## 3 Methodology  
The sample size was taken from a revealed preference survey, which was conducted by the Hungarian Census Bureau in 2014. This government body conducts a periodic survey every decade [29]. The study used data on Budapest city, which covered around 8500 travelers, and these data contained the daily activity plan of each traveler and other related information, such as socio-demographic variables. Budapest is the largest city in Hungary, and it contains 18% of the whole population of the country [29]. The daily activity plans of travelers included information about their transport mode, departure time, arrival time, travel time, activity type, car ownership, employment status, age, parking fees, parking process time, and family size. In this study, travelers who use their car to travel for either work or shopping destinations were studied. These two types of travelers were chosen because of their frequent travel to either work or shopping, and they are more likely to use P&R system to save time searching for parking spaces, avoid extra cost for parking, and avoid congestion at the city center. While other travelers are less likely to use P&R facilities because they are not frequent travelers and their behaviors are different than workers and shoppers, for example, the value of travel time is lower than for shoppers and workers [30; 31]. From the literature, the P&R system can be used mainly by those travelers who travel for work or shopping using their conventional personal cars [32]. Thus, around 1782 travelers were derived from the collected data to be used in this study, and this sample size is considered sufficient for a city such as Budapest because the percentage of types of travelers used in this study is not high compared to other travelers who used public transport, for example. Table 1 shows that 90% of the travelers are workers, and 10% are shoppers. The sample size was prepared in accordance with the MATSim requirements. As a result, four files were created to be used in each scenario: (1) the existing transport mode (base scenario (1)), (2) AVs scenario, (3) P&R scenario (base scenario (2)), and (4) P&R and AVs scenario, as shown in Figure 1.  
The MATSim tool, in which the utility of all travelers was optimized, as discussed in detail later, was used in this study. The requirements for conducting a simulation of MATSim are mainly the road network, population, facilities, public transport network and schedule, and vehicle characteristics. These requirements were satisfied and prepared using the JOSP MATSim plugin to derive a road network from OpenStreetMap (OSM) [33] and BKK, which is the operator of public transport in Budapest and contains an updated file on public transport (GTFS) [34]. The aforementioned daily activity plans were simulated using the MATSim tool, which applies the co-evolutionary algorithm in optimizing the utility of travelers, where the MATSim loop is executed many times, as shown in Figure 2. \begin{table}
\begin{tabular}{|c|c|c|c|} \hline \multirow{2}{*}{**Item**} & \multirow{2}{*}{**Sample Size**} & \multicolumn{2}{c|}{**Activity Type (\%)**} \\ \cline{3-4}  & & **Work** & **Shopping** \\ \hline
**Daily activity plans (travelers)** & 1782 & 90\% & 10\% \\ \hline \end{tabular}  
*: Home-based activity.  
\end{table} 
Table 1: Sample size characteristics *. Figure 1: Simulation scenarios of work and shopping travelers. The MATSim tool is built in the Java programming language, and it is characterized as a detailed disaggregated microsimulation tool, which can simulate large projects in a competitive time, compared with other software. It has the ability to study more details concerning daily activity plans at the micro-level than other software does. The MATSim loop was executed for all simulations in this study. The existing transport mode of the travelers was evaluated in terms of travel time and travel distance, based on their daily activity plans, to judge the possible benefit of P&R availability.