## 6 Conclusions  
This article has described an agent-based simulation model to study the integration of public transport services and a ride-pooling system, this initiative being one of the International Union of Public Transport (UITP) proposals for complementing public transport services in urban areas with less coverage to take advantage of being close to neighbour urban centres with a higher density of PT services. The simulation model assumes that users may book trips or make requests for prompt service to a centralised system of dispatching, which is able to resolve the requests by assigning them a ride-pooling vehicle that will drive them directly to their destination or to a suitable access point of the PT network, thus starting a second leg in PT. In this case, it will lead the client to a station or stop already close to its destination or where another RP vehicle will complete a third leg ending at the destination. Additionally, if the client has good public transit connectivity from the beginning of his journey, the system may decide to serve him directly via public transportation, which will lead the client to a station close to his destination or where an RP vehicle will complete a second leg ending at the destination. The simulation system is composed of an adaptation of the MaaS Simulator with its own MaaS Dispatcher (originally a ride-pooling simulator), which is a public transport route planner based on the rRAPTOR model ([13]), and the Outer Dispatcher, which by means of a system's batch scheduler groups periodically the requests and determines the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **\#Req.** & **Freq.** & **Total batch Time** & **Step 1 Time** & **Step 2 Time** & **Step 3 Time** \\ \hline
**Exp. 1** & 10.01 & 6.56 s & 0.35 s & 0.12 s & 0.16 s & 0.07 s \\
**Exp. 2** & 10.49 & 11.03 s & 4.59 s & 1.02 s & 2.56 s & 1.02 s \\
**Exp. 3** & 10.46 & 12.10 s & 4.61 s & 1.01 s & 2.33 s & 1.28 s \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Performance statistics. Average CPU running times distribution per batch. \begin{table}
\begin{tabular}{c l l l l l} \hline \hline  & & **Revenues** & **Salaries** & **RP-Fuel** & **Profit** \\ \hline
**Exp. 1** & **Total** & 28,214.25 € & 21,125.00 € & 1669.77 € & 5419.47 € \\  & **Central Period** & 24,298.28 € & 11,375.00 € & 1294.05 € & 11,629.24 € \\ \hline
**Exp. 2** & **Total** & 22,055.57 € & 21,125.00 € & 1567.54 € & \(-\)636.97 € \\  & **Central Period** & 19,328.97 € & 11,375.00 € & 1242.79 € & 6711.18 € \\ \hline
**Exp. 3** & **Total** & 22,353.19 € & 21,125.00 € & 1596.23 € & \(-\)368.03 € \\  & **Central Period** & 19,497.56 € & 11,375.00 € & 1267.14 € & 6855.42 € \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Profit analysis for 10–12 h, central period (without warm-up and cool-down periods). intermodal composition of the trips and the number of legs for the requests of a batch by means of an optimisation model, whose parameters are heuristically determined by two previous pre-processing steps. The system has been tested on the inner region of Barcelona's densely populated metropolitan area. The simulations show that travel times and user fares are competitive, especially for the two- and three-leg trips and that the system is appealing as it may not only act as a feeder for the central PT system but also for the RP system, since commuters in the surrounding areas may become its clients. The simulation experiments conducted in this paper have been made by setting the main system parameters and policies either using the most common values accepted in the available literature for systems with some similarities or by reasonable judgement based on the characteristics of the testing scenario. Conceptualization, methodology, E.L., E.C., J.B. and K.N. ; writing--original draft preparation and formal analysis, E.L., E.C. and J.B.; software, data curation and visualization, E.L.; project administration, supervision and validation, E.C., J.B. and K.N. All authors have read and agreed to the published version of the manuscript.