The Speed of Shared Autonomous Vehicles Is Critical to Their Demand Potential

Abstract

Under a 2021 amendment to German law, the KelRide project became the first public on-demand service operating electric autonomous vehicles (AVs) without fixed routes on public roads. This paper addresses two notable gaps in the literature by (1) conducting an ex post evaluation of demand predictions for a non-infrastructure (Mobility-on-Demand (MoD)) project and (2) using real-world data to analyze how demand responds to key Autonomous Mobility-on-Demand (AMoD) system parameters in a rural context. Earlier simulation-based demand forecasts are compared to observed booking data, and the recalibrated model is used to investigate the sensitivity of passenger numbers to vehicle speed, fleet size, service area, operating hours, and idle vehicle positioning. Results show that increasing vehicle speed leads to a superlinear rise in passenger numbers—especially at small fleet sizes—while demand saturates at large fleet sizes. A linear increase in demand is observed with expanding service areas, provided fleet size is sufficient. Extending operating hours from 9 a.m.–4 p.m. to full-day service increases demand by a factor of two to four. Passengers numbers also vary notably depending on the positioning of idle vehicles. Consistent with empirical findings, the analysis underscores that raising AV speed is essential for ensuring the long-term viability of autonomous mobility services.

1. Introduction

Demand responsive transport (DRT) systems offer a more flexible and dynamic service compared to conventional public transport (PT). These services present great potential, especially for rural and suburban areas, where the density of conventional PT supply is often low [1], and for economically disadvantaged individuals [2,3]. However, it remains an open research question as to how to regulate and configure DRT services such that they provide good service quality and act as a complement to PT rather than competing with it. Unregulated private companies tend to compete by concentrating on areas with affluent neighborhoods and demand density, which is where PT supply density is also at its peak [2,4,5]. In some areas—especially rural areas, where PT ridership is usually very low—travel times and operation costs could be reduced by even replacing existing rail lines with DRT [6]. However, research and pilot projects indicate that DRT (which is used as a synonym for MoD) systems will barely approach a profitable state as long as driver wages account for more than two-thirds of operational costs [1,6,7,8,9,10]. Currently, the only promising solution is presented by AVs. The past decade has brought profound technological advances to the AV market that require the clearing of legal aspects and investigation of societal and environmental impacts. Most importantly, it must be understood whether there is demand for AMoD and how it could benefit populations in medium- and low-density areas, where car ownership is often disproportionately high.

In Europe, autonomous driving is still limited to piloting research projects. Under a 2021 amendment to German law, the KelRide project became the first public AMoD service without fixed routes to operate on public roads [11,12,13]. The project envisaged several expansion stages with regard to the fleet of electric and autonomous minibuses. It involved agent-based transport simulation to support decision-making for the configuration of the service and to investigate potential demand reactions. One simulation study conducted prior to the introduction of the AMoD service indicated that the service area should be adjusted when the fleet size is increased, which was realized at the beginning of 2024, resulting in in Europe’s largest contiguous operating area for autonomous driving on public streets [13,14]. The study at hand makes the following contributions:

• We present an ex post validation of the simulation predictions presented by Schlenther et al. [13] against the reality. The validation reveals the importance of having precise details of DRT service parameters, such as vehicle speed and fleet size. This part features the report of some of the key findings of one of Germany’s lighthouse research in autonomous driving.
• We build on [13] by reviewing fundamental assumptions and improving them by calibrating the AMoD service with (now) existing real demand data.
• We present a detailed sensitivity analysis of further adjustments to the configuration of the AMoD service with regard to future demand potentials, including sensitivities to the expansion of the service area, fleet, and operating times, as well as increased AV speed.

This paper addresses two notable gaps in the literature by (1) conducting an ex post evaluation of demand predictions for a non-infrastructure (MoD) project and (2) using real-world data to analyze how demand responds to key AMoD system parameters in the context of a rural town. The aim is to contribute to a better understanding of the reaction of transport demand to DRT services, particularly those operated with AVs, and to understand how to integrate DRT services into existing transport systems in rural and suburban areas or small towns. The cruciality of this task is exemplified by the public–private partnership between the Kansas City Area Transportation Authority and MoD provider Bridj. The service increased the mobility of the population but was discontinued in 2017 due to difficulties in anticipating demand and lack of funding [15,16,17].

The remainder of this study is structured as follows: Section 2 explores the existing scientific literature on the topics of ex post validations of travel demand predictions, as well as DRT simulation. Section 3 provides details on the course of the KelRide project, during which previous demand predictions were made. These demand predictions are then evaluated against real-world observations, and the causalities of differences are explained. Section 4 explains how the previous model proposed by Schlenther et al. [13] is recalibrated to incorporate the lessons learned from Section 3, as well as updates to the configuration of the AMoD service. Section 5 then details the setup of a case study to explore demand sensitivity towards AV speed, fleet size, operating times, and service area. The results are presented in Section 6 and lead to an additional exploration of demand variance in reaction to vehicle locations in cases with small fleet sizes. Finally, the methods, limitations, and results are discussed in Section 7, and conclusions are provided in Section 8.

2. State of Research

As mentioned in Section 1, the present study makes two contributions to the scientific literature:

• An ex post validation of demand forecasts based on simulation, as presented in Section 3; and
• An assessment of the demand sensitivity to specific configuration parameters of an AMoD system in a small town.

While ex post validation of simulations is not widely covered by the scientific literature, MoD has been a research focus for more than a decade, especially with regard to AVs. The present section aims to provide an overview of the relevant literature on both aspects in the given order. The overview provided for the second aspects hereby complements the literature review presented in [13], which includes (1) existing DRT models in rural and suburban areas, (2) simulation of autonomous DRT, and (3) investigation of DRT configurations with particular regard to service areas.

2.1. Literature on the Ex Post Validation of Travel Demand Predictions

This paper refers to demand prediction as a term for the reaction of the overall transport demand to a new transport or mobility offer. Predictions for these demand reactions are to be distinguished from predictions on the development of the overall transport demand (due to socio-demographic developments). Models that predict these demand reactions typically need the overall transport demand as an input. The present study uses an activity-based transport demand model. The generation of these transport demand models should be validated itself before the models are applied in order to predict demand reactions to new mobility offers. There exists a significant body of research on validation activity-based transport demand models [18,19,20].

In contrast, there is limited research that compares demand predictions to real data. Particularly, the authors of the present study are not aware of any study that compares demand predictions for non-infrastructure projects that are derived from simulation with real data. However, there is research on validation of demand prediction for infrastructure projects.

Flyvbjerg et al. [21] investigated 210 infrastructure projects in 14 nations and found significant differences in forecasts for rail and road projects. The authors report that for roughly 70% of passenger forecasts for rail projects are overestimated by more than two-thirds, and the average overestimation is 106%. Across 183 road projects, the authors found 50% with a difference between actual and projected transport demand of more than ±20%. The authors further state that forecast accuracy did not improve over the studied 30-year period. In other studies, the authors observed that the substantial overestimation of demand and revenue, particularly for rail projects, is typically accompanied by a similarly significant underestimation of costs [22,23]. Thus, reasons for inaccuracy in rail forecasts are attributed primarily to political drivers rather than technical uncertainty [21]. For road projects, the major reason for inaccuracy is found to relate to uncertainties about trip generation and land-use development.

Further complementary insights are provided by Berechman [24], who identify flawed model specifications, outdated input data, and arbitrary benchmark assumptions as key contributors to inaccurate demand forecasts. The authors also highlight that many models neglect dynamic responses such as relocation or behavioral adaptation, as well as disruptive technological or climatic developments. Similar to Flyvbjerg et al. [21], the authors argue that institutional and political incentives can lead to deliberate manipulation of forecasts in the context of large-scale infrastructure planning.

Similar findings are presented by Nicolaisen and Driscoll [25], who provide an overview of 12 studies that evaluate demand forecasts for rail and road infrastructure projects and emphasize the distinction between uncertainty and inaccuracy. The authors find a tendency of underestimation for road projects and overestimation for rail projects. According to Nicolaisen and Driscoll [25], all 12 reviewed studies offer inaccurate forecasts of exogenous variables (economic growth, car ownership, fuel prices, etc.) as part of their explanation for prediction inaccuracy. Nine studies refer to model specification as an explaining factor, while it often remains unclear what models were used. Nicolaisen and Driscoll [25] discuss the relation of improvements in accuracy and model sophistication over time. It is further acknowledged that demand predictions for road projects often neglect induced demand.

One study that is referred to by Nicolaisen and Driscoll [25] evaluated ridership and cost forecasts used in a federal transit project selection process in the United States of America [26,27]. The author compared the forecasts against actual ridership data and found that all of nine projects had significantly lower actual ridership than expected, with eight projects yielding less than 50% of the expected ridership. The author explains that

Overly optimistic assumptions about the frequency and speed of service […] made the largest contribution to the over-estimation of their future ridership levels

([26], p. viii),

while specific specific forecast inputs, such as projected demand sensitivities, explained less than half of the gap. Among the recommendations for improving forecast accuracy are the performance of sensitivity studies on underlying variables and the acknowledgment of uncertainty in ridership forecasts. The present study takes up these points by conducting an analysis of the sensitivity of demand to assumptions about the operating pattern of a DRT service or, more specifically, the positioning of idle vehicles.

Since the publication of [27], the Federal Transit Administration of the United States (FTA) has commissioned three more so-called Predicted versus Actual (PvA) studies on the ridership and capital costs of transit projects, which were published in 2003, 2007, and 2020 and are summarized in [28]. The results show the ridership forecast accuracy significantly improved after the the first PvA study in 1990, with 9 out of 19 projects ending up in a 20 percent range and some projects having higher ridership than predicted. To address the greatest accuracy issue, FTA decided to mitigate false demographic forecasts by using current-year forecasts instead of horizon years. This relates to Flyvbjerg [23], who argue for the use of traffic demand during the first year of operations for measurement of accuracy. The second largest contribution to inaccuracy in [28] is observed to involve model properties and the projects being the first of a kind in a region. As a result of the lessons learned, the FTA provides standardized and simplified forecasting software called STOPS [28]. Finally, a 2023 report acknowledges the coronavirus pandemicas an example of how exogenous variables influence the accuracy of rider prediction (for the worse) but, nevertheless, states that predictions have improved over time [29].

The present study conducts an ex post evaluation of demand predictions for a non-infrastructure (MoD) project. The demand predictions to be evaluated are performed through application of a well-known and widely adopted framework for agent-based transport simulation as documented by Schlenther et al. [13]. Moreover, the present study attempts to quantify uncertainty of predictions that are related to specific model specifications. Therefore, the present study makes a meaningful contribution that aims to promote transparency and methodological improvements.

2.2. Literature on the Configuration and Operation of DRT and Implications for Demand

Most of the following refers to studies that use simulation as their tool for planning, impact assessment, and decision support. Espinoza-Molina et al. [30] provide a systematic overview for research based on backcasting analysis.

Fagnant and Kockelmann conducted multiple studies on the implications of AMoD operation in Austin, Texas, USA, including investigation of strategic repositioning of idle vehicles (rebalancing) [31] and multiple representative travel days [10], as well replacement of randomly selected subsets of private trips [32] (with Bansal). As of 2025, Waymo operates an AMoD system in Austin, as well as in other areas in the USA, although without bundling requests (pooling) [33].

Hörl et al. [8] evaluate the performance of multiple operational strategies for AMoD in a case study of Zurich, Switzerland. The authors conclude that the service configuration including customer-vehicle assignment and rebalancing heavily influences wait times and costs. Similar conclusions can be drawn from Alonso-Mora et al. [34], who present a mathematical model for DRT request assignment including rebalancing and quantify the trade-off between fleet size, capacity, wait time, travel delay, and operational costs in the example of a public taxi dataset from New York City, USA.

Dandl et al. [35] find that the aggregation level and the reliability of demand forecasts, which are mainly used for vehicle repositioning, highly influence the performance of DRT systems.

Liu et al. [36] present a framework that couples Bayesian optimization of MoD design in an outer-loop and mode-choice and DRT simulation based on [34] in an inner loop. The framework is calibrated using the Manhattan taxi dataset, and the choice model is calibrated against stated-preference data collected in New York City, USA.

Engelhardt [37] uses the FleetPy agent-based simulation framework for extensive investigation of operational aspects such as request-vehicle assignment, rebalancing, and reservations in various urban use cases. However, the author states that the limitations of his work include the lack of representation of other transport modes, especially for the modeling of customer behavior.

The present study uses the Multi-Agent Transport Simulation (MATSim) framework in order to assess impacts of DRT configuration on demand. For this work, ridepooling is considered, which refers to the potential bundling of multiple customer requests during their ride. There exist two ridepooling extensions in the MATSim framework that are based on the following [38]:

• The first MATSim extension is described by Ruch et al. [39] and is related to [34]. It is used by Sieber et al. [6], who investigate the replacement of four conventional rail lines by DRT in a rural area in Switzerland and conclude that with self-driving cars, travel times and operational costs can be reduced in three of those cases. Sieber et al. [6] predefine the demand for each of the areas and regard multiple operational strategies, similarly to Ruch et al. [39].
• The second extension is described in a study that simulated real-world taxicab demand in Berlin [40]. This extension, called DRT, was further extended to reflect rebalancing, and multiple strategies were investigated with static demand in Berlin [41] and the rural region of Vulkaneifel in Germany [42], as well as with demand reaction in Berlin [4]. The DRT extension of MATSim was also used to investigate the replacement of all car trips in Berlin by DRT [43], as well as for the present study. In a similar domain as [6], Lu et al. [1] investigate the replacement of school buses by DRT in one of the least populated areas in Germany under various operation strategies and find potential for substantial reductions in operational costs, while DRT could serve additional purposes.

The two mentioned MATSim extensions are compared by Zwick and Axhausen [44] using static real-world demand from the largest ridepooling operator in Europe, MOIA [45]. The authors find that the two extensions produce similar results in terms of travel and wait times but differ in terms of efficiency.

Most of the studies mentioned above take a static DRT demand as an exogenous input and focus on metropolitan areas. These studies investigate hypothetical future mobility offers and partially determine the necessary fleet sizes for these predefined demand levels. Only some use real-world demand data. None of the studies regards the demand sensitivity to DRT in small towns or rural areas with respect to the availability of other transport modes for users. Zwick et al. [46] compare the introduction of an AMoD system for large, medium-sized, and small towns, using an incremental logit model for mode choice, as well as predefined demand scenarios where all car trips are replaced. While the authors find that the service efficiency significantly increases with trip density, operational parameters and patterns are not varied. Moreover, the mode-choice model is not calibrated against real-world data but, rather, assumes that traveling with DRT is perceived as similar as to being a private car passenger.

There are other studies that investigate demand sensitivity and perform demand predictions for DRT services:

• Kuhlen et al. [47] present a spatial regression model for the prediction of DRT demand based on origin–destination relations. Their model represents an improvement compared to Zwick and Axhausen [48], who use spatial regression on a zonal level with regard to sensitivity to service area size. However, the predictions are not backed by physical simulations and are therefore not sensitive to changes in operation strategies such as rebalancing or stop network design, and Kuhlen et al. [47] state limitations regarding transferability to other areas.
• Vosooghi et al. [49] use MATSim with user-specific taste variations to simulate multiple DRT fleet sizes and vehicle capacities in the metropolitan area of Rouen, France. The authors also compare the operational pooling scheme against serving single requests and conclude that all of the variables influence the system’s performance. In another study, Vosooghi et al. [50] assess the impacts of charging infrastructure on operations.
• Diallo et al. [51] compare three scenarios for the deployment of AVs as private vehicles or as part of a DRT system with and without ridepooling for case studies in Montréal, Canada, and Lyon, France. The authors conclude that AVs can account for significant transport-mode shares, with most of the modal shift coming from private cars, PT, and walking trips.
• Hörl et al. [52] perform dynamic a demand estimation experiment for a hypothetical large-scale AMoD service in Paris, France, using agent-based simulation. The authors formulate research questions regarding the usage of DRT in a stop-based system and as a feeder to PT, which are both addressed in the present study.
• Schlenther et al. [53] recently described a transport model for Hamburg, Germany, that includes mode-choice calibration based on real-world MOIA data and apply it to investigate various DRT pricing strategies for integration with PT.
• Agriesti et al. [54] present another framework that integrates a behavioral model with mesoscopic traffic assignment including car-following behavior to assess demand reactions to large-scale AMoD operations, focusing on fleets that are constrained either in size or in driving style. The authors apply the framework to a case study of Tallinn, Estonia. The authors also provide an extensive overview of the existing literature.

The present study fills a research gap by modeling a small existing AMoD system in a small town of about 17,000 inhabitants while investigating demand sensitivity to multiple operational parameters, in addition to using real-world data on the fleet specifications; the stop network, including the rebalancing of target locations; and bookings. Specifically, the operational parameters that are varied include vehicle speed and operating times, which are not thoroughly regarded in the literature and are of importance for the transition period to fully automated vehicle operation (cf. Section 3), as well as service area and fleet size. The tool of choice is agent-based transport simulation (MATSim) including physical and behavioral simulation (for more details, see Section 4.1). It is to be noted that Agriesti et al. [54] refer to Liu et al. [55], who have investigated the effects of different operational speeds for AVs on the demand using a simplified logit model, but the speed is only estimated and not simulated (no traffic assignment), and the considered area of Chicago, USA, is urban.

3. Ex Post Validation of Demand Predictions for the KelRide Project

In the KelRide project, an AMoD service was integrated into an existing human-driven MoD service called ‘Landkreis Kelheim Express Individuell (KEXI)’ as a subsegment [12]. Whereas the human-driven vehicles were equipped with combustion engines, the AVs employed electric propulsion systems. Based on an evaluation of this pre-existing human-driven DRT segment (hereafter referred to as ‘conventional KEXI’), data on detailed road mappings, and on technical limits regarding the total road kilometers combined with the AV depot location in Donaupark, the KelRide consortium set the initial AMoD service area to cover the areas of Donaupark and the old town of Kelheim (shown in purple in Figure 1).

Subsequently, demand predictions were performed for various service expansion options with regard to fleet size and service area, using agent-based transport simulations [13].

Three possible expansion cases for the service area were investigated, which are illustrated in Figure 1. The first case describes the expansion from the initial core area to the northeast with the aim of connecting a shopping center that represents a demand hotspot for the conventional KEXI (cyan). In the second case, in addition to the shopping center, the service area was expanded to include the Bauersiedlung residential area (orange). The third case describes an expansion from the core area to include the residential area of Hohenpfahl south of the Danube (red). Note that both the conventional KEXI and the AMoD service are stop-based, and as a consequence, the polygons in Figure 1 refer to the stops that are covered by each area.

The simulation results in [13] showed similar effects on demand and operation for the second and third cases, both of which yielded an approximately 60% higher demand with about twice the number of vehicle kilometers per day compared to the first case (connection of the shopping center only). The results are discussed in more details below.

In the end, the decision was made to extend the AMoD service area to the northeast to include the shopping center and the Bauersiedlung. However, compared to the original design, which is shown in purple, blue, and orange in Figure 1, the service area with the corresponding stop network was adjusted such that four stops in the Bauersiedlung area were not included. Instead, multiple stops west of the old town were connected. This area is hereafter referred to as Area 2024 and presented in more detail in Section 5. The expansion from the initial area to Area 2024 was originally planned for summer 2023 and finally implemented at the end of 2023. The reasoning for the decision included that a deployment in Hohenpfahl could not be realized since (1) there are many very steep and narrow road sections that presented challenges for AV operation at the time and (2) the extension to include the Bauersiedlung could strengthen the use cases for shopping and school traffic.

The demand predictions presented in [13] were conducted prior to the initial AMoD service roll-out. Consequently, no real demand data was available for calibration. Therefore, the authors of that study

“assume[d] that the AV service is generally perceived similarly as the conventional KEXI and we apply the same marginal utility ($\beta$) parameters retrieved from the conventional KEXI calibration […]. This assumption can be justified by the fact that the overall nature of the two transport services is essentially the same, while operational differences, such as vehicle speed, service areas, travel times and wait times, are explicitly modeled. In reality, public perception of the autonomous service might necessitate adjustments to the parameters, as the population of Kelheim, for example, might be particularly biased or open-minded toward autonomous vehicles. The later stages of the project will reveal the actual demand response to the service and enable calibration.”

([13], p. 9).

This is where the present study picks up, written approximately two years later.

The actual demand response to the initial AMoD service operating from 9 a.m. until 4 p.m. in Donaupark and old town was disappointingly low. During the 12 months of actual operation between September 2022 and December 2023, with two vehicles until July 2023 and three thereafter, 77 rides with a total of 178 passengers were registered, excluding test drives. No detailed data on operation days is available, but the the number of passengers per operated day was around 0.8. This stands in contrast to 41 passengers per day predicted for the corresponding base case in [13].

Since that discrepancy was not observed to shrink over time, reasons were identified by making test rides in the field. These revealed the following insights:

• The average vehicle speed was significantly lower than 18 km/h, which was assumed in [13] based on the manufacturer’s specifications. Reasons included frequent emergency braking due to other vehicles and pedestrians getting close to the AVs, protruding tree branches, and loss of connectivity to the control center. During some tests, the average vehicle speed was around 9 km/h with passengers on board. As the initial service area was rather small (circa 0.37 km²), the total travel time, including the wait time for pickup, often was not competitive with the time of walking (for non-handicapped persons).
• Following Römer et al. [56], who present findings from 17 other AMoD pilot projects in Germany and state that vehicle speed is crucial for the acceptance of the technology and needs to further improve in the future, vehicle speed is declared to be a variable for sensitivity analyses (see Section 5).
• Despite the fact that two AVs plus an additional AV as a backup were planned to be regularly available, only one vehicle could be supplied on some days. Reasons included unavailability of the technical operators and of the vehicles due to maintenance or technical issues (According to the current legal restrictions, technical operators still need to be on board of the AVs, which concerns SAE Level 3 [57]). For the final project stage beginning in 2024, data on the actual supply was available and was used to recalibrate the model for the present study (see Section 4.2). The fleet size was expanded prior to that stage, leading to higher vehicle availability.
• During the final project stage in 2024, a qualitative empirical yet unpublished study revealed that the public perception of AVs is dominated by the car–driver perspective (which is plausible, given the car mode share of 59%). AVs are primarily seen as traffic obstructions in this context. It was pointed out that the prevailing negative opinion of autonomous KEXIs discourages people from using the vehicles.
• Further reported burdens were difficulties in the booking process, as well as the fact that the AMoD service, in contrast to the conventional service, is not connected to the train Station in Saal an der Donau, the adjacent town to the east of Kelheim [13], which reduces the number of use cases, particularly for people commuting to other cities by train.

In contrast to assumptions that needed to be made in [13] and are cited above, the AMoD calibration for the present paper could be based on real demand data. Moreover, the present paper considers the possibility of further expanding Area 2024 such that the AMoD service includes the train station in Saal an der Donau. This further expanded service area will hereafter be referred to as Area All-City. More information can be found in Section 5.

4. Methodology

In a previous study, an agent-based transport model for the study region of Kelheim was established with the MATSim simulation framework [13,58]. The present study uses the recent version v3.1.1 of that transport model, which is available under a general public license [59]. This section iterates over necessary knowledge about MATSim’s fundamentals in order to understand the methods and findings of the present paper before explaining relevant changes in the Kelheim model compared to the previous study. More details on MATSim can be found in [58].

4.1. MATSim

In MATSim, the transport demand is represented by synthetic persons (agents) who travel through time and space according to a plan that holds information about the activities each individual aims to perform in a (daily) sequence [58]. Activities are associated with a coordinate-specific location; a corresponding type such as work, leisure, or home; and some information on the desired start and end time or duration. The trips between the activities are associated with a transport mode and can be split into several so-called legs, which represent different stages of a trip, connected by zero-duration activities marking interchanges. For example, a typical DRT trip would consist of an access walk leg to the assigned origin DRT stop, followed by an interchange activity, the main leg with DRT, another interchange activity at the destination DRT stop, and an egress walk leg to the actual destination activity. The initial demand is fed into a co-evolutionary process to interact with the transport supply. The process is illustrated by Figure 2. In the case of the Kelheim model, the initial demand is synthesized based on mobile phone data and provided by Senozon Deutschland GmbH, who describe the synthesis process in [60].

All agents execute their plan within a physical traffic simulation (mobsim), where the agents interact with the transport supply, leading to experiences of travel times, travel costs, etc., as well as external effects (congestion, greenhouse gas emissions, etc.). In terms of the transport supply, the infrastructure is represented by a unidirectional graph consisting of geo-referenced nodes connected by links, which hold information on capacity and free speed. Moreover, PT supply is represented by vehicles traveling along the network according to a corresponding schedule that specifies transit stops, lines, and departure times.

The traffic flow is typically represented by a queue model. When vehicles travel along a link, the earliest time that the vehicle can exit the link at the end is computed based on the maximum vehicle speed and the free speed of the given link. The actual exit time might be delayed as a consequence of congestion at the end of the link.

Dynamic transport services such as DRT can be either stop-based or provide door-to-door service and are further defined by a corresponding fleet, where each vehicle can have an independent operating time [38]. Recent developments enable the user to optionally define driver shifts [61].

In MATSim, a DRT customer sends a transport request at the time of arrival at the origin stop. This means that wait time is spent while traveling and not during an activity. The DRT operator is represented by a so-called optimizer [38], which is in charge of the assignment of requests to vehicles. As request bundling (ridesharing or ridepooling) is considered, each request submitted at time $t_0$ is associated with a latest pickup ($t_{P{U}_{latest}}$) and a latest dropoff ($t_{D{O}_{latest}}$) time, which are computed as

$$t_{P{U}_{latest}}=t_0+t_{wait}$$

(1)

and

$$t_{D{O}_{latest}}=t_0+\alpha ·t_{unshared}+\beta ,$$

(2)

where $t_{wait}$ is the maximum allowed wait time and $\alpha$ and $\beta$ are configurable parameters to tune the maximum travel time based on the unshared travel time [62]. Note that the computation of the travel time includes the wait time. Very recently, Lu and Kühnel [62] introduced the separation of constraints for maximum detour time and maximum wait time. These developments were presented after the experiments for the study at hand were performed. Based on specifications provided by the operator of the MoD service, $t_{wait}$ = 1200 s = $\beta$ and $\alpha$ = 1.6 are used. For each potential insertion of the request into the schedule of a vehicle, the optimizer determines the total insertion cost as detailed in Appendix A.

The optimizer is not allowed to reject requests. This reflect the fact that the KEXI service is meant to integrate with the existing PT service in Kelheim, as regulated PT in Germany has a transport obligation. However, as a consequence, in situations with high demand–supply ratios, the average wait time might be considerably higher compared to a rejecting operation scheme. The optimizer greedily assigns active vehicles to the requests by minimizing the total insertion costs. If a request cannot be assigned to any vehicle before the end of all vehicle operating times, it is rejected (despite the setting to avoid rejections).

After the execution in the physical simulation, each activity plan is associated with a score utility ($S_{plan}$) according to Equation (3) [63].

$$S_{plan}=\sum _{q=0}^{N-1}{S}_{act,q}+\sum _{q=0}^{N-1}{S}_{trav,mode\left(q\right)}$$

(3)

The score ($S_{plan}$) reflects the agents’ overall experience during plan execution, where $S_{act,q}$ reflects the performance of activity q, with time spent at activities normally rewarded with a positive score and late arrivals or departures associated with a negative score value. The $S_{trav,mode\left(q\right)}$ component reflects the performance of a given leg (q) depending on the chosen transport mode and has the form shown by Equation (4) [63],

$$S_{trav,mode\left(q\right)}=C_{mode\left(q\right)}+\sum _x{\beta }_{x,mode\left(q\right)}·x_q$$

(4)

where $C_{mode\left(q\right)}$ is the alternative-specific constant (ASC) per travel mode; $x_q$ represents the value of a resource spent on traveling, such as travel time, wait time, money, transferring from one vehicle to another, etc.; and ${\beta }_{x\left(q\right)}$ is the marginal utility induced per unit of $x_q$. The values of the $\beta$ parameters are usually negative, which means that $S_{trav,mode\left(q\right)}$ presents the disutility of traveling and leads to the minimization of travel effort. A DRT request that was rejected by the optimizer (because it was submitted too late in the day) imposes a strong negative score on the agent’s plan.

In a replanning step, a subset of agents can create a copy of their plan and mutate it given pre-defined strategies such as travel mode choice, departure time choice, or route choice. Before a new iteration of the described procedure consisting of physical simulation, scoring, and replanning is performed, agents choose one of their plans based on the assigned score, typically according to a multinominal–logit model. New plans that were just generated by mutation in the replanning step are always chosen. The maximum choice set size for plans per agent is five (the plan with the worst score is removed when mutation would lead to a sixth plan). The process of simulation, scoring, and replanning is typically repeated multiple hundreds of times (the present study uses 1000 iterations) and is called the innovation phase of the simulation. In the Kelheim case, the replanning strategy weights are changed over the course of the iterations, with a higher proportion of agents allowed for innovation at the beginning of the simulation than at the end of the innovation phase. After the end of the innovation phase, a predefined number of iterations is performed without plan mutation, i.e., the agents only choose one plan from their existing choice set, which is then executed and scored. The entire process is considered a co-evolutionary learning algorithm, where agents minimize their travel disutilities and maximize their plan execution score and a stochastic user equilibrium is approximated [58].

4.2. Recalibration of the MATSim Kelheim Scenario

Two changes in the calibration of the Kelheim model were made. First, the input values for the modal split were changed (see Appendix B for more details). Secondly, additional booking data on the conventional KEXI became available during the course of the project. Taking into account all booking data from 2022 and 2023, the conventional KEXI is recalibrated with the process described in [13] to match target values of 132 bookings and 159 passengers per day, traveling a euclidean stop-to-stop distance of 2.2 km in about 530 s. It was decided to exclude the previously considered period from July to December 2021 because the demand was significantly lower than for the rest of the time. Following the explanations in [13], all the cases including DRT are simulated with five random seeds and consider the average value of each result parameter. This helps to increase the robustness of results. In addition, it should be mentioned that the full KEXI supply and demand are still simulated, while the overall transport demand is modeled at a 25% sample size. For detailed discussions on this, please see [13].

One important contribution of the present study is the calibration of the KEXI AV(AMoD service), which became possible after the introduction of the service in the real world. The following describes the modeling of the AMoD service at the end of the KelRide project in May 2024. The result presents the base case for the predictions in Section 6. This includes all operational aspects, including the strategic positioning of idle vehicles, which is described in Section 4.3; the service area and times, as described in Section 5; and the fleet size, and vehicle speed, as described below.

The base-case calibration uses real booking and operation data from the AMoD service available from the first week of 2024 onward. One of many challenges in using the data was to identify, then remove test rides carried out by technical operators and other project personnel. In addition to the number of passengers per day, the average vehicle availability could also be determined from the data. Based on these analyses, it was determined that an average of 2.3 vehicles was available at any given time. As the physical simulation can only represent discrete vehicles, the size of the fleet for the average working day was set to two AVs. Furthermore, the average number of passengers per day is observed to be 4.4. in the base case, and AVs are limited to 12 km/h (cf. Section 3).

The average number of bookings per operated day is observed to be 2.5, with an average group size of 1.7 passengers per booking. In the calibration process, the ASC is tuned in order to match this number of daily bookings as closely as possible and achieve a value of 2.6. After each simulation, the result is multiplied by the observed group size to obtain the simulated number of passengers per day. This implies the assumption that investigated policies do not influence the average group size per booking.

Unfortunately, no detailed valid data on travel distances and in-vehicle times was available for the AMoD service. As a consequence, the $\beta$ parameters for perception of travel time and distance are set equivalent to those of PT.

4.3. Rebalancing

During the KelRide project, it was decided to strategically position idle AVs within the service area. This process is often referred to as rebalancing. Service operator Via described their algorithm only vaguely, stating that idle vehicles are evenly distributed throughout the service area. In cooperation with the responsible licensing authority, six waiting points were defined in the original service area (Area 2024), exceeding the maximum number of physical vehicles that could theoretically be in operation simultaneously, which is five. The criteria for the selection of locations included the necessary space for parking and turning, as well as ensuring an undisturbed flow of traffic. These original waiting points were transferred to the model (see Figure 3).

In order to mimic the rebalancing logic, a simple heuristic algorithm is implemented in the simulation: After a vehicle becomes idle, it is sent to the spatially closest waiting point with free capacity. And by limiting the number of waiting points (and their capacity), it can be ensured that the waiting locations are spread out.

Table 1. Different fleet sizes and associated waiting points. See Figure 3 for the locations of the waiting points. For the ‘≥10’ case for Area 2024, waiting points 1 and 9 are used twice (see text).

Fleet Size	Waiting Points Area 2024	Waiting Points Area All-City
2	2, 7	5, 8
5	2, 7, 1, 3, 8	5, 8, 1, 4, 6
≥8	2, 7, 1, 3, 8, 4, 9, 10	5, 8, 1, 4, 6, 2, 10, 11
≥10	2, 7, 1, 3, 8, 4, 9, 10, 1, 9	5, 8, 1, 4, 6, 2, 10, 11, 3, 7

provides details. For example, when simulating the base case with two vehicles, waiting point numbers 2 and 7 are provided. These specific waiting points are selected because waiting point 7 represents the real-world vehicle depot and number 2 covers the opposite side of Area 2024 and is surrounded by a high school and sport facilities, where project partners anticipated demand. When increasing the fleet, the set of real-world waiting points is prioritized. Section 6.3 contains a sensitivity study of the waiting point selection.

For fleet sizes of ten and above in cases with the original service area (Area 2024), the capacity for waiting points 1 and 9 is set twice as high as for the others because this is where demand hotspots in the real data were observed. This means that when ten vehicles are idle, these stations will host two vehicles, whereas the other stations will host one vehicle each.

Below, a larger service area (‘Area All-City’) will be investigated. For this, three additional waiting points are defined and numbered 5, 6, and 11. At the same time, the capacity of waiting point 1 is reset to the same as all other waiting points, and waiting point 9 is removed completely. This keeps the maximum number of waiting points at ten while covering the larger area.

5. Case Study Motivation and Parameter Variation

It was expected that the first expansion of the AV KEXI (AMoD) service area at the beginning of 2024 in combination with an expansion of the fleet would have a positive impact on AMoD demand [13]. However, demand for AMoD in Kelheim remained low in the first few months after the expansions, although it was also possible to speed up the vehicles from an effective 9 km/h to an effective 12 km/h (while leaving the maximum speed at 18 km/h). With a view to the future, the question arose as to what extent on-demand services in small and medium-sized cities such as Kelheim can reduce dependence on subsidies in the future and become self-sustaining while also providing added value for society. Against this background, this study presents a sensitivity study for the AMoD service. It analyzes the effects on demand of further expansions in fleet size, service area and vehicle speed. It also analyzes the effects of extending the operating times, which, in reality, run from 9 a.m. to 4 p.m. and therefore outside the peak hours. The results of the study—in particular, the correlations between the analyzed variables and demand—should be transferable to other small to medium-sized cities with partly separate network areas.

The status quo as of April 2024, as described in more detail in Section 3, forms the base case for the analysis of the AMoD service expansions and adjustments in terms of service area, operating times, vehicle speed, and fleet size. More specifically, this describes two AVs serving all stops marked as black dots in Figure 3 with an average speed of 12 km/h between 9 am and 4 pm. The simulation is calibrated to 2.6 bookings per day, equivalent to 4.4 passengers per day.

Simulations are run for the following parameter variations including all cross-combinations:

• AMoD Service Area: An extension of the 2024 AV KEXI service area, which is illustrated by the black dots in Figure 3 and hereafter referred to as Area 2024, to the entire existing MoD stop network from the conventional KEXI. The latter case covers all stops shown in Figure 3 and is referred to as Area All-City.
• Fleet Size: Increases in the fleet size from the 2 AVs in the base case to 5, 8, 10, 20, 50, and 100 vehicles.
• Operating Times: An increase in the operating times from 9 am to 4 pm in the base case to a full day’s operation (referred to as ‘all-day’).
• AV Speed: Increases in the effective speed from 12 km/h in the base case to 18 km/h and 30 km/h.

For each simulation setup, five simulations with different random seeds are run before the average of each result parameter is obtained. Analysis regards the number of passengers per day, the average wait time per booking, and the average ride distance, which includes detours due to pooling.

6. Results

In this section, we present an analysis of the relationship between service configuration and demand, followed by the implications of the service configuration for fleet efficiency.

6.1. The Relationship Between Service Configuration and Demand

Figure 4 visualizes the obtained number of AMoD passengers (a), average wait time (b), and average customer ride distance (c) for each simulated AMoD configuration. Each subfigure is divided into four facets—one per cross-combination of service area and operating times. The AV speed is indicated by the line color, and the x-axis indicates the simulated fleet size. Note that each data point shows the average value from five simulation runs on the y-axis.

First, the impact of the fleet size (x-axis in Figure 4) is analyzed. In the simulation, the number of passengers for the existing service area with the current AV speed of 12 km/h (red line in the bottom left) can be increased by approximately 7.5-fold if the full AV fleet of five vehicles is used instead of just two vehicles. A deployment of eight vehicles achieves an increase factor of 14 times more bookings per day. A saturation of demand and an associated stabilization of the average wait times is observed to start at a fleet size of 20 AVs and complete at 50 AVs for 12 km/h and 18 km/h at 100 AVs and for 30 km/h (To check this, further simulation experiments were carried out with the Area All-City and fleet sizes of more than 100 vehicles, which led to the same level of demand, though not shown in Figure 4).

In the simulation, an increase in AV speed (compare the facets in each subfigure of Figure 4) also results in a significant increase in realized demand, especially when considering the current status quo. Specifically, for the smaller Area 2024 and part-day operation, the number of passengers increases 5.5 times if the two AVs travel at an average speed of 18 km/h instead of 12 km/h and about 15 times if the average speed is 30 km/h. With a fleet size of 50 vehicles, the increase factors are approximately 2 (for 18 km/h) and 3 (for 30 km/h).

The expansion of the service area increases the number of bookings (see the change from red to turquoise for the same line shape within a graph). However, this requires a sufficiently large fleet size. At the existing AV speed (12 km/h; red lines), the service area expansion is only worthwhile with a fleet size of around ten AVs or more, as otherwise, the wait time for customers increases too much (see Figure 4b). At higher speeds, a higher demand is already achieved in the simulation with eight AVs in the Area All-City compared to the existing Area 2024. The maximum relative increase potential through area expansion is 30 km/h with full-day operation and a fleet size of 100 AVs and represents a factor of around 2.8. For 20 AVs with a speed of 12 km/h and part-day operation, the factor is around 1.4.

Figure 4c allows for the elaboration of the interplay between service area and AV speed by showing that AMoD customers travel longer distances with increasing speed and in a larger service area. Note that ride distance refers to the distance covered on board of the AV, including detours due to pooling. The larger the fleet, the shorter the average wait time so that journeys over shorter distances are increasingly worthwhile. This is partly due to the fact that the maximum travel time constraint includes the wait time. However, this effect is relatively small compared to the previously mentioned effects. It is also clear that there is no major increase in ride distance in the smaller existing Area 2024, as this is limited by the size of the area. The significant increase in the average travel distance for higher speeds in the cases of the larger service area means that the agents in the simulation are prepared to accept longer wait times (cf. Figure 4b).

For the smaller Area 2024, the results generally show a negative correlation between the average number of passengers per day and the average wait time per booking, i.e., as the wait times decrease, more people use the service. The AV speed does not strongly affect the level of wait times that can be achieved with 20 or more vehicles in this case. However, it remains to be explained why the general level of wait times increases with vehicle speed when considering the larger Area All-City. This can be observed in Figure 4b by comparing the lines in the facets on the right-hand side. The reason is that with increasing vehicle speed, trips starting from farther away from AV waiting points become increasingly worthwhile, as more remote parts of the service area are better connected due to shorter wait times. This is illustrated by Figure 5, which shows the locations of origin activities for AMoD trips in all five simulations for both 12 km/h and 30 km/h and with ten vehicles operating part-day in the Area All-City. As these remote areas—for example, to the northwest edge or the area around waiting point 5—become demanded more frequently, the average wait time increases.

Finally, it is observed that extending operating times can significantly increase demand (compare the facets from the bottom up in Figure 4). The faster the vehicles travel and the more the vehicles are used, the greater the effect in terms of the absolute increase. In relative terms, however, the increase in the number of passengers between part-day and full-day operation becomes less strong with higher speeds and fleet sizes. Accordingly, the effect is highest in relative terms with the current configuration of the status quo. Overall, the simulation shows a potential increase in the range of a doubling to a quadrupling of demand.

The findings regarding the relationship between service configuration and demand are summarized as follows:

• With increasing fleet size, the number of passengers initially increases superlinearly but eventually saturates.
• Passenger numbers increase superlinearly with vehicle speed—more strongly at small fleet sizes and less pronounced but still superlinear at larger fleet sizes.
• The number of passengers grows approximately linearly with the service area, provided that fleet size is sufficiently large.
• Extending operating times from 9 a.m.–4 p.m. to full-day operation increases passenger numbers by a factor of two to four.

6.2. The Relationship Between Service Configuration and Fleet Efficiency

In the following, the operator’s perspective in terms of the efficiency of the service in relation to the configuration is analyzed. The analysis uses the metrics of the number of passengers transported per vehicle hour and per vehicle kilometer for the efficiency analysis, as these relate to the return on investment for variable operating costs. It is to be noted that for AVs, the marginal operating costs per time may be significantly lower than for human-driven vehicles if not zero.

As mentioned earlier, superlinear growth of demand in relation to fleet size is observed for eight vehicles or fewer when regarding 12 km/h and 18 km/h. This effect is reversed for larger fleet sizes, as Figure 6a shows using the quotient of passengers and the total operating time of all vehicles. At a speed of 30 km/h, the quotient already decreases with the step from two vehicles to five vehicles.

Figure 6 further indicates that increasing the fleet size up to eight vehicles is beneficial when operating in Area 2024 both in terms of demand per vehicle hour and demand per mile. However, increasing the fleet size further decreases the demand per vehicle hour, while the demand per vehicle km rises up to a saturation point at about 20 AVs.

Increasing vehicle speed clearly increases the number of passengers that can be transported per vehicle hour. Regarding the demand per vehicle kilometer, one can observe a significant impact of the vehicle speed for small fleet sizes. However, the level of saturation at fleet sizes of 20 AVs or more is not strongly affected by the AV speed.

Expanding the service area is beneficial in terms of time efficiency but not in terms of the passengers per vehicle kilometer and, thus, seems not to increase profitability for the AMoD service segment.

Finally, an extension of the operating times is not beneficial for the operator regarding either metric. Only when fewer than ten vehicles are operated at 30 km/h can the number of passengers per vehicle kilometer be kept at the same level.

6.3. The Relationship Between Waiting-Point Location and Wait Time and Demand

Figure 7 shows the trip start locations of AMoD trips colored by wait time for the 12 km/h cases with five and ten AVs, including the active waiting-point locations of the vehicles. It is clearly demonstrated that the location of waiting points is decisive for the wait time of customers: trips that start in a close surrounding of a waiting point tend to have lower wait times than trips starting farther away. The fact that the number of waiting points increases with the fleet size (cf. Section 4.3) leads to more areas being covered by light-colored points, meaning that more areas receive good service quality, which results in higher demand and a lower average wait time (cf. Figure 4).

Following this line of thought, it remains unclear which waiting points to operate at low fleet sizes. Multiple possible waiting-point combinations can theoretically serve the purpose of distributing vehicles evenly, which is the target strategy of the operator (cf. Section 4.3). Figure 7a clarifies that, especially with low fleet sizes (and vehicle speeds), the waiting-point locations will be decisive for whether demand arises at the border of the service areas or not and for wait times. In order to investigate the impact of spatial waiting-point distribution on the wait time and the demand in the traffic simulation, a corresponding sensitivity analysis is conducted.

As is explained in more detail in Section 4.3, the number of AV waiting points is equal to the fleet size for all simulation cases with ten or fewer AVs. The overall number of considered waiting points is ten. For the previously analyzed simulations, waiting-point subsets were predefined such that vehicles are spread throughout the service area and demand hotspots known from real data are covered.

In order to test the effect of the waiting-point subset selection on the average wait time and demand, the selection is now varied. Specifically, the simulation is run with nine additional randomized waiting-point subsets for fleet sizes of five and eight with part-day operation at both 12 km/h and 30 km/h AV speeds in Area All-City. As a maximum of ten waiting points is considered in the simulation, no other selections for larger fleet sizes are run. Together with the previous results, results for a total of ten different waiting-point subsets are obtained for all the given fleet sizes. Remember that for each simulation setup (or AMoD configuration), the simulation is run with five different random seeds, and the results are averaged.

Figure 8b demonstrates that the average wait time varies considerably at low fleet sizes, depending on the selection of waiting points. The variance decreases as the fleet size and waiting-point subset size increase from five to eight. For five AVs operating at 12 km/h, the variance in observed average wait times is 1710 s², and the maximum is 1.43 times higher than the minimum. For eight AVs operating at 12 km/h, the variance in observed average wait times is 441 s², and the maximum is 1.27 times higher than the minimum. The variance of the average wait time also significantly decreases with increasing vehicle speed: For eight AVs operating at 30 km/h, the variance in observed average wait times is 43 s², and the maximum is 1.04 times higher than the minimum.

Analyzing the observed average number of passengers per day shown in Figure 8a, it becomes clear that the combination of small fleet sizes and low vehicle speeds significantly increases the variance of the simulation results. While the ratio of the maximum to minimum number of average passengers per dayis 1.57 for five AVs and 1.2 for eight AVs at 12 km/h, it amounts to 1.08 and 1.07, respectively, at a vehicle speed of 30 km/h. Additional experiments for two AVs, which are not included here, confirm this trend. This phenomenon is related to fleet occupancy and led to the exclusion of the results for two AVs in the large Area All-City, as discussed in more detail in Appendix C.

The lines in Figure 8 connect the simulation results analyzed in the previous subsections. Their analysis underscores the need for sensitivity analyses such as the present one, as it becomes clear that the single result taken for a fleet size of five AVs showed results at the edges of the bandwidth, with atypically low wait times and a high demand for 30 km/h.

To summarize the results of the sensitivity analysis, small fleet sizes and low vehicle speeds increase the variance and, thus, decrease the accuracy or robustness of the simulation results with respect to the obtained average waiting time and the number of passengers.

7. Discussion and Outlook

In this section, the possible measures for extending operating time and service area and increasing fleet size and vehicle speed for the specific case of AV KEXI in Kelheim are interpreted. The limitations of the study are then discussed and related to the scientific literature and to possible improvements in the future.

7.1. Discussion and Interpretation of the Results

It can generally be concluded that, given the current technological status quo of the AMoD system, extending operating times to full-day operation can be considered a relatively inexpensive and easy option to increase demand, since it can be performed without additional hardware. An increase in the size of the fleet leads to more demand due to better service quality but (in Kelheim) only up to a saturation point of about 20 vehicles.

The results of this study further indicate that the AMoD service area should not be expanded without increases in vehicle speed and the effective fleet size. Vehicle speed, in general, is crucial for the level of demand and the spatial coverage, which is also influenced by the number of vehicles and waiting points. In order to provide a meaningful mobility option in the long term, the AV speed needs to be increased through technological advancements. This is emphasized by findings from Römer et al. [56], who collected qualitative key findings from 17 pilot projects that integrated AVs into PT in Germany. During the KelRide project, AV speed could be increased due to vehicle software and sensor technology. Technical operators reported that further speed improvements might be achieved by ensuring that roadways are consistently cleared of obstacles (e.g., tree branches). More generally, speed enhancements could also result from regulatory and infrastructural measures, for example, by allowing AVs to operate in dedicated lanes or through vehicle-to-infrastructure communication with traffic signals. However, it remains unclear whether the research and development costs to increase vehicle speed are worth the revenue margin for the operator. To support this assessment, the results were shared with project partners, who conducted a comprehensive total cost-of-ownership analysis for AMoD services [65]. From a transport planning perspective, the increase in the total demand with higher speeds indicates a great benefit for the population. Therefore, the further development of the technology could be of social interest, and public funding could be considered as an option.

7.2. Limitations

The main behavioral parameters are the ASC and the marginal direct disutility of in-vehicle travel time. The marginal disutility of in-vehicle travel time is used to calibrate the distance distribution of a given mode and the ASC to calibrate the total modal share.

One limitation of this study is that the actual AMoD service area in Kelheim was too small to obtain a meaningful distance distribution. As a consequence, the same marginal disutility of in-vehicle travel time as for PT is used. The more these parameters differ, the more the extrapolation to a larger AMoD service will suffer. Steck et al. [66] support the approach taken by obtaining nearly identical marginal utilities of in-vehicle travel time for shared AV and PT based on a mixed logit model with a Box–Cox transformation for time and cost, estimated from combined revealed and stated preference data collected from 485 respondents in Germany. Furthermore, the validity of the presented model is supported by the rich data basis available for all other transport modes, including booking data from the human-driven MoD service, person activity plans derived from mobile phone data, and nationwide travel surveys, which provide robust insights into overall travel behavior and mode choice.

As a result of calibration against real-world data, the ASC of the electric AMoD is less attractive than the ASC of the human-driven MoD service. Thus, if the services were configured exactly the same, i.e., vehicles were traveling at the same speed, the human-driven MoD would yield a higher number of passengers.

Instead of complex algorithms, the present study uses a simple heuristic to mimic the rebalancing behavior described by the fleet operator, which is to maintain a balanced spatial distribution of vehicles. Schlenther et al. [4] showed that maintaining equal vehicle density throughout a service area can lead to equal wait times and, thus, increase PT accessibility and the overall MoD demand. In contrast to the present study, the metropolitan area of Berlin and a fleet size of 2000 vehicles is regarded.

It is to be noted that the Kelheim DRT stop network crosses two river branches and spans the border between the towns of Kelheim and Saal an der Donau. The area around the border of the towns is mainly characterized by industrial use and a freeway. One of the most popular stops is the only one in Saal an der Donau. These conditions can have a considerable influence on the outcomes of the study.

It should also be noted that the overall transport demand density, which is at 25% for the present study, can limit the DRT demand level when looking at high fleet sizes. Therefore, the maximum potential for the AMoD demand in Kelheim might be underestimated here.

Another limitation of the present study is that no fleet size optimization was conducted. The demand observed at fleet sizes of 20 and more vehicles could possibly be served with fewer vehicles at similar service quality levels. The following process, which is similar to the approach described by Winter et al. [67], could be used in the future to determine the minimum fleet size to serve the observed demand at the observed average wait time: (1) retrieve the wait time and the demand for a given configuration, (2) run the simulation again without mode choice and with two vehicles, and (3) increment the fleet size until the wait time from simulation with mode choice (i.e., (1)) is met. Lu et al. [68] conducted such experiments with static demands, i.e., without step (1), and found that operating small DRT services might be more profitable in Kelheim than in Manhattan, New York. Winter et al. [9] conducted fleet sizing experiments for an autonomous DRT service in Arnhem, Netherlands, and reported similar findings, where the level of service quality significantly improves with increases in the fleet size from a minimum to an optimum. Specifically, Winter et al. [9] found that the passenger’s generalized travel costs account for around two-thirds of the system costs.

7.3. Transferability

Taking the above limitations into account, it can be concluded that the (absolute) level of demand for a given MoD configuration is subject to local characteristics such as travel behavior, general demand density, and network topology. For example, the Kelheim population is relatively car-oriented and skeptically biased towards AV, and the town’s street network is crossed by two river branches, resulting in lower demand than anticipated at the beginning of the KelRide project. However, the findings of the sensitivity analysis in this paper—particularly the need to provide citizens with meaningful use cases by ensuring a sufficient density of AVs operating at speeds above 12 km/h in areas that connect multiple points of interest—can be transferred to other rural and suburban regions.

7.4. Outlook

The present study revealed limitations of the MATSim model specifications when (very) small, finite fleets are simulated, along with mode choice, i.e., when the fleet is much smaller than the demand potential. Future investigations could look into the inter-relation of the rejection dynamic and mode choice, building on Appendix C.

Furthermore, the present study uses a transport model that depicts an average day during the week and, thus, does not capture seasonal effects. Seasonal effects on MoD demand, including weather characteristics, were investigated in a separate study for the human-driven KEXI and found to be fairly low [69]. Moreover, the present study aims at understanding the sensitivity of AMoD demand to configuration parameters rather than predicting specific days. While it would be relatively straightforward to feed the simulation with accurate booking and supply data from a specific day, currently available mode choice calibration methods require relatively high effort, so reproducing several specific days from different seasons with dynamic demand (i.e., mode choice enabled) was beyond the scope of this study. This provides a lever for future work aimed at digital twin-like transportation modeling.

Finally, the simulation could be improved by modeling user-specific taste preferences, which were observed in qualitative surveys in the KelRide project.

8. Conclusions

This study presents an ex post validation of earlier simulation forecasts against real booking data from Europe’s largest MoD service deploying AVs on public roads in Kelheim, Germany. Building on newly available booking data, as well as refined service specifications from the associated research project, the transport model is re-calibrated to reflect the status quo as of April 2024.

Subsequently, a detailed analysis of the simulated sensitivity of demand and average wait times to potential expansions of the AMoD system is conducted, focusing on service area, fleet size, operating hours, and vehicle speed. Consistent with empirical findings from qualitative surveys, the results suggest that increasing vehicle speed through technological advancement is essential for ensuring the long-term viability of autonomous mobility services. In the specific case of Kelheim, the presented results indicate that the AMoD service area should not be expanded without increases in vehicle speed and the effective fleet size.

In addition, the variance of simulation results is analyzed in relation to the locations where vehicles idle. The results show that small fleet sizes and low vehicle speeds increase the variability in average wait time (i.e., service quality) and the demand, highlighting the vulnerability of simulated system performance under constrained conditions.

Overall, the ex post validation and sensitivity analyses underscore the importance of using highly accurate data and detailed algorithmic descriptions to produce reliable simulation forecasts. Agent-based traffic simulations can closely replicate real-world complexity and, thus, offer a valuable decision-making tool. While the results are derived from the case of Kelheim, the methodological approach and key insights are transferable to similar contexts. Therefore, the presented findings are of relevance for both scientific research and industrial stakeholders.