## 5 Case Studies and Simulation Results  
To show the significance of including the RB limitation as it relates to a dynamic LSB in the decision-making process, two case studies are examined. In the first case study (scenario 1), it is assumed that the vehicle can achieve RB even at very low speeds; however, dynamic LSB is not considered in the objective function when calculating the optimum speed trajectory. In this scenario, although RB capability exists in the vehicle braking system and is considered when calculating the overall consumed energy, the low-speed RB limitation does not have any role in the decision-making process. All other limitations related to the RB capability discussed earlier are considered for this scenario. In the second case study (scenario 2), the dynamic LSB obtained in Section 2 is considered in the objective function based on the proposed approach. A schematic representation of the data processing stages for this scenario is given in Figure 5. In both scenarios, the MILP method is used to form the objective function and RB constraints in Python, while CPLEX is utilized as a solver to generate the final speed profile. IBM CPLEX is one of the most well-known solvers for MILP optimization problems and is guaranteed to solve the problem to optimality [22]. Subsequently, the MATLAB/SIMULINK model is used to calculate the final energy consumption of the vehicle for the generated speed profile. The same route shown in Figure 3 is used for both scenarios with a maximum speed limit restriction of 35 mph. Furthermore, the parameters of Table 1 are used to obtain the desired speed profile using MILP. The imposed travel time mentioned in Table 1 includes the time spent at each stop sign, which is three seconds, and the total time spent for all steps. Furthermore, both simulations are performed with 0% grade and zero wind velocity. Figure 5: Schematic representation of data processing stages for scenario 2. A rear-wheel drive AEV with a single electric motor and a weight of 1000 kg is considered in both scenarios. The vehicle will start from standstill and come to a stop at the end of the route in less than 140 s while adhering to route speed restrictions. The parameters of the AEV under study are summarized in Table 2. The maximum rate of acceleration/deceleration for this study is set to 4 m/s\({}^{2}\). The results of the optimum speed profiles obtained from the MILP model for both scenarios are shown in Figures 6 and 7. The results demonstrate that the optimal speed profiles have differences during the cruising, deceleration, and braking periods between the two scenarios. This is a direct influence of considering the RB LSB in the decision-making process. The results of simulating the obtained speed profiles for both cases using the MATLAB/SIMULINK model are depicted in Figure 8. This simulation is carried out to accurately calculate the energy consumption and capture variations in the electric motor and battery while driving with the optimum speed reference generated by MILP. A breakdown of energy consumption and recuperation is presented in Table 3. In this table, total energy is defined as the difference between the energy consumption during acceleration/cruising and the energy recovered through RB. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Value (Unit)** \\ \hline Route length & 1000 m \\ Distance resolution & 10 m \\ Speed resolution & 0.5 mph \\ Imposed travel time & 140 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters related to the route in MILP model.