## 3 Methodology
### Scenario Two: Daily Activity Plan Simulation When AVs Were Used Instead of Personal Cars  
In this scenario, MATSim was used to simulate a sample size of 1782 daily activity plans. A specific algorithm was used, as discussed before in the methodology. Several trials were executed to determine the required fleet size to serve all of the demand based on the 95 th percentile of the waiting time. The generated demand by 1782 travelers was fulfilled using several fleet sizes of AVs, and the fleet size that made the travelers wait not more than 10 min (acceptable waiting time) was chosen. The results showed that 425 AVs can serve 1782 travelers (car users), which suggests that one AV can replace around 4 conventional cars (1782 conventional cars divided by 425). The average waiting time was 3.7 min, and the 95 th percentile of the waiting time was 10 min, which is acceptable based on the perception of people. Moreover, the empty time is the time when the AV fleet moved to pick up  
\begin{table}
\begin{tabular}{|c|c|c|c|} \hline
**Scenario** & **Average Travel** & **Average Trip Time** & **Total Daily Travel Time Including** \\  & **Distance (km)** & **(Minutes)** & **Parking Process (Minutes)** \\ \hline (1) & 8.5 & 20.1 & 69.5 \\ \hline \end{tabular}
\end{table}
Table 2: Trip mobility indicators of travelers for the base scenario.  
Figure 3: Leg histogram of the car transport mode with respect to time.  
travelers, while the occupied time is when the AV fleet transported travelers to their destinations. In addition, the ratio of empty to occupied driving times gives an indication of the extra travel distance, compared with conventional cars, which was 26.5%. All of the mentioned results are reported in Table 3. Moreover, the average total travel time can be calculated as in the previous scenario, excluding the parking process time. The total average daily travel time was 39.5 min, excluding the average total waiting time (11.4), since travelers would prefer to remain in their activities and track the location of the AV to avoid waiting for it on the street.  
In Figure 4, the time profile of the AVs illustrates the peak periods that contributed to determining the fleet size, besides the location of the activities and the departure time of the travelers. The green color is the time when the AVs were inactive, blue shows the empty driving time, gray is the occupied time, orange is the pick-up time, yellow is the drop-off time, and the values show the number of AVs. This figure was produced when the maximum score was reached, and the system reached a stable state. It is worth mentioning that the simulation was run using Intel(R) Core (TM) I7-7500U CPU @ 2.70 GHz-2.9 GHz and 8 GB RAM laptop, and the running time was 11.70 h.  
Figure 4: Time profile of the AV fleet, when the AV fleet size and the utility of travelers were optimized.  
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline
**Scenario** & \begin{tabular}{c} **Fleet** \\ **Size** \\ \end{tabular} & \begin{tabular}{c} **Average** \\ **Trip Time \({}^{*}\)** \\ \end{tabular} & \begin{tabular}{c} **Average** \\ **Waiting** \\ **Time \({}^{*}\)** \\ \end{tabular} & \begin{tabular}{c} **95 th Percentile** \\ **Waiting** \\ **Time \({}^{*}\)** \\ \end{tabular} & \begin{tabular}{c} **Occupied** \\ **Time \({}^{**}\)** \\ \end{tabular} & \begin{tabular}{c} **Empty** \\ **Driving** \\ **Time \({}^{**}\)** \\ \end{tabular} & \
\begin{tabular}{c} **Drop Off** \\ **Time \({}^{**}\)** \\ \end{tabular} &
\begin{tabular}{c} **Pick Up** \\ **Time \({}^{**}\)** \\ \end{tabular} \\ \hline (2) & 425 & 13.1 & 3.7 & 10.0 & 827.5 & 218.6 & 59.3 & 118.7 \\ \hline \end{tabular}
\end{table}
Table 3: Trip time components of travelers in scenario (2), when the AV fleet was used.