# Efficient Position Change Algorithms for Prolonging Driving Range of a Truck Platoon
## 4 Performance Analysis and Simulation Results  
In this section, we evaluate the performance of the heuristic algorithms that we have proposed: \"Fuel Amount Heuristic (FAH)\", \"Traveling Time Heuristic (TTH)\", and \"Sorted Time Slot (STS)\". The performance metrics that we focus in this section are the total driving range and the number of position changes. Position change operation helps save the fuels of the trucks participating in the platoon by exploiting FAH and TTH. Furthermore, \"STS\" aims to reduce the number of position changes. To simulate the algorithms in a more realistic environment, we first define some parameters used in the algorithms. The trucks are driving at the constant speed of \(s=85\) km/h and inter-distance spacing at 6 m, as it presents the most reliable longitudinal spacing that \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(P\)} & \multicolumn{6}{c}{\(k\)} \\ \cline{2-7}  & **0** & **1** & **2** & **3** & **4** \\ \hline \multirow{4}{*}{\(i\)} & 1 & 1 & 2 & 3 & 1 & 2 \\  & 2 & 2 & 1 & 2 & 2 & 1 \\  & 3 & 3 & 3 & 1 & 3 & 3 \\  & 4 & 4 & 4 & 4 & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A position change matrix \(P\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(P^{\prime}\)} & \multicolumn{6}{c}{\(k\)} \\ \cline{2-7}  & **0** & **1** & **2** & **3** & **4** \\ \hline \multirow{4}{*}{\(i\)} & 1 & 1 & 2 & 3 & 1 & 2 \\  & 2 & 2 & 1 & 2 & 2 & 1 \\  & 3 & 3 & 3 & 1 & 3 & 3 \\  & 4 & 4 & 4 & 4 & 4 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: A reordered position change matrix \(P^{\prime}\). may provide the highest fuel-saving. Each truck exhibits the same fuel consumption rate at \(r=32.6\) L/100 km, which is known as the average EU tractor-trailers [12], and starts with the same amount of initial fuel of 300 gallons or 1135.62 L, i.e., \(F_{i}(0)=1135.62\) L for all \(i\in V\). We assume that there is no fuel consumption in the process of the position change. Furthermore, we also assume that there is no road or load-related fuel consumption. For the fuel consumption reduction parameter \(g(i)\), we use the results studied by [PERSON] et al. [5]. Thus, we set \(g(1)=4.3\%\), \(g(2)=10\%\), and \(g(3)=14\%\). We further assume that from the fourth position and after, the consumption reduction rates are the same as 14%, i.e., \(g(i)=14\%\) for \(i\geq 3\), since there is no available information about the reduction rates after the third position in the existing literature. Figure 1 shows the increased driving distance compared to the fixed order truck platooning in percentage over a various number of trucks. For \"Fuel Amount Heuristic (FAH)\", we set \(c\) with two different values. The first is to set \(c\) as an amount of fuel needed for 100 km traveling, based on fuel consumption rates, called \"Full Rate\". The second one is to set \(c\) as the amount of fuel needed for 50 km traveling, called \"Half Rate\". For \"Traveling Time Heuristic (TTH)\", we set \(\delta\) to 1 h and 2 h. We vary the number of trucks \(n\) from 2 to 6. The values of parameters used in this simulation are summarized in Table 4.  
Since the initial fuel amounts are the same, the fixed order positioning represents the lower bound of the driving range. The comparative simulation result shows that changing vehicle positions by the proposed algorithms increases the cumulative fuel consumption reduction within the platoon, making the total driving range much longer with the same initial fuel capacity. Furthermore, it indicates that the higher the number of trucks in the platoon, the longer the driving distance. To be specific, the percentage of the increased range rises from approximately 2.8-3.0% in two-truck platooning to 6.7-8.1% in six-truck platooning. The result is justified by the concept of average reduction rates of \(n\) trucks. The operation of changing positions is to make the reduction rates of the trucks similar. In other words, the average reduction rate of the \(n\) trucks becomes \(\frac{\sum_{j=1}^{n}g(j)}{n}\).