) and \(g(2)\). The reduction rate difference is \(5.7\%=(g(2)-g(1))\). Thus, it takes 100 km/0.057 = 1754 km of driving to create this much fuel difference. Considering the speed of the trucks \(s=85\) km/h, it takes about 20 h. Thus, the position change happens 2 or 3 times the total driving. This count is for the first and second trucks. There are position changes at other positions, too. So it is quite reasonable to have 5 position changes when \(n=4\) for Full Rate FAH. Regarding the results of TTH, we have 22 time slots for \(\delta=``1\) Hour\" at \(n=2\). The count rises to approximately 46 rounds when \(n\geq 3\). This number is quite reasonable considering the analysis of the driving time. Since the total driving time becomes more than 41 h due to the position changes, when \(\delta=1\) h, we should have more than 41 position changes during the platooning. Similarly, position changing every \"2 Hours\" shows half of the \"1 Hour\" total number of position changes for each \(n\). One question is why we have only half of the position changes at \(n=2\) compared to that of \(n=3\). The reason is quite straightforward. When \(n=2\), at every 2 h, the fuels of the two trucks become the same so that there is no need to change the positions, which results in half of the expected position changes. However, for \(n\geq 3\), this is not the case. For example, when \(n=3\), suppose that in the first time slot, we have sequences \((1,2,3)\). Then, in the second time slot, we should have the sequence of \((3,2,1)\). At the end of the second time slot, truck 1 and 3 have the same amount of fuel, but not truck 2. After the third time slot, there is no way to make the fuels of the three trucks the same. Therefore, for \(n\geq 3\), we have a similar number of sequence changes to the driving hours. Figure 1: Increased Driving Distance over the Number of Trucks in Platoon.