Agent-based decision-support model for bus route redesign in networks of small cities and towns: case study of Agder, Norway

Abstract

Small cities and towns often struggle to provide high-quality public transport services to daily commuters. This is reflected in the modal split, where the share of car users dominates. Such a problem requires a modern solution, where transport planners can verify the impact of potential transport network improvements on the travel behavior of the residents before the changes are actually deployed. This study aims to demonstrate the usefulness of employing an agent-based simulation tool in the decision process for redesigning an express service regional bus route connecting a network of small cities and towns. The model was initially developed as a Mobility as a Service simulation solution for suburban areas of European metropolises. The model is adapted and applied to a case study for the region of Agder, Norway, simulating the impact of nine different scenarios on the patronage of a specific bus route. The simulation model proposes to upgrade the classic agent structure to a persona profile designed specifically for the case study. The main objective of this research is to identify the scenario that maximizes patronage while minimizing total route travel time and additional costs. The results suggest that the proposed model can be successfully adapted from suburban metropolitan areas to the realities of the considered case study, and potentially other similar regions. Specifically, out of the nine proposed scenarios, the model identified four promising ones. One of the four scenarios also fits the cost constraints imposed by the transport provider. The model provides a solid approach for analyzing complex transport systems that are practically impossible to consider in detail if the analysis is done without computer support. Thus, the results can be used as a decision support system for public transport planning and operations in networks of small cities and towns.

1 Introduction

The increase in accessibility to motorized transport for the wider public has shifted the commuting patterns of humans, increasing their daily travel ranges. Regional public transportation (PT) systems represent a crucial element in ensuring access to a more diverse job market for the population living outside walking or biking distance from their jobs, and also in reducing the environmental footprint of daily commuting at a regional level. Nevertheless, if the PT offer cannot compete with the advantages of car commuting, the cost of running the PT system becomes economically unviable, which increases car dependency. As a result, there is a clear need to maximize the return on investment for PT by attracting more paying customers towards this sustainable transport mode.

Transport network planning has become increasingly complex in recent decades. Consequently, PT providers are exploring new avenues for verifying the feasibility of proposed solutions for routing and optimization problems. In recent years, transport planners have used computer-based simulation models to evaluate route option alternatives and the impact of schedule changes on ridership and occupancy with increasing success. Several studies have addressed such approaches (Manser et al. 2020; Narayan et al. 2017; Cats et al. 2014). Nevertheless, there have been few such applications employed by PT providers working in geographical areas where small cities and towns represent the predominating urban forms. This is generally due to the lack of resources, both human and financial, that PT providers in such areas are confronted with, but also because such research generally focuses on large cities and metropolises such as Melbourne, Australia (Liyanage and Dia 2020) and Zurich, Switzerland (Manser et al. 2020).

The use of agent-based simulation programs, such as PTV’s Visum (PTVGroup 2021) or MATSim (MATSim 2021), is even more of a rarity in small-size public transport authorities (PTAs), due to the extra layer of travel data and effort necessary for defining the activity of the agents. Therefore, most of the PT planning work is still carried out in a classic way, without employing simulation models. The increased volume and complexity of the available data, combined with the necessity to better respond to customers’ needs, topped by a growing competition with private vehicles, is now exceeding the capacity of human analysis. To achieve better results, there is a clear need to employ computer simulations in public transport improvement decision-making processes, even in the case of smaller PTAs.

The present research aims to bridge the gap between using classic PT network design processes and employing an agent-based simulation model for solving PT planning-related problems. This approach is applied to a specific case study, simulating the viability of different scenarios for modifying a current express service (ES) bus route, as defined by Vuchic (2007), connecting a network of small cities and towns. The study demonstrates the usefulness of employing an agent-based simulation tool in the decision process for redesigning the route. The simulation model also proposes to upgrade the classic agent structure with qualitative data input from a set of persona profiles designed specifically for the case study.

The model was initially developed as a Mobility as a Service (MaaS) simulation solution for suburban areas of European metropolises in the frame of the OptiMaaS project.¹ MaaS is a relatively new concept, developed in the past decade, and its definition is still under development. According to Arias-Molinares and García-Palomares (2020, p. 254), the core elements of MaaS are: “a unique single platform (app or website), real-time information on all available modes in the city (public and private), multimodal transportation (intermodal journey planners), technological integration to plan, book and pay for mobility needs, and personalized bundled mobility packages according to user’s particular requirements”. The only aspect of MaaS considered in the present case study is the multimodality, highlighted by Tønnesen et al. (2021) as an under-investigated aspect in Norwegian transport planning from the perspective of access, egress, and transfer. The model is adapted to the region of Agder with its current realities. The main objective of the study is to develop a decision-support system for PT planning, based on the initial OptiMaaS model. The decision-support system would be targeted at public transport providers and planners and would help identify the scenario that maximizes PT patronage while minimizing total route travel time for the users and additional costs for the operators.

The remainder of this paper is organized as follows: Sect. 2 presents the current state of the art with regards to agent-based modeling and simulation for PT and also the use of persona profiles in PT research; Sect. 3 gives an overview of the methodology applied in the present study; Sect. 4 presents the selected case study; Sect. 5 gives an overview of the persona profiles generation and allocation; Sect. 6 describes the simulated scenarios; Sect. 7 introduces the achieved results; Sect. 8 presents the discussion while Sect. 9 provides the gained conclusions based on the results.

2 State of the art

2.1 Current approaches for route planning and optimization

Route and tour planning are fundamental problems in transport optimization and have a long history. Finding the shortest route or path from A to B on a given road network can be solved in polynomial time (Dijkstra 1959). Even if the basic shortest path finding algorithm is simple, there have still been advances in recent years. The most relevant developments are in the following topics:

• (i) Performance and scalability, such as computing the optimal route in (fractions of) milliseconds on a continental scale (Botea 2011; Bast et al. 2006).

• (ii) Multiobjective and non-linear criteria in shortest path algorithms (Berger et al. 2010; Aifadopoulou et al. 2007).

• (iii) Dynamic algorithms, that take into account real-time traffic conditions (Schultes and Sanders 2007; Delling and Nannicini 2012).

• (iv) Multimodality, i.e., consideration of multiple travel modes for the trip (Aifadopoulou et al. 2007; Delling et al. 2013).

A more detailed overview of path planning algorithms is given in a survey paper by Bast et al. (2016). The most relevant variant for this article is multimodality. The simulation model presented in the current research employs an intermodal route planner, where multiple transport modes can be used on the same trip (Prandtstetter et al. 2020).

2.2 Agent-based modeling and simulation in the field of transport

A vast gap exists between purely mathematical approaches and solutions that include user behavior aspects in the simulation process for PT planning and optimization (Venturini et al. 2019; Schafer 2012). One possible explanation for the existence of this gap could be the difficulty of standardizing the generation of user profiles relevant for different regions around the globe, combined with the need for complex data sets for running such simulation models.

The introduction of user behavior into simulation models created the agent-based simulation approach. Classic simulation models overlook the element of randomness, an element that is present in the decision-making process of users regarding their daily travel behavior and activity scheduling (Kaddoura et al. 2015). This element is introduced in the agent-based modeling and simulation (ABMS), which is “a relatively new approach to modelling systems composed of autonomous, interacting agents” (Macal and North 2010, p. 151).

In the case of mobility behavior, the attributes and behaviors of the agents, as well as the relationships and methods of interaction, are generated using quantitative data sets, such as travel surveys or mobile tracking GPS data (Chen et al. 2016). So far, no references were found where ABMS agents were designed using a blend of quantitative (e.g., travel surveys) and qualitative data (e.g., interviews).

Two important applications for ABMS in the field of transport research are the prediction of travel demand (Balmer et al. 2008) and travel behavior (Leng and Corman 2020; Čertickỳ et al. 2015). Using ABMS offers PTAs the opportunity to verify the outcome of implementing different scenarios (routing, frequency, capacity, etc.) before the actual deployment of a project. This approach, which makes ABMS a central element of decision support systems, already exists in fields such as disaster relief distribution (Fikar et al. 2016; Othman et al. 2017) and e-commerce architecture (Šperka and Slaninová 2012). Therefore, ABMS can also be employed both as central elements of decision support systems for PT planners and decision makers and also as exploratory tools for researchers and transport developers.

2.3 User profiles in transport planning

The need to forecast travel demand is a core element in the design of any PT system. For that purpose, human travel behavior analysis developed as a research field in its own right. In most cases, the user segmentation approach employed in travel behavior analyses is quantitative (Haustein and Hunecke 2013), with different variables identified in quantitative data sets being scrutinized (Chng et al. 2016; Ha et al. 2020; Ma and Ye 2019). Nevertheless, such data lacks an important feature: the inclusion of user attitudes and needs as factors in the travel mode choice decision-making process of the users (Markvica et al. 2017; Le Loo et al. 2015).

A new type of user behavior analysis and profiling, entitled “personas”, has been introduced in transport research relatively recently (Hörold et al. 2013; Oliveira et al. 2017), being initially developed for the field of software design (Brickey et al. 2011). Personas are a generalization of potential behavior types, which do not claim completeness (Grudin and Pruitt 2002) but can provide help in progressing from abstract goals towards more tangible assumptions (Pfeifer et al. 2019). Some popular uses of personas in mobility behavior analyses include research on development and acceptance of future mobility concepts (Kong et al. 2018) and scenario thinking for urban mobility developments (Vallet et al. 2020).

There has been criticism on the lack of solid empirical grounding in relation to the use of personas as core elements of user-centric approaches (Salminen et al. 2020; Chapman and Milham 2006; Miaskiewicz and Kozar 2011). Therefore, methodologies for creating more “reality grounded” personas have been further developed (Salminen et al. 2020, 2022). Gonzalez de Heredia et al. (2018) proposed three methods for creating holistic and detailed personas: based on new survey data, combining data from multiple existing surveys, and iterating between qualitative data from interviews linked with quantitative data from surveys.

The persona profiles used in the present research were developed using the third method proposed by Gonzalez de Heredia et al. (2018), a similar data sourcing approach as the one employed by Hörold et al. (2013). For that purpose, both quantitative (travel surveys) and qualitative (interviews and expert group input) data were collected and analyzed for the development of the persona profiles.

2.4 Present study

The present study proposes a comprehensive approach for simulating transport networks. The approach moves beyond classical mathematical optimization models, introducing specifically designed user profiles as part of an agent-based computer simulation-optimization framework. These similarities and differences are summarized in Table 1. The results are meant to help PTAs, urban planners and other decision makers verify the potential impact of public transport route and network modifications. They are also meant to facilitate decision making with regard to public transport planning and operation.

Shim et al. (2002, p. 111) presented the three core components of classic decision support systems: “(i) sophisticated database management capabilities [...], (ii) powerful modelling functions [...], and (iii) powerful, yet simple user interface designs that enable interactive queries, reporting, and graphing functions”. Our proposed approach is in line with the first two core components proposed by Shim et al. and is meant to be a stepping stone for the development of a decision support system targeted at PTAs providing transport services in networks of small cities and towns.

Table 1 Similarities and differences of the present study in relation to agent-based simulations and classical optimization approaches for public transport

The primary contributions of this study are:

• Showcasing the adaptation potential of an existing transport simulation model, initially designed for metropolitan urban areas, to a regional setting with the purpose of evaluating potential express service PT solutions.

• Bridging the gap between persona use in mobility research and agent-based simulations.

• Proposing a novel agent design and data collection procedure based on survey data to facilitate the introduction of user behavior and user needs in the transport simulation model and the modal choice decision-making process.

• Applying the adapted model to the specific case of a small cities and towns network.

• Highlighting the potential impact of using transport simulation models in supporting decision making for public transport planning.

3 Methodology

The general data flow and processing consists of three parts, presented in the following: Subsect. 3.1 describes the data processing; Subsect. 3.2 the simulation-optimization framework; and Subsect. 3.3 the simulation/evaluation module. Figure 1 illustrates the overall simulation-optimization framework.

3.1 Data processing

Several types of input data are needed, as can be seen in the flowchart presented in Fig. 1. At the very beginning, the mobility demand generator (see Subsect. 3.2.1) pre-processes raw data from travel surveys, public transport usage data, map data, and other meta-data about the considered region. The output from the generator is a fixed demand in the form of a list of trips a number of agents need to perform within a certain time period (for example, from Origin A to Destination B at Time C as part of a normal working day routine). Additionally, information about the user types, in the form of persona profiles (for example, age group, car ownership, children in care), is fed into this model so that it can later be used to simulate the travel behavior.

Fig. 1

Flowchart for gathering and processing input data for the simulation algorithm

Based on the resulting mobility demand, which combines the needs and preferences of the users with the existing transport infrastructure, initial mobility offers are generated. Mobility offers are represented by the most common transport options for each trip (such as public transport, car, bike, or walking route). They are computed by using an intermodal routing engine (Prandtstetter et al. 2020), because the model should allow intermodal routes (for example, when a person uses a bike and changes to a bus for his commuting trip). The routing engine requires data about the underlying map (street network) and the public transport schedules, which are commonly available in General Transit Feed Specification (GTFS) format. Both the mobility demand and the initial mobility offers are computed only once in the data pre-processing step and are fed into the simulation algorithm.

Fig. 2

Overview of the proposed simulation-optimization framework architecture and employed data sets

3.2 Simulation-optimization framework

In this framework, a specific scenario is considered, such as an increased frequency for the bus schedule. Based on the scenario specification, the search space of the optimization algorithm is defined. In the bus schedule example, this could consist of adding three extra buses within a certain time period, and the goal is to search for the best updated schedule. Together with the mobility demand, the initial mobility offers, and an initial pricing scheme for these offers, it forms the input data for optimization.

New solution candidates are generated by either adding/deleting mobility offers (e.g., adding a new bus line), altering existing mobility offers (e.g., reducing the walking time to the nearest public transport stop), or altering the pricing scheme of the mobility offers. These changes to the transport system are evaluated by simulating the user behavior in response to the changes. For this, a numerical value, or a so-called utility value (see Sect. 3.3.1) is assigned to each mobility offer based on a choice model, which takes user behavior parameters and persona attribute values into account. To model the user decisions, for each mobility demand the mobility offer is chosen with a likelihood proportional to the utility rate. In the end, all chosen mobility offers are subsequently passed to the evaluation solution evaluator as described above. A sketch of this framework is shown in Fig. 2. The following sections provide a more detailed description of each component.

3.2.1 Mobility demand generator

The mobility demand generator generates a set of mobility demands based on the steps in Fig. 1. This is later used to represent the mobility patterns of the analyzed user groups in the given context. Each mobility demand consists of a user ID, a corresponding persona ID, an origin location, a destination location, and a trip start time. The sequences included in the mobility demand generator are:

• 1. Extract data from a mobility survey: The extraction of mobility demand data is the key for the whole model. The start and end location of the trip, trip start time, and user data must be provided. This is usually based on available travel journals or (national, regional, or local) travel surveys. Hörl and Balać (2020) described an example of such a methodology.

• 2. Draw a population sample: The model requires a minimum sample size in order to provide robust results. According to Llorca and Moeckel (2019), a sample size of at least five percent is necessary to correctly represent the behavior of the population. Other researchers have recommended larger sample sizes (Kagho et al. 2022; Ben-Dor et al. 2021). Depending on the sample size of the mobility survey (previous point), the extracted data can be completed by other input data sources (if the sample size is too small) or reduced (if the sample size is too large). The survey sample employed in the present research (1800 trips) represents approximately three percent of the whole population aged 20–66 (according to data provided by Agder Fylkeskommune) living in the coastal municipalities served by Line 100. If we only consider the employee group, our survey sample size is around five percent.

• 3. Geographical filter for a target area: If a nationwide travel survey is used, the input data can be filtered so that it represents the considered area. A basic approach is to only consider trips starting or ending within the area. Additionally, customized personas are used to reflect differences in the overall mobility behavior of several representative user groups of the considered area. This information is often not contained in national travel surveys but can be inserted in a separate step either in an elaborate way when specifically considered in the survey design (e.g., Rasca et al. 2023), or in a simpler way by considering demographic data of the region of interest.

• 4. Generate daily travel plans: The goal of this step is to align trips with respect to the semantics of the traveling person. Trips should not be considered independently, but as a sequence (activity chains). This not only influences the mode choice (that is, which modes are preferred for which trip purpose) but also adds constraints (for example, beginning a trip on a day with a private car should end with returning the car to the home location).

3.2.2 Initial mobility offer generator

The goal of the initial mobility offer generator is to generate a set of mobility offers for each mobility demand generated in the previous step. Each mobility offer consists of a list of route segments, in which the overall route is partitioned. Each partition represents a continuous trip using the same mode. A mode switch (or a transfer between two different public transport lines) occurs between two consecutive route segments of the same offer. The information about the transport mode (and specific lines for public transport), the travel time (calculated by the intermodal routing engine), the length, and the quality of the partition are stored for further use. Note that this module only creates the initially available offers; that is, the offers of the baseline scenario without any additional options induced by measures.

The users’ choice of these routes is often based not only on the travel time but includes other factors, such as the number of transfers for public transport; therefore, many different reasonable routes are computed. There are several approaches described in the literature on how to find a set of alternative routes from a given source node to a given destination node, see, e.g., Bader et al. (2011), Delling and Wagner (2009), and Bast et al. (2013). The present model uses a via-node approach, in which the fastest route from the source to the destination node is computed while visiting a node out of a list of via nodes in between. The list of via nodes is given by nodes on a perpendicular line of a direct line from the source to the destination. An intermodal routing engine then computes routes using single or multiple modes.

3.2.3 Solution generation and optimization

The simulation-optimization framework is able to optimize the solutions with respect to implementing mobility stations, finding optimal locations, etc. The algorithms within the optimization module are based on generating an initial candidate solution and applying metaheuristic methods (Glover and Kochenberger 2006) such as variable neighborhood search. Since optimization is not used for strategic planning of the transport system in our particular study, we will not go into the details of this component.

3.3 Simulation/evaluation module

In the simulation component, the user choices of the routes are simulated. When an optimization part is used, this represents the evaluation component of the optimization algorithm. If no optimization is used, this is the main component of the overall framework. The goal of this part is to simulate the user’s choice of a mobility offer for each of their mobility demands. This is achieved by parametrized utility functions assigning a utility value to each mobility offer, a value that is based on the properties of the routes and the personal preferences of the users (extracted from the persona profiles).

The first step in this method is to sort the mobility demands by their departure times in ascending order. Then a user choice is simulated for each mobility demand following the ascending order. However, in some cases, previously chosen offers by the same or a different agent might influence the choice possibilities of the current mobility demand, depending on the realities of the simulated case. For example, in Agder, car and bike sharing were not available as transport options at the time that the present research was conducted. Therefore, if a private car or bike is used for a trip by an agent in the simulation, it will be used for the return trip as well. To ensure this is correctly represented in the model, before a choice is made, a filter is employed to remove infeasible mobility offers/trip chains. Our assumption for the case of Agder is that the private cars/bikes are always available at the home location of the corresponding agent at the start of the day and have to be returned to their home locations by the end of the day (for example, after the last mobility demand of the agent). For each mobility offer, the following conditions are checked:

• If the offer uses a limited resource, check its availability.

• If the first chosen offer of the same agent is not a private car/bike, all further car/bike choices are infeasible until the agent returns to the home location.

• If the previously chosen offer of the same agent was a car/bike and the current location will not be visited again, set all other modes as infeasible. This ensures that the car/bike always returns to its home location.

This reality might differ depending on the case selected. For example, in the OptiMaaS model, car and bike sharing were included as transport options, meaning that the agents could have return trip chains with diverse transport modes.

In the next sections, we will show how the user choice is simulated given that all remaining offers are feasible.

3.3.1 Mobility offer evaluation

A key component in the simulation is the evaluation of mobility offers. Each offer is evaluated using a set of evaluation functions taking the offer properties, the user behavior model, and the persona attributes into account. The evaluation approach is based on utility functions which are often used in the literature for estimating a personal utility of a choice (Modesti and Sciomachen 1998). In the present study, the approach is based on the utility functions of the route choices (Balac et al. 2019; Becker et al. 2020) which used the following functions for the different modes of transport:

$$\begin{aligned} U_{walk}= & {} \alpha _{walk}+\beta _{traveltime,walk} \cdot t_{traveltime,walk} \end{aligned}$$

(1)

$$\begin{aligned} U_{cycling}= & {} \alpha _{cycling}+\beta _{traveltime,cycling} \cdot t_{traveltime,cycling}\nonumber \\{} & {} +\beta _{age,cycling}(age-18)+\beta _{quality,cycling} \cdot {quality} \end{aligned}$$

(2)

$$\begin{aligned} U_{car}= & {} \alpha _{car}+\beta _{traveltime,car} \cdot t_{traveltime,car}\nonumber \\{} & {} +\beta _{cost} \cdot \left( \frac{distance}{40km}\right) ^{\lambda _{ distancecost}} \cdot {cost}_{car} \end{aligned}$$

(3)

$$\begin{aligned} U_{pt}= & {} \alpha _{pt}+\beta _{traveltime,pt} \cdot t_{traveltime,pt}+\beta _{waitingtime,pt} \cdot t_{waitingtime,pt}\nonumber \\{} & {} +\beta _{numtransfers,pt} \cdot {numtransfers}+\beta _{cost} \cdot \left( \frac{distance}{40km}\right) \cdot {price}_{pt} \end{aligned}$$

(4)

The parameters $\alpha$ and $\beta$ reflect the user attitudes towards the different modes and the associated importance of the attributes (e.g., travel time, distance) of the routes. These values are often estimated by applying a multinomial logistic regression model to the results of a stated preference travel behavior survey (Frei et al. 2017). Since performing such a survey is out of the scope of this project, in a first step we used the $\alpha$ and $\beta$ values from a previous Norwegian study (Raustøl 2013) in combination with the most recent Norwegian official values of travel time (Flügel et al. 2020). As the set of values identified in Raustøl (2013) was incomplete (see Table 2), the missing $\beta$ values were estimated starting from the latest Norwegian values of travel time (VOT) and the proportion of $\beta$ values available in Frei et al. (2017). The $\beta$ values for travel time are measured in minutes, while the $\beta$ value for travel cost is measured in Norwegian Kroner (NOK). The VOT formula employed, sourced from Athira et al. (2016), is:

$$\begin{aligned} VOT=\frac{\beta _{traveltime}}{\beta _{cost}}\times {60\,NOK/hour} \end{aligned}$$

(5)

In a second step, we applied the automatic parameter tuning package irace (López-Ibáñez et al. 2016) to calibrate the two missing $\alpha$ parameters towards the area under investigation. With a known mobility modal split for the target area, calculated from the results of the survey (Car 66.03%, Bike 18.25%, Walking 9.19%, and Public Transport 6.53%), the goal was to obtain a parametrized user behavior model that approximates these values. After running irace for 20 000 iterations, the results of the calibrated model reflected the modal split resulting from the survey. Therefore, the $\alpha$ parameters could be used. Studies similar to ours use the values computed for Zurich, Switzerland, which were originally presented in Frei et al. (2017) and used in Balac et al. (2019) and Becker et al. (2020).

Table 2 Parameter values used in the model

In addition to the $\alpha$ and $\beta$ parameters, the mode preferences of the agents were considered by utilizing their preferred transport mode in the utility functions. This was achieved by assigning a numerical value on a scale of one (poor option) to five (very good option) for each persona and for each transport mode based on the outputs from the persona profile design (Rasca 2022). This assigned preference value can modify the utility rate with a range between 10 percent and 50 percent (corresponding to 1–5). For example, the utility rate for walking for persona $p_1$ is computed as follows:

$$\begin{aligned} U^{p_1}_{walk}=U_{walk}+\frac{p^w_1}{10} |U_{walk}|, \end{aligned}$$

(6)

where $p^w_1$ is the preference value for walking of persona $p_1$. Note that, in our approach, the trip options are generally multimodal, which means that when PT is chosen, the first leg and the last leg are performed by walking and their (dis)utility is added to the trip utility.

3.3.2 Look-ahead approach for mobility offer evaluation

Considering the choices of the mobility demands of the users independently generates a bias towards the most attractive mode for the first mobility demand. As the choice of a car or bicycle as a transport mode for the first trip often determines the remaining choices for the other mobility demands of the day, a “looking ahead” mobility offer evaluator was developed to reduce this bias. This was achieved by changing the utility computation of each offer through also considering the offers for the future mobility demands of the same person. Specifically, for a given mobility demand, each offer is temporarily fixed and all the remaining choices of the agent are simulated given that the fixed offer is chosen. As a result, the new utility of the offer is the sum of the utility of the offer and all the chosen future offers (determined by simulation). This total value is then used instead of only the utility value of the actual offer for the user decision module.

3.3.3 User decision module

After evaluating the mobility offer, the user decision module simulates the decision of the user about the chosen offer based on the utility values. Like many others before (Hörl et al. 2018; Grether et al. 2009; Jánošíková et al. 2014), the present approach also relies on a multinomial choice model for the probabilistic decision-making, which is as follows. Let $O_d$ be the set of mobility offers of mobility demand $d \in D$, and $\hbox {S}_{{di}}$ the utility of mobility offer i with $i \in O_d$. Then, the probability that offer i is chosen out of the set $O_d$ is given by:

$$\begin{aligned} P_d(i |O_d)=\frac{e^{\mu {S_{di}}}}{\sum _{j\in {O_d}}{e^{\mu {S_{dj}}}}}, \end{aligned}$$

(7)

where $\mu$ is a scale parameter to set the importance of the utility value. The choice for each user and demand is then simulated by taking a sample of the resulting probability distribution, which gives the set of chosen mobility demands.

3.3.4 Limitations

The limitations of the current research need to be addressed before presenting the results. We will highlight two types of limitations: data-related, and methodology-connected.

Concerning the data-related limitations, note that the survey over-represented individuals with higher education. This issue has been previously encountered in electronically-conducted surveys in Norway (Roche-Cerasi et al. 2013). Furthermore, the distribution of the survey respondents in situ was not entirely consistent with the real population distribution. For example, very few respondents living in Fevik were registered, despite Fevik being an important component of Grimstad municipality. Furthermore, no detailed travel journals were collected.

As the data collected did not allow for the calculation of a dedicated VOT, the most recent pre-determined VOTs for Norway were used (Flügel et al. 2020), as well as pre-determined $\beta$ parameters, where available. One limitation regarding the sourced $\beta$ parameters is that they were calculated for a specific sample of cyclists. Nevertheless, when calculating the VOT based on the formula sourced from Athira et al. (2016), we found the results achieved with the $\beta$ parameters sourced from Raustøl (2013) to be very close (on average a deviation of approximately six percent) to the VOTs used as reference.

In terms of methodological limitations, only one express-service bus route’s redesign was considered in the present case study. Nevertheless, the model can be employed for more complex endeavours. For the sake of simplicity, the model, which is regarded as a pilot study, did not include an occupancy feature or a crowding penalty and crowding disutility.

4 Case study

4.1 The region of Agder, Norway

Agder is the southernmost region of Norway, covering a territory of 16,434 $\hbox {km}^{2}$ and hosting a population of approximately 300,000 inhabitants. Roughly 80 percent of the population is concentrated in the coastal area. The municipality of Kristiansand, with a population of approximately 112,000 inhabitants, is the largest urban area and also the capital of the region. The predominant urban forms in Agder are small cities and towns (SCTs). Regional bus routes connect Kristiansand with the other main urban settlements in the region, the most popular route being bus Line 100 connecting Kristiansand to Arendal via Lillesand and Grimstad (Fig. 3).

Fig. 3

Map of the regional bus network in Agder (courtesy of Agder Kollektivtrafikk AS)

The public transport provision outside the boundaries of Kristiansand is limited in terms of frequency and density of the PT network. This, combined with a low-density of habitation, increasing urban sprawl, high car dependency and easy access to free parking generates a modal split that strongly favors the car (approximately 70 percent) to the disadvantage of public transport (approximately 5 percent). The mode share of PT is situated below the national average of Norway, which was 10.9 percent in 2019 (Statista 2020).

As a signatory of the Paris Agreement, Norway has introduced new sustainability targets for the public transport sector, challenging all regions to increase their share of PT usage. Agder Kollektivtrafikk A.S.² (AKT), which is the PTA in Agder, is looking for strategies that would help attract new customers and increase the sustainability of the mobility sector in this region.

4.1.1 Bus Line 100

The regional “Line 100” bus route connects Kristiansand to Arendal (see Appendix A) and consists of four main routes, each with its own variations in terms of end stops and route lengths (see Table 3). The line is the most popular in the region, connecting the largest municipalities in Agder (Kristiansand and Arendal) and the two campuses of the University of Agder, located in Kristiansand and Grimstad. The route also includes the largest Norwegian shopping area, Sørlandssenteret, and the most visited Norwegian tourist attraction: the Dyreparken zoo and amusement park.

Table 3 Line 100 route variations, typical frequencies, transit times and number of stops. Graphic overview in Appendix A

4.1.2 Redesign of the express service for Line 100

Line 100 has 62-seat single articulated buses equipped with seat belts, onboarding through the front door and alighting through the middle door, pre-paid tickets with on-board validation at the front door, maximum driving speed of 90 km/h on highway, stations part of the sidewalk or curb environment, with modest passenger shelters, and middle-door lifts for passengers with disabilities. The stops and stations are designed to allow in-line, double berthing. Larger stations allow for bike transfer (bike parking facilities available in the stations’ vicinity) and a limited number of stations provide park-and-ride facilities. In all scenarios considered in the present research, the conditions stated above are assumed.

There are several transfer options between Line 100 and other important regional routes (see Fig. 3), such as Line 150 (Arendal to Tvedestrand), Line 133 (Lillesand to Birkeland), or Line 35 (Kristiansand to Kjevik airport).

Bus services are subcontracted by the PTA in Agder. The costs associated with 1 km of service on the L100 in January 2021 when the study was performed were 40 NOK (Norwegian Kroner), which gives an approximate cost of 221 592 NOK for a typical workday schedule for the entire Line 100.

An analysis of the survey data collected in 2019 in the Agder region revealed that the minimum desired frequency for buses in Agder is 20 min (Rasca and Saeed 2022). When the present study was conducted, the regular frequency of Line 100 was 30 min between 5:00 and 16:30, with exceptions in the rush hours when the ES routes (100D and 100E) are running. Currently, the schedule of the ES routes is not optimized for providing a higher frequency with regular intervals during rush hours. The multiple variations in the routes for the same line (see Table 3 and Appendix A) can make it difficult for new potential customers to understand the schedule.

AKT has been exploring options to reorganize the two ES route options (100D and 100E) into one unified route (100 Express or 100E). For that purpose, they performed a consultation of the current users of the existing two express lines (100D and 100E). The results of the consultation revealed that the customers wish for more direct connections between the municipalities, faster transit times and schedules better fitting to their needs. Therefore, the transport planning team at AKT proposed a revision of the ES route options of Line 100 by merging the 100D and 100E route variations into a new 100E.

The new route would have direct, non-stop buses connecting Kristiansand to Lillesand, Grimstad and Arendal, running in parallel in the morning rush hours towards Kristiansand and in the afternoon rush hours outwards from it. For the opposite direction at the rush hour times, the buses would run between Kristiansand and Arendal passing through the regular 100C route in Grimstad. The proposed schedule can be seen in Appendix A.

4.1.3 Requirements from the Public Transport Authority in Agder

The model architecture and solutions evaluation for the case of Agder were designed in accordance with the requirements of AKT, the PTA in the region. These requirements formed a set of key performance indicators (KPIs) used in the solution candidate evaluator step. The five main requirements, targeted at the employees’ user group, were:

• KPI.1—minimize end-to-end transit time for the ES route of Line 100.

• KPI.2—increase ES line patronage compared to current values. Patronage estimations were based on the results from RS 2019.

• KPI.3—increase rush hour frequency on Line 100.

• KPI.4—minimize waiting time for users.

• KPI.5—identify best solutions (increased patronage and frequency) for a daily cost increase on the ES line of maximum 10 percent.

• KPI.6—maintain the purpose of the ES line as an inter-city commuting service.

4.1.4 Data collection

The present research employed both quantitative and qualitative data. This section presents the data collection methods and sources.

• Quantitative data collection

The data sets used for the model initialization cover the regional transport infrastructure (roads, speed limits) and the public transport network, with a focus on Line 100 (location and name of PT stations, routes, timetables and trips of the individual vehicles with their respective sequences of stations and arrival/departure times). The data for Line 100 are loaded from GTFS files provided by AKT, the PTA in Agder.

Demographic data for the population of Agder (age, education, family size), and car ownership data for the region were provided by the Agder Regional Council. The demographic and car ownership data were used for the persona distribution in the frame of the simulation.

Collecting travel behavior survey data is considered time-consuming and expensive, so researchers recommend the use of existing travel survey data where available (Heyken Soares et al. 2019). In the case of Agder, the latest national travel survey data available at the time the present study was conducted, were from 2011. The current PTA in Agder was formed in 2015 through the merger of two previous PTAs, with consequent changes in the operations and PT offer. Therefore, we could not consider the 2011 data as reflective of the current daily commuting realities. As a result, a dedicated Regional Travel Survey (RS 2019) was performed between June and September 2019 in Agder as part of the OPTCORA³ project. The survey data were used for two purposes: to construct the persona profiles and as input data for the simulation model (agent routes, schedules and movement). The RS 2019 survey structure and the collection method for the N = 1861 responses are described in detail by Rasca et al. (2023).

The RS 2019 survey data used in the simulation model for the trip generation were: postal code of home location, GPS coordinates of employment location, time of travel, and travel mode. The last component was used to determine the modal split used in the calibration phase. For the persona profile creation, the following data were used: demographic profile, car ownership, parking availability, commuting habits, public transport accessibility and satisfaction, and personal drivers for increasing PT use.

The collected qualitative data was a critical element in structuring the persona profiles. The process, presented in detail in the research of Rasca et al. (2023), employed: (a) a panel of local and international experts in the field of public transport who supported the development and validation of the persona profiles; and (b) a series of 32 semi-structured interviews performed with employees of organizations located in the proximity of Line 100 that took part in the survey. No incentives were offered for participating in the interviews.

5 Persona profiles generation and allocation

The process of generating the 20 persona profiles for Agder is described in detail in Rasca et al. (2023). The core steps of the process are presented in Fig. 4, showing how both qualitative (semi-structured interviews, expert panel) and quantitative (travel survey and latent class cluster analysis (LCCA)) methods were employed. Once the persona profiles were created (see Appendix B for overview of persona profiles), a preference for different transport modes used for the daily commute was calculated. The method for this calculation is presented in Rasca (2022).

Fig. 4

Steps of the persona design process (Rasca et al. 2023)

The 20 persona profiles (see Appendix B) were distributed in the analyzed area, striving to represent as closely as possible the target population group (adults aged 18–66). The process included (1) the segmentation of the adult population in each municipality of Agder in groups of similar age and education level as the personas designed; (2) separating each group in representative proportions for each of the corresponding four base persona profiles, as defined by Rasca et al. (2023); (3) randomly allocating personas to the trips starting in the postal codes of the studied area, respecting the distribution achieved in the previous two steps.

6 Scenario description

The application of the simulation-optimization framework is based on inputting predefined scenarios into the model, once the model has been calibrated, and comparing the results to the initially assessed situation.

The nine scenarios (see Table 4) were generated by a group of experts composed of transport planners employed by the PTA in Agder, transport researchers from the University of Agder and the AIT Austrian Institute of Technology. The scenarios were based on: data gathered from users of PT in Agder based on the regular customer surveys conducted by AKT, data gathered from non PT-users (RS 2019 and interviews), and the professional experience of the experts themselves. The scenarios aimed to include both improvement requests from the inhabitants of Agder (users and non-users of PT) and employees of the companies that participated in the RS 2019 (for example, increased frequency, shorter travel time, better timetable), as well as requests formulated by the PTA (increase of patronage, minimization of operating costs).

The approach to generating the nine scenarios took into account two main perspectives: the routing aspect and the frequency of service provision. The routing analysis included aspects such as: catchment areas for existing bus stops and proposed ones, occupancy profile of the line based on onboarding and alighting on each station, density of the inhabited area on the bus route, and density of the available services (employment, education, health, leisure) on the bus route.

Table 4 Description of the nine scenarios used in the simulations

Table 4 presents an overview of all scenarios proposed for simulation. The base case, or Scenario zero (S0), represents the current status of the network achieved by calibrating the model. Scenario 1 (S1) represents the solution proposed by AKT with the introduction of the new 100E, while the remaining scenarios are those proposed by the expert group. Scenarios 2–6 (S2–S6) simulate different route alternatives with similar schedules and were intended to verify the best route option in relation to transit time, costs and increase in usage. Scenarios 7–9 (S7–S9) simulate the introduction of a 20-minute minimum frequency covering different lengths of rush hours for the best route option identified in the previous step.

The request of the PTA to keep the cost increase limited to 10 percent meant that the possible frequency variations were limited to be almost non-existent. Therefore, the decision was to simulate two scenarios (S7 and S8) with moderate schedule changes, and one scenario (S9) with large schedule changes, with the goal of showcasing the PTA the potential patronage increase brought by improving the service frequency.

It should be noted that adding an off-highway stop to the ES route, in order to service a new location (such as Lillesand), brings an additional transit time of at least three minutes to the end-to-end route.

7 Results

The proposed scenarios were separated into two categories: the first six scenarios (S1–S6) provided route variations, while the last three provided frequency changes using the best route solution identified in the previous step. The following two subsections present the results achieved when comparing simulation outputs for scenarios in each of the two categories.

7.1 Selection of the fast transit route option

For the identification of the best performing fast transit route scenario, the following KPIs were employed: KPI.1 (minimize transit time), KPI.2 (increase patronage), KPI.4 (minimize waiting time, both at the first stop of the journey and in transit stations for users traveling with multiple buses to the destination), and KPI.6 (maintain focus on intercity trips). The data sets presented in Tables 5 and 6 match the results achieved with each of the four KPIs. In the case of KPI.6, both the information sets regarding the average travel distance and the share of long trips were found to contribute to the information regarding intercity trips. Therefore, KPI.6 is repeated in the headings of the tables.

The selection of the best-performing route for 100X occurred in a three-step process, using the four KPIs as reference for the identification of best-performing solutions: (1) simulate the route with a minimum number of stops based on prioritized stops identified by the transport planners (S1–S2); (2) choose the best-performing solution from the previous step and simulate three route options that contained a fast transit stop in Lillesand (S3–S5); (3) choose the best-performing solution from the previous step and add a stop in Sørlandssenter shopping area (S6). Once all three steps were performed, the results were analyzed and the route with the best potential outcomes according to the KPIs could be identified.

Table 5 Simulation results for the base case (S0) and the first five scenarios (all results presenting averages refer to average per trip)

Table 5 summarizes the simulation results for the base-case scenario and scenarios S1–S5. The four KPIs analyzed are presented in comparison, with statistically significant results for KPI.2, representing the patronage variation, marked in bold.

An increase in waiting time is a clear negative aspect and can be observed in all scenarios. Note that the schedule of the connecting feeder lines and connecting routes was not altered to fit to the newly proposed route schedules, so waiting times may be negatively affected by this aspect. In terms of the average travel time (KPI.1), it is not possible to clearly determine its variation as having a positive or negative impact. This is because an increase in average travel distance may also trigger an increase in average travel time per trip. Therefore, the ES patronage variation (KPI.2) and share of long trips in all bus trips (KPI.6) were used to determine the best-performing scenario in this phase.

We observe that S2 clearly outperforms S1 in terms of positive patronage variation. The two scenarios (S1 and S2) show similar average waiting times, average travel times per trip, and shares of long trips in all bus trips. The only notable difference between the two scenarios is in the average travel distance, which is slightly higher in the case of S1. Considering these results, the conclusion of the first step of the process is that the proposed 100X (S2) route will be used for further analysis in step two.

The introduction of an ES stop in Lillesand (S3–S5) brings a clear increase in patronage, but also increases the average travel time and length of the trips compared to S2. The best performing scenario that includes a stop in Lillesand is S4, with a 105.3% patronage increase (considerably higher than S3 and S5), similar waiting times to S5 but better than S3, and a slightly higher average travel time and average travel distance compared to S5. Overall, it can be concluded that S4 is the scenario that should be used for further simulations in the third step.

It has to be noted that S4 and S5 are using theoretical ES stops for Lillesand, as the physical bus stop infrastructure for these cases does not exist yet. Therefore, the best-performing S4 would need additional infrastructure investments for an ES stop at Møglestu in Lillesand before it can be deployed.

The third step of the process simulates the addition of a stop in Sørlandssenter to the route S6. The results for S6 show that the patronage suffers losses compared to S4, and does not show statistically significant changes in terms of waiting time compared to S4. A clear decrease in the average travel distance is visible, as well as a reduction in the share of long trips. Therefore, the addition of a stop in Sørlandssenter is not considered beneficial, as the increase in overall route length (and therefore cost) is not compensated by a ridership increase.

Given that S4 requires an infrastructure investment for building a new bus stop, and that S4 surpasses the 10% cost increase even before altering the ES route’s frequency, the PTA opted to choose the route solution that did not include Lillesand. Therefore, the selected route was the one proposed in S2. In the following scenario simulations, targeted at testing the impact of different frequencies on the best-performing route, S2 will be used as the ES route option.

7.2 Selection of the best frequency option

In this section, we present the results achieved when altering the schedule and frequency of the ES line (scenarios S7 to S9). The results are summarized in Table 6.

In the case of Scenario 7, we observe that a moderate price increase (20.95 percent, see Table 3), produces a large impact on the ES patronage (89.5 percent). At the same time, the impact of a larger price increase (74.88 percent) which is simulated in the case of S8 further improves the patronage compared to S7 by only 31.6 percent. All other KPI results tend to be similar between S7 and S8.

In the data from RS2019, 33 percent of the respondents stated that their work schedule usually starts between 07:00 and 08:00, 29.3 percent between 08:00 and 09:00, the rest either having flexible work hours (with a start most commonly between 07:00 and 09:00 in Norway) or working in shifts. Therefore, the fact that an increased frequency relevant to the morning and afternoon rush hours has the biggest impact on the ridership and is consistent with the user profiles in Agder and their travel habits.

Table 6 Simulation results for frequency variation scenarios (S7–S9). All results presenting averages refer to average per trip

The results analysis for S9 suggests that a 10-min frequency in the rush hours for the same duration as S7 has the potential to bring an additional 63.1% increase in patronage compared to S7 and brings more than two and a half times more customers to the ES lines than the base-case scenario S0, at a 127.29% cost increase. This highlights the importance of having frequencies that allow users to “forget the timetable”.

The introduction of regular time intervals and increased frequencies, combined with a unique ES route proved to have a strong positive effect on the patronage. Nevertheless, once the timetable and routing were regularized for the ES option, the price increase was higher than anticipated. Therefore, none of the proposed schedules falls within the 10% cost increase limit required by the PTA.

8 Discussion

To better understand the outcomes of the study and for an easier comparison between the impact of different scenarios on the patronage of the ES option of Line 100, a simplified decision tree has been constructed (Fig. 5) based on the results presented in the previous section.

Fig. 5

Decision tree based on simulation results for costs and ridership for the nine scenarios

The analysis of the route options for the ES of Line 100 (S1–S6) suggests that it is necessary to prioritize higher density urban areas outside Kristiansand (Lillesand, Grimstad, Arendal) that are not serviced by metropolitan transport lines, as Sørlandssenteret is. At the same time, the positioning of the ES stops needs to be carefully considered. Low-density locations, which make it necessary for users to employ another means of transport to reach the bus stop (as is the case in S3), have a negative impact on patronage. It is also important to consider the connection with other local and regional feeder lines, the simulation for S4 where the location of the bus stop also serves Line 133 showing a clear increase in patronage. This confirms the findings of Hansson et al. (2022) and Tønnesen et al. (2021), who stressed the need to ensure a high level of accessibility to bus stops, both from the perspective of service quality as well as multimodal access, such as car and bicycle parking possibilities. The routing simulations used an identical schedule for S0 and for S2–S6, indicating that a redesign of the ES route is crucial in increasing patronage for the user group.

The imposed financial limit of a maximum 10% cost increase left very little room for possible measures in relation to frequency improvements. Financial limitations are some of the most common issues for PTAs serving low-density areas, whose services often depend on national and regional subsidies. Employing a simulation model like the one proposed in the present study may support PTAs in motivating the need for increased funding for service improvements with data-based predictions, which have a better chance of success in accessing extra funding.

The schedule and frequency alterations present considerable opportunities. When analyzing the results for S7, we observe that the simple regularization of the schedule to a predictable frequency of maximum 20-minute intervals for two hours during the morning and two rush hours in the afternoon brings an additional 63.2 percent in patronage compared to S2. Extending the same frequency interval to a duration of six hours of ES service per day (three in the morning and three in the afternoon) further increases the patronage by 31.6 percent in the case of S8.

An increase in frequency to 10-min intervals (S9) for 4 h a day brings an additional 126.3% increase in patronage compared to S2. Consequently, if major financial investments are to be made in order to attract more car commuters towards PT, the results of our research suggest that the first focus area should be the increase of frequency during rush hours and not necessarily the extension of the ES service during lower demand periods of the day.

When analyzing the ES average travel distance in general and average travel distance per long trip in particular, we observe that the introduction of more intermediate stops (S3–S6) has a clear negative effect on both (KPI.6). This shows that more trips with a shorter distance are happening, possibly connecting intermediate stops directly. Such an effect can be seen as both negative and positive, depending on the purpose set by the PTA. If the total end-to-end travel time (KPI.1) of scenarios S2–S6 is considered in relation to KPI.6, an increase in travel time for the same share of long trips is observed for S6. That goes against the requirement of the PTA to reduce the travel time of the passengers.

An interesting aspect of the results is the average waiting time for all scenarios simulated, which increases for almost all newly proposed scenarios with values up to 63.2 percent. The only scenario that comes close to the waiting time of the base-case scenario is S9. This peculiar behavior can be explained by the fact that the schedule of the feeder lines and connecting routes which is now designed to meet the timetables of S0, has not been adapted to the proposed scenarios. Therefore, waiting times for S1–S9 should be compared to each other, rather than with S0.

The ES patronage increased considerably (more than 70 percent) in seven out of the nine proposed scenarios, irrespective of end-to-end route travel time. While this percentage increase seems very high, the head count is in fact a reasonable number (the initial value was of 19 passengers, and the simulated values reached 35–42 passengers) when one considers the initial low share of PT users in the modal split. However, we cannot expect this change to take effect immediately, since it takes time for people to learn about the changes and to adapt their commuting behavior. The indicated increase should be seen as a medium to long-term target after the system settles.

The route simulations also showed that direct rush hour connections between the serviced municipalities, which ignore intermediate stops and consequently decrease the frequency possibilities due to budgetary constraints (as in the case of S1), may not have a strong positive impact on the patronage compared to today’s figures. Therefore, it is recommended that a single ES route is put in place, preferably with regular service intervals that allow for predictability for the customer’s route planning.

The results of the present research confirm the potential of ABMS models to support the development and optimization of future mobility services, such as MaaS, taking into account both the realities of multi-modal journeys and the behavior of simulated agents (Cisterna et al. 2021; Djavadian and Chow 2017). The achieved results underline the importance of being able to verify proposed routing and frequency solutions before deployment. Even though S1 responded to the stated preferences of current ES users, the simulation results for it did not show any added value to the patronage, despite cost increases. Therefore, investing resources into calibrating a simulation model like the one proposed in the present study and using it to verify the potential impact of diverse PT network redesign initiatives can provide PTAs with support in decision-making processes. This falls in line with the first two core components of decision support systems defined by Shim et al. (2002) and sets the foundation for developing the model into a decision support tool for transport planners and PTAs.

The challenges of using the proposed methodology in other case studies around the world also need to be discussed. The current approach demonstrates the adaptability of such a model to two different urban typologies: suburban areas of European metropolises and networks of small cities and towns. Nevertheless, the lack of a user interface makes it challenging to employ the model for a wider audience. Furthermore, an extensive amount of data is necessary to calibrate the model, which can be difficult to collect and organize in a correct format.

9 Conclusions and further research

The results of the present study suggest that the proposed model can be successfully adapted from simulating transport behavior in complex suburban metropolitan areas to the less complex realities of coastal regions hosting networks of small cities and towns serviced by ES bus-based PT. The model proved useful in assessing the viability of different routing and frequency scenarios for the same ES bus route. The model provides a solid approach for analyzing complex transport systems, adding the extra layer of user profiles and preferences to the traditional statistical data set. Thus, the results can be used as decision support systems for transport and urban planners, PTAs, or even national authorities when route improvements are considered.

When discussing frequency improvements versus an extension of service time span for the ES routes, the results suggest that frequency increases during critical time windows have better results in terms of patronage increase than extending the ES service.

The results also show clear differences when adding stops in low-density habitation areas versus higher density areas. This underlines the importance of focusing on the accessibility level of PT stops on ES routes, as the station-to-station transit time is not a sufficient incentive for choosing a specific mode of transport.

The present research combines methods that were previously employed for the simulation of travel habits, using multi-modal transport means, in European metropolitan suburban areas with a fresh approach to integrating tailor-made user profiles (or personas) in agent-based simulations. The proposed approach shows a high potential for increasing the accuracy of travel behavior simulations for specific regions.

The proposed method’s applicability, tested in this case on an ES bus route, is not limited to bus-based services or to the long-distance commuting of employees. Future applications may include a whole range of other transport services (rail-based, car or bike sharing, etc.), depending on the purpose and local realities of the specific studies.

Several other points of interest have also been identified as presenting potential for further research. Firstly, we have observed two major improvement points for the model analysis and output: (1) an occupancy feature to identify the need for supplementing capacity at different service times; (2) a crowding penalty should be introduced in the user decision model to better simulate the user decision-making process. Regarding the usability of the model, a user-friendly interface would be necessary to increase the chances that the staff of the PTAs and other actors in the transport sector would employ the model.

For more realistic results, the model should be applied to a wider user database, covering more diverse user groups (highschool and university students, pensioners, unemployed individuals, etc.). This, combined with a more detailed travel journal for the agents, would provide a more detailed picture of the agents’ travel mode decisions and the interactions between the agents themselves. At the same time, further studies that determine the regional VOTs, passenger’s cost (sum of access, waiting, riding, and egress time values), and crowding disutility would be necessary for further development of the model in representing user behavior and decision making.

Some questions about the implementation and validation remain unanswered until the results of an analysis performed with the use of the model are applied. The results themselves can not be validated until they are tested in real life, and the question of “How long will it take for the users to adapt to the new schedule?” is also part of the validation process.

Appendices

Appendix A: Overview of the current schedule for Line 100 and the proposed schedule for express service 100E

See Fig. 6 and 7.

Fig. 6

Current schedule for Line100. Scenario 0

Fig. 7

Proposed schedule by AKT for new 100E express service route variation of Line100. Scenario 1

Appendix B: Overview of persona profiles

See Fig. 8.

Fig. 8

Overview of the persona profiles used in the study (Rasca et al. 2023)