Modeling of an Urban Ropeway Integrated into a Crowded Transit System

Abstract

In many moderately sized European cities, the public transport systems based on trams and buses are operating at their capacity limits. Ropeways have proved to be a suitable transit extension in several Latin American cities. Few travel demand models attempt to forecast the impact of urban ropeways. So far, all of these models do not consider the specific properties of a ropeway. This paper seeks to estimate a mode choice model that includes a ropeway as a separate transport system. Relative to bus operation in European cities, ropeways promise improved timetable keeping, with fewer delays at the start because of high service rates, and they also offer improved passenger comfort with higher capacities. These benefits must be reflected in the travel demand model by mode-specific parameter settings that are estimated based on a survey. A stated choice experiment was conducted, in which respondents compared realistic trip situations using a ropeway with traditional urban transport modes, with aspects including access and egress time, waiting time, travel time, travel costs, reliability, and crowding. The situations of choice were selected from observed trip data to be as realistic as possible. Using a mixed logit (ML) model, the parameter estimation indicates that crowding and reliability as well as the personal attitude of potential users have a statistically significant influence on the choice behavior of people in Graz, a moderately sized city in Austria.

Keywords

planning and analysis behavior analysis mode choices preference survey data analysis ropeway

Numerous moderately sized European cities of 250,000 to 500,000 inhabitants face the problem that their existing transit networks based on buses and trams are already reaching their capacity limits, and further population growth will make the situation worse. Increasing passenger numbers lead to more crowded vehicles, and thus decreasing reliability, with delays as a result of bunching effects. This also reduces the comfort level and leads to passenger dissatisfaction and, in the worst case, to a modal shift and a higher usage of individual motorized transport. Dense historical city centers with narrow streets and limited space often do not allow a capacity extension to the currently used public transport level. The demand for a subway system, however, is too low for a satisfactory cost–benefit ratio. An urban ropeway using an above ground level can be a cost-effective and efficient alternative for these cities.

At the present time, no European city has experience in setting up a ropeway system within its existing transit network. The projects accomplished to date were built for special events in several cities (London, Koblenz, Lisbon) and have not become integrated parts of the cities’ transit systems. The term ropeway is used in this paper for any form of public transport that is operated on cables above ground, such as gondola lifts, aerial tramways, and metrocables.

The ropeway industry proposes ropeways for urban transportation, using cabins with a capacity of up to 35 persons running at service intervals of between 30 to 60 s, with an operating speed of up to 8 m/s (tricable detachable gondolas [TDGs]) ( 1 ). As a result of the high frequency, passengers can arrive at any time at a stop without experiencing long waiting times, except in cases where large groups arrive simultaneously. The service intervals lead to low crowding levels and high transport capacities that can compete with a tramway operating with short service intervals (<3 min). In addition, a ropeway is not affected by traffic congestion, and passengers have a different riding experience compared with known bus and tram services, including a bird’s-eye view.

A literature review reveals a few modeling approaches for ropeways, but no approach consider these mode-specific properties. We therefore estimate a mode choice model in this work that takes into account crowding, reliability, and the personal attitude of potential passengers in a stated choice experiment. This will have the effect of improving the scientific database for modeling urban ropeways within travel demand models.

This paper is structured as follows. First, we provide a review of scientific literature of urban ropeways and stated choice experiments with a special focus on crowding and reliability. Next, we present a case study that includes a stated choice experiment and a model estimation for an urban ropeway in Graz, Austria, a city with approximately 300,000 residents and an annual population growth of 2%. Finally, we conclude with the results of the estimated mixed logit (ML) model and discuss our findings.

Literature Review

Urban Ropeways

In the past decade, the introduction of urban ropeways in Latin American cities and the possible launching of urban ropeways in several European cities has led to a rise in the available literature for this research field. This literature ranges from general analyses of the system and system comparisons with traditional public transport modes, extending to planning, construction, and operation, and also including case and feasibility studies. This literature review summarizes the most important work for this research. A detailed literature overview to urban ropeways can be found in Tiessler et al. ( 2 ).

Initially, the description of the system is fundamental for the understanding of this uncommon urban transport mode. Alshalalfah et al. ( 3 ) and Dale et al. ( 1 ) give a good overview of the different ropeway systems and technologies, system components, and implemented projects. The two main types are reversible ropeways that travel back and forth between two stations, and circulating ropeways.

Circulating ropeways are the appropriate system for a powerful and reliable service in an urban area. The advantages of these systems compared with reversible ropeways are the continuous service, usually resulting in no noticeable waiting times at the station, higher capacities, and intermediate stops, as well as shorter distances between stops. The most commonly used systems are monocable detachable gondolas (MDGs) and TDGs. An MDG uses one cable that fulfills the task of suspension and towing. A TDG uses two support cables and one hauling cable. The maximum transport capacities per cabin reach 10 passengers for an MDG and 35 passengers for a TDG. Based on these cabin capacities, 4,000 (MDG) to 6,000 (TDG) passengers per direction per hour (ppdph) are the maximum capacities for these two systems ( 3 ). Urban ropeways that have been implemented usually reach capacities of between 2,000 and 4,000 ppdph, depending on cabin size and frequency. Table 1 presents a comparison of several system indicators between traditional urban public transport modes and urban ropeway systems currently operated worldwide (as of July 2022). The indicators for public transport are calculations based on vehicle capacities and service rate of the Association of German Transport Companies (VDV) ( 4 ).

Table 1.

System Indicators of European Transit Systems and Implemented Urban Ropeways

Transport system	Station distance (m)	Average travel speed (km/h)	Usual service interval (s)	Vehicle capacity (passengers)	Average capacity per hour (passengers)	Capacity in peak hour (passengers)
Bus	250–500	15–20	600–900	80–125	480–750	1,000–1,500
Tram	300–800	15–20	360–600	150–210	1,500–2,100	3,000–4,200
Ropeway (MDG)	350–4,800	12–21	12–18	4–10	1,200–2,400	1,200–4,200
Ropeway (TDG)	900–4,500	20–30	30–60	up to 35	2,000–4,200	2,000–4,200

Note: MDG = monocable detachable gondola; TDG = tricable detachable gondola.

Apart from the literature that analyses the system characteristics, a large body of work is also available for case and feasibility studies. The greatest number of operational urban ropeway systems are located in Latin America. The metrocable system of Medellín, Columbia, in particular is investigated in great detail and from many different perspectives, such as the planning and decision-making process ( 5 ), the sustainability impact ( 6 ), or the changed travel behavior of customers ( 7 ). Jurado and Mesa-Arango investigated the impact of the perception of waiting times and user behavior of ropeway passengers ( 8 ). Because of the low quality of the available bus services with no other transit alternatives, the demand exceeds peak hour capacity on ropeway line K.

Alshalalfah et al. published a scientific feasibility study on an urban ropeway in Makkah, Saudi Arabia ( 9 ). The study deals with alternative route layout, technologies and costs in three corridors, and also includes a simplified travel demand forecast. Other, non-scientific, feasibility studies were developed for the German cities of Bonn ( 10 ), Trier ( 11 ), and Cologne ( 12 ), and also for Edmonton, Canada ( 13 ). Most of these studies provided a travel demand forecast in a simplified manner similar to Alshalalfah et al. ( 9 )

Hofer et al. introduced a five-step methodology for the demand estimation in a macroscopic transport demand model for an urban ropeway in Graz, Austria ( 14 ). The methodology included stated choice interviews with people who would be affected by the new transport system (commuters, residents, and tourists). Based on the interviews, the authors developed an independent utility function for a ropeway founded on the choice probability depending on travel time differences between traditional means of public transport (bus and tram) and the planned ropeway. A Weibull function was used for the description of the choice probability. The parameters for the utility function of the mode choice model were not estimated.

Tiessler et al. investigated the potential travel demand for a ropeway line that may supplement the transit system of Munich, Germany ( 15 ). They applied an aggregated travel demand model and conducted an online survey with a stated choice part concerning the route choice in the planning area. The different route scenarios depended on transport modes and travel times. The survey showed that passengers prefer connections, including a ropeway instead of a bus, even if the bus is faster. Similar to Hofer et al. ( 14 ), Tiessler et al. ( 15 ) used the choice probability between the options to generate input data for the travel demand model of Munich.

Crowding in Stated Choice Experiments

Crowding in this context means that there is a high density of passengers in a vehicle or at a station. Tirachini et al. point out that passengers react differently to crowding, and the reasons behind the dislike they have for this phenomenon go far beyond the simple physical discomfort caused by the high density of persons in a public transport service ( 16 ). Passengers list a set of sensorial, psychological, and social issues that includes, for example, perceptions of risk of personal safety and security, increased anxiety, stress and feelings of exhaustion, and invasion of privacy. Moreover, Schmöcker et al. point out that crowding also affects reliability because of longer boarding and alighting times at served stops, as well as the route choice of passengers because they prefer to have a seat available ( 17 ).

A general valid definition of transportation crowding does not exist because of the individual perception of passengers. Wardman and Whelan reviewed rail-crowding studies in the United Kingdom and found that the crowding effect is activated from occupancy rates between 60% and 90% ( 18 ). The German Highway Capacity Manual (HBS) defines six levels of quality for public transport systems based on the saturation (ratio of seats and stands over passenger volume) ( 19 ). The six levels A to F (where level A describes enough space in the vehicle and level F describes overcrowded conditions) depend on trip length, with higher saturations accepted for short trips. According to VDV, the saturation should not exceed 65% during peak hours and 80% during the peak 20 min in the peak hour; otherwise, the attractiveness of the service for the passengers decreases ( 4 ). The vehicle capacity is based on the number of seats plus the floor space for standing passengers, with four passengers per m² (= 0.37 passengers/ft²).

The literature delivers different approaches for integrating crowding in stated choice experiments. These approaches range from written descriptions (e.g., Lu et al. [ 20 ] and Douglas and Karpouzis [ 21 ]) to a graphic representation of available seats). Rietveld et al. display crowding in their study about public transport in the Netherlands as a percentage of available seats relative to seating capacity ( 22 ). Fröhlich et al. apply four crowding levels, which are displayed by sketched illustrations of passengers in a train or a bus for each crowding level in their SP survey on traffic behavior in Switzerland ( 23 ). Hensher et al. investigated the influence of crowding on the mode choice of commuters in a planning study for a metro rail system in Sydney ( 24 ). Crowding was represented in this study by the availability of seats versus standing room in existing and new public transport modes. The authors used a written description and schematic diagrams of the seating configuration for each mode, showing the seated and standing people. A total of 16 crowding levels were used for bus, train, and metro modes.

Reliability and Delays in Stated Choice Experiments

The term reliability is used to represent the punctuality of a transport mode. Passengers want to predict their arrival time based on the timetable. König and Axhausen found that, apart from safety, reliability is one of the most important factors of influence for the decision-making behavior of transport users ( 25 ). However, there are different metrics to define reliability. In long-distance railway travel, all trips not exceeding a delay of 1 min (Japan), 3 min (Netherlands), 5 min (Germany) and 10 min (United Kingdom) are considered to be on time without any penalty on reliability ( 26 , 27 ). For short-distance transit rides, no such national thresholds exist. Delays may occur during a transit ride or while changing transit lines. Passengers are usually more annoyed if the delay is the result of longer waiting times at stations. Thus, travel time and waiting time are weighted differently in the mode choice model, but reliability is added as an additional property.

The simplest method to quantify reliability is to use constants without a time value, defining only a delay or no delay, as was done by Small in his research ( 28 ). Gorham et al. describe reliability in the form of delayed departures in minutes ( 29 ). Vrtic and Fröhlich define the reliability by a percentage probability for a delay of 10 min minimum ( 30 ). To achieve a better understanding of the delays, they explained the probability of them by the number of delays out of 20 trips. Lu et al. only used the latter option in their study ( 20 ). Small et al. had a higher complexity by using graphical distribution for delays ( 31 ).

The Contribution of the Article

As shown in the literature review on ropeways, only a few publications include travel demand models. In particular, the mode-specific properties have not been investigated so far, and mode choice was based purely on travel time. This study considers additional mode-specific properties and provides additional data that are relevant for modeling ropeways as a potential transport mode in urban transit systems. If buses and trams are crowded above a specific level, potential passengers, who have opportunities for choice, will decide against using transit. With the continuous availability of ropeways, crowding levels in cabins and the reliability expressed by punctuality are experienced differently than they are in buses and trams. Apart from these quantifiable properties, the attitude of individuals toward ropeways will influence their decision to use it. Because many Austrians have previously used ropeways in the Alps for touristic trips, many people have an opinion about this travel mode. The attitude on ropeways is also one factor that was considered in this study.

Methodology and Case Study

The methodology used for our case study can be categorized in five steps, as shown in Figure 1. First, mobility surveys in January 2022, performed as revealed preference surveys, delivered basic data of the existing mobility behavior of residents in a planned ropeway corridor as well as in the city of Graz, Austria. The reported trips were then analyzed, with a special focus on crowding and reliability of the used or possible public transport lines, as well as the reliability of private transport. The results of this analysis and the determined parameters of the planned TDG delivered input data for the choice set creation of the stated choice interviews (step 4) in March 2022 with 129 respondents. The final step includes a model estimation of a mode choice model and an analysis of results.

Figure 1.

Methodological approach of the study.PT = public transport.

The ML Model

The following is a brief description of the well-known ML model for readers who are unfamiliar with the notation. Logit models were first used in transport modeling in the 1960s, when they were applied for parameter estimations in stated choice experiments. Starting with a binary logit model, research progressed to multinomial logit and nested logit models. With the development of simulation methods, it was possible to handle more complex models such as ML models.

The two main advantages of ML models are, first, that they capture preference heterogeneity through the randomization of coefficients among the respondents with a pre-selected distribution. Second, we can allow a flexible variance-covariance of random term and solve the restrictive assumption (IIA). There are two approaches for ML models. The random-coefficients approach, which is used in this work, and the error components approach ( 32 ).

The utility of person n for an alternative j can be described with Equation 1 ( 33 ):

U_{nj} = {β^{'}}_{n} x_{nj} + ε_{nj}

(1)

where $x_{nj}$ are observed variables relating to alternative and decision maker, $β_{n}$ is the vector of coefficients (marginal costs) of these variables that must be estimated for person $n$ , and $ε_{nj}$ is a random term that must be independent and identically distributed. The coefficients vary across decision makers in the population with density $f (β)$ . In comparison, $β$ is fixed in a standard logit model. The probability conditional on $β_{n}$ of alternative $i$ for person $n$ is shown in Equation 2 ( 33 ):

\frac{L_{ni} (β_{n}) = e^{β_{n}^{'} x_{ni}}}{\sum_{j} e^{β_{n}^{'} x_{nj}}}

(2)

However, we do not know $β_{n}$ and therefore we cannot condition on $β$ . Thus, the integral of $L_{ni} (β_{n})$ is the unconditional choice probability over all possible variables of $β_{n}$ . Equation 3 shows this ML probability with $f (β)$ as its continuous density function ( 33 ).

P_{ni} = \int (\frac{e^{β^{'} x_{ni}}}{\sum_{j} e^{β^{'} x_{nj}}}) f (β) d (β)

(3)

Typical distributions for the coefficients are normal, lognormal, triangular, or uniform distributions ( 32 ). Traditional discrete choice models in transportation use travel time and costs for the explanation of decision-making behavior. In recent years, several studies investigated crowding within transit vehicles and the reliability of transit systems in the decision-making process.

Revealed Preference Surveys

A revealed preference online survey was conducted at a corridor along the planned path of a ropeway. Residents living inside this 300-m wide corridor had to fill in continuous travel diaries to analyze their existing mobility behavior. In addition, questionnaires and access links for the online survey were distributed at public transport spots and main entrance roads to collect data from residents outside the corridor and also from commuters. The online survey was also promoted on social media.

The proposed introduction of a ropeway in a European city is always a hotly debated topic in the city where it is planned. Many people form their own personal opinions and this process is reinforced by statements made in political discussions, whether for or against a ropeway. Consequently, we added an attribute to our model that pays special attention to the personal opinions of the respondents concerning this uncommon urban transport mode. This attribute helps to increase the explainable part of the choices made and reduces the influence of the mode-specific constants. We collected data concerning previous experiences of respondents with ropeways in general and personal attitudes to the planned introduction of a ropeway transport mode in the city. The lack of familiarity with this new system or a high level of dislike will influence the individual choice behavior. If respondents had used a ropeway previously, they graded their perception of safety. Finally, we asked the respondents about their perception concerning crowding and reliability in public transport modes.

Analysis of Reported Trips and Creation of Stated Choice Interviews

The reported trips of the travel diaries were analyzed, with a special focus on the public transport lines used and the routes driven by car, to create questionnaires for the stated choice interviews. It was then possible to calculate reliability probabilities for different times of the day, based on obtained reliability data of the local public transport operator. Trips with a delay less than 5 min compared with the timetable were defined as reliable trips. In the case of car trips, we calculated the quickest routes with a dynamic routing algorithm and determined time-of-day delays through variation of the departure time based on reported departure times. A variation of the reliability attribute was generated through a deduction/addition of maximum 20% to the observed reliabilities.

We also investigated the used and the potential public transport lines of the reported trips for the attribute of crowding, and analyzed the utilizations of these lines in the obtained data of the local public transport operator. We used the crowding approach of HBS ( 19 ) and VDV ( 4 ) and defined four levels of crowding similar to Fröhlich et al. ( 23 ). The crowding levels were based on the 65% capacity, which is the sum of the available seats and standing room of each transit vehicle. These four levels were “low” (<33% of 65% capacity), “middle” (33%–66%), “high” (67%–100%) and “overcrowded” (>100%). The crowding levels were provided as sketched illustrations similar to those of Fröhlich et al. in their stated choice experiment ( 23 ). Sketched illustrations provided the best response rates in similar surveys.

The creation of the ropeway trips considers the specific properties of the transport mode. That no traffic congestion is encountered means an urban ropeway has a very high reliability level and we assume that the probability of delays will not exist, since a very reliable TDG will be selected in the event of a ropeway being introduced in Graz, Austria. The probability of a delay for the ropeway in the questionnaires is therefore always 0%. The planned TDG offers a continuous service with a service interval of 42 s and a maximum capacity of 3,000 ppdph. Reflecting on the planned route with 11 stops, this will usually lead to no noticeable waiting time and low occupancy rates for each cabin. For this reason, we assumed only three levels of crowding: “low,”“middle,” and “high.” Empirical data of existing ropeways in European cities, as well as travel demand modeling of feasibility studies, indicated that the capacity exceeds demand in all cases because the ropeway systems are not served as backbones and supplement the existing public transport system only. In the case of rare single events, overcrowded situations may occur on European TDG ropeways, but they will be much fewer than in Medellín’s MDG ( 8 ). Additionally, Medellín’s ropeway faces much higher demand because of an unattractive bus service. Rare overcrowding events are addressed by adding three additional levels of waiting time to the usual not noticeable waiting time of 0 min, because the high volume of passengers affects only the waiting time in the ropeway station and not the in-vehicle travel time. Overcrowding in the cabin itself will not occur because of technically supervised weight limitations in the TDG. As mentioned before, the travel times of ropeways are independent of passenger volumes because boarding time does not vary as it does in bus or tram travel. Thus, bunching effects can also be ignored.

The travel speed of a TDG reaches 7.5 m/s between stations. At stops, a future urban TDG will stop twice for passenger egress and boarding, totaling a 44 s delay. There will be no bunching or passing of single cabins, which follow in a 42 s headway. Considering a deceleration and acceleration rate of 1 m/s², the TDG will travel at an average speed of 6.0 m/s with 11 stops and 11.8-km line length. The system will contain 85 cabins with 35 passengers maximum, of which 12 can be seated. The system is planned to operate between 5 am and 11 pm with a capacity of 3,000 ppdph. Major stops are at ground level while elevators and escalators will move passengers to upgraded stops. An additional access time of 1 min was used for ropeway trips in the choice sets.

Figure 2 illustrates a choice scenario for the trip purpose of work with the possible transport modes of car, public transport (bus and tram), or ropeway, and Table 2 shows the various levels of used attributes. We pivoted the alternatives in the choice tasks around the recorded travel times of the respondents to reduce hypothetical bias. Based on defined choice sets with different combinations of levels per attribute, every respondent had randomly chosen choice sets. The choice sets were distributed equally among all respondents.

Figure 2.

One choice set of the survey conducted 2022 in Graz.

Table 2.

Levels of Attributes per Used Attribute

Transport mode	Attribute	No. of levels	Levels
Car	Walking time to car	3	+20%, +/−0%, −20%
	Walking time to destination	3	+20%, +/−0%, −20%
	In-vehicle travel time car	5	+20%, +10%, +/−0%, −10%, −20%
	Reliability/Probability of a delay of 5 min	8	0%, 10%, 15%, 20%, 25%, 30%, 35%, 40%
Public transport	Walking time to stop	3	+20%, +/−0%, −20%
	Walking time to destination	3	+20%, +/−0%, −20%
	Waiting time	5	+2 min, +1 min, +/−0 min, −1 min, −2 min
	In-vehicle travel time public transport	5	+20%, +10%, +/−0%, −10%, −20%
	Reliability/Probability of a delay of 5 min	8	0%, 10%, 15%, 20%, 25%, 30%, 35%, 40%
	Crowding	4	Low (<33%), middle (33%–66%), high (67%–100%), overcrowded (>100%)
Ropeway	Walking time to stop	3	+20%, +/−0%, −20%
	Walking time to destination	3	+20%, +/−0%, −20%
	Waiting time	4	0 min, 2 min, 4 min, 6 min
	In-vehicle travel time ropeway	5	+20%, +10%, +/−0%, −10%, −20%
	Reliability/Probability of a delay of 5 min	1	0%
	Crowding	3	Low (<33%), middle (33%–66%), high (67%–100%)

Results

Descriptive Overview of Data

Table 3 provides an overview of the socioeconomic data and the experiences and personal attitudes of the survey respondents with regard to ropeways. We received 129 valid interviews, with 9 choice sets for employed respondents and 6 choice sets for unemployed respondents. Of the respondents, 40.6% were female and 59.4% male. Almost half of the respondents live in the defined 300-m wide ropeway corridor. The age distribution shows that all age classes were represented in the study population. There is a high share of people aged between 18 and 25 because of the promotion of the survey on social media. Young males are overrepresented. Over half of the respondents were employed and 91.9% had already used a ropeway, mostly in ski resorts or hiking regions. Only 7.1% of respondents had used an urban ropeway in a city as a public transport mode. With the frequent use of ropeways in Austria, respondents are used to this mode of transport and have a strong sense of security when using it. Only 4.5% do not feel at all safe. The main reason for this was fear of heights.

Table 3.

Descriptive Overview of Data (Sample Size = 129 Respondents)


Sociodemographic data and opinions about ropeways
Gender
Female	40.6%
Male	59.4%
Local distribution
Residents living in the ropeway corridor	46.1%
Residents who live in other parts of the city	25.3%
Commuters	28.7%
Age distribution
18–25	27.9%
26–35	15.3%
36–45	12.6%
46–55	18.9%
56–65	10.8%
66–75	3.6%
>75	1.8%
Not specified	9.0%
Type of employment
Students	21.6%
Employed	55.9%
Pensioners	8.1%
Unemployed	5.4%
Others (housewives or househusbands, no specification)	9.0%
Experiences with and preferences for ropeways
Did you ever use a ropeway?
Yes	91.9%
No	8.1%
Where did you use a ropeway?
In a ski resort in winter	94.9%
In a hiking region in summer	85.4%
In a city to get to a sight	36.4%
In a city (use as public transport mode)	7.1%
Do you feel safe while using a ropeway?
Yes, I feel very safe	54.0%
Yes, I feel pretty safe	35.9%
No, I feel a little insecure	5.6%
No, I don’t feel safe at all	4.5%
How often would you use an urban ropeway?
Daily or multiple times a week	24.7%
Multiple times a month	27.1%
Seldom	32.9%
Never	15.3%
Should Graz build an urban ropeway?
Yes	49.4%
No	50.6%

Table 3 also shows that the opinion about the introduction of a ropeway in Graz, Austria, is split between two equally sized groups, with a slight tendency against it. The main reasons for wanting a ropeway were its resiliency and no-delay transport (39%), high comfort of riding (11%), no noticeable waiting times (10%), lower crowding (19%), and the use of an innovative means of transport (16%). The main reasons against a ropeway were fear of heights (11%), low comfort travel (19%), and the opinion that a ropeway is not suitable for urban public transport (28%), plus safety issues (8%). Safety was mentioned in connection with the evacuation of the cabins in the event of emergency, and female respondents in particular had concerns about using a ropeway at night, specifically because there is no driver in a cabin to provide help in the event of an incident. The question about possible usage of this new system showed that 15.3% of respondents would refuse to use a ropeway.

Results of the Model Estimation

The estimation of parameters and specification (likelihood ratio) tests for the final model are shown in Table 4 in the last two columns (n = 1,068 observations). The final ML model was selected from several estimated models, and the model estimation was made with the program R-Studio by using the mlogit package.

Table 4.

Results of Final ML Model

		MNL		NL		ML
Attribute	Modes	par	(t-ratio)	par	(t-ratio)	par	(t-ratio)
Access
Walk (min)	Bus, tram	−0.1378	−5.1954	−0.1672	−5.2606	−0.1662	−6.3473
Walk (min)	Ropeway	−0.0582	−3.5424	−0.0855	−3.6098	−0.0740	−6.7781
Walk (min)	Car	−0.1943	−1.6133	−0.1903	−1.3784	−0.2219	−1.3324
Public transport main mode
Mode-specific constant	Bus, tram	1.5021	2.2963	1.2746	1.5026	1.5837	2.5005
Mode-specific constant	Ropeway	−0.1005	−2.2063	−0.1160	−2.1637	−0.1728	−2.5241
In-vehicle travel time (min)	Bus, tram	−0.0747	−4.3195	−0.0847	−4.5312	−0.0797	−4.6528
In-vehicle travel time (min)	Ropeway	−0.0511	−4.4713	−0.0776	−4.5355	−0.0707	−9.0641
Crowding (levels)	Bus, tram	−0.2663	−1.9257	−0.3765	−2.9114	−1.3396	−4.7475
Crowding (levels)	Ropeway	−0.5466	−2.0079	−0.5734	−2.2070	−1.5584	−6.0772
Reliability/Delays (%)	Bus, tram	−1.6109	−1.2900	−1.2704	−0.8296	−1.1329	−2.2541
Waiting time (min)	Bus, tram	−1.1244	−2.9375	−1.1452	−3.2138	−1.8300	−4.9967
Waiting time (min)	Ropeway	−0.4250	−3.4142	−0.5732	−3.4146	−0.7228	−9.1676
Fare (€)	All PT	−0.0589	−1.4979	−0.0941	−1.4798	−0.0866	−2.7566
Car main mode
In-vehicle travel time (min)	Car	−0.0781	−3.2103	−0.0984	−3.6642	−0.1156	−3.6842
Reliability/Delays (%)	Car	−0.8666	−1.7656	−1.0136	−1.5678	−0.8877	−1.2964
Travel costs (€)	Car	−0.0361	−0.7346	−0.0560	−1.4547	−0.0832	−1.2259
Egress
Walk (min)	Bus, tram	−0.1036	−3.1020	−0.1343	−3.5417	−0.1328	−4.0122
Walk (min)	Ropeway	−0.0992	−4.3799	−0.1411	−4.1764	−0.1095	−5.2206
Walk (min)	Car	−0.0992	−4.3799	−0.1411	−4.1764	−0.1095	−5.2206
Sociodemographic attributes
Opinion ropeway (0,1)	Bus, tram	−0.7381	−3.2601	−0.7009	−2.3408	−0.7874	−3.3374
Opinion ropeway (0,1)	Ropeway	0.4808	2.9452	0.5781	2.3752	0.6647	5.4586
Current car user (0,1)	Bus, tram	−0.5108	−2.2762	−0.7643	−2.3177	−0.6206	−2.8917
Current car user (0,1)	Ropeway	−0.6330	−3.5971	−0.9606	−3.0319	−0.8377	−6.2723
Residence in ropeway corridor (0,1)	Bus, tram	−0.6812	−1.7877	−0.2914	−0.6148	−0.6907	−1.8386
Residence in ropeway corridor (0,1)	Ropeway	0.6109	2.1392	0.6984	2.0150	0.6407	2.7378
Residence in other parts of city (0,1)	Bus, tram	−0.7304	−2.0826	−0.8404	−2.0811	−0.8055	−2.2653
Residence in other parts of city (0,1)	Ropeway	−0.1429	−0.4863	−0.2941	−0.6792	−0.2475	−1.1004
Ropeway relevant attributes
Pretty safe feeling in a ropeway (0,1)	Bus, tram	−0.0456	−0.1996	−0.0848	−0.2798	−0.1106	−0.4843
Pretty safe feeling in a ropeway (0,1)	Ropeway	−0.1759	−1.0569	−0.2475	−0.9679	−0.2564	−2.0553
Insecure feeling in a ropeway (0,1)	Bus, tram	−0.5245	−1.2123	−0.7902	−1.2872	−0.7036	−1.4378
Insecure feeling in a ropeway (0,1)	Ropeway	−0.6017	−1.9859	−0.9459	−1.9853	−0.9118	−2.8557
No safe feeling in a ropeway (0,1)	Bus, tram	0.9370	2.2897	0.9173	1.9380	1.0523	3.1440
No safe feeling in a ropeway (0,1)	Ropeway	−1.2010	−2.2083	−1.2485	−2.0527	−1.2735	−2.4268
Never used a ropeway (0,1)	Bus, tram	0.4588	1.2155	0.2214	0.4159	0.4987	1.3206
Never used a ropeway (0,1)	Ropeway	−1.4940	−3.5576	−1.8473	−3.1567	−1.9871	−4.5738
Standard deviation parameter distribution of random parameters
Waiting time (min)	Bus, tram					1.7529	7.962
Waiting time (min)	Ropeway					2.6705	16.0412
Crowding (levels)	Bus, tram					4.6599	25.2375
Crowding (levels)	Ropeway					7.4607	27.2276
Reliability/Delays (%)	Car					9.1222	2.6152
Reliability/Delays (%)	Bus, tram					3.3930	13.1264
Model fits/specification tests
LL (β)		−887.49		−886.14		−827.53
LL (0)		−1,088.0		−1,088.0		−1,088.0
Likelihood ratio test		401.1		403.7		520.9
Adjusted likelihood ratio test		366.0		368.7		485.9
McFadden R²		0.1843		0.1855		0.2394
Number of respondents		129		129		129
Number of observations		1,068		1,068		1,068

Note: MNL = multinomial logit; NL = nested logit; ML = mixed logic; LL = log-likelihood; par = parameter; PT = public transport.

Discussions of Estimation Results

The log-likelihood and McFadden R² are relative to a model with only alternative specific constants. The ML model reaches a McFadden R² of 0.2394. Taking a closer look at the results, the mode-specific constant is positive for traditional public transport and slightly negative for the ropeway (relative to the car-specific constant set to 0.0). They are both statistically significant, and the values show that there remain significant unobserved influencing effects, especially for traditional public transport, including buses and trams. The unobserved effects for the ropeway are much lower.

Our fixed parameters were the in-vehicle travel time, access and egress times per mode, and the travel costs per mode. The in-vehicle travel time and access and egress times per mode were estimated as an alternative specific variable. For in-vehicle travel time, we observed a higher disutility for car compared with ropeway and traditional public transport. The mean parameters of access and egress times are higher than the parameters of in-vehicle travel times. This corresponds with the results of other studies ( 16 , 30 , 34 ).

The three defined random parameters were waiting time, crowding, and reliability. We applied lognormal distributed random parameters to exclude negative values with 250 Halton draws. All random parameters are statistically significant. We estimated crowding and waiting time separately for ropeway and traditional public transport. In contrast, we estimated reliability separately for car and traditional public transport. Reliability for car trips is not statistically significant.

The influence of waiting time for public transport is higher than the influence of waiting time for the ropeway. Crowding in buses or trams (−1.3396) has a lower influence on mode choice than crowding in a ropeway (−1.5584). We assume that the smaller cabins and the height of traveling make passengers feel more uneasy than in common buses and trams.

The results show that opinions about ropeways have a statistically significant positive influence on the use of an urban ropeway. The opinion about a ropeway was binary coded with 0 as a bad opinion and 1 as a good opinion about this transport mode that does not yet exist. A person with a positive opinion about ropeways selects a ropeway in the choice experiment (0.6647), while people with low opinions prefer traditional transit (−0.7874). These results confirm the recorded statements of respondents about the ropeway and their choice behavior. Current car usage has a statistically significant influence on choice behavior. Current car users are unlikely to select a ropeway because of a higher negative parameter compared with traditional public transport (−0.6206 versus −0.8377).

In addition to current car use and respondents’ opinion about an urban ropeway, we also investigated the influence of home location in the city and sense of safety when using a ropeway. Those two variables were dummy coded with the reference levels “commuters” and “feeling very safe.” Results show that respondents living in the ropeway corridor prefer to use this new transport mode. Respondents’ perception of safety shows a slight tendency toward ropeway use depending on the level of safety. However, these influences are not all statistically significant because the Austrian population has a high level of safety and familiarity with ropeway use.

Travel costs had the lowest influence on choice behavior (−0.0866 for public transport and −0.0832 for car). There are two reasons for these results. First, the majority of the participating car users are able to park their cars free of charge at their work places and, as a result, their remaining driving costs for the short distances in the urban area of Graz, Austria, are very low. Second, the ropeway will be integrated as a part of the public transport fare system and will result in no additional costs for public transport season pass holders.

Without presenting the details, we also tested a normal distribution, allowing negative values for the random parameters instead of a lognormal distribution. This resulted in a better goodness of fit (0.3187 versus 0.2394 for McFadden R²). However, the normal distribution led to a lower statistical significance (10 out of 35 variables with p-value > 0.1). Moreover, the normal distribution led to a better model fit because unrealistic long waiting times and delays, as well as higher crowding levels, are accepted.

Multinomial logit and nested logit models were tested as well. Nevertheless, the R² was much lower compared with the ML approach, as shown in Table 4.

Conclusion

Summary

In this paper we estimated a mode choice model for urban transport in a moderately sized European city with the inclusion of an urban ropeway. Mode-specific properties of this new urban transport mode were added in a stated choice experiment. The mode-specific properties include high reliability with no delays as a result of not having to deal with traffic congestion. No waiting times can be noticed at the access because of short service intervals (<1 min) when no large groups attempt simultaneous cabin access. In addition, low crowding levels in the cabins are expected because of high capacities of up to 6,000 ppdph. Previous studies on ropeways did not include reliability, delay, and crowding in their demand modeling. Instead, ropeways were considered as a regular part of public transport without an estimation of mode-specific parameters.

We introduced a five-step methodology, including a revealed preference survey as well as stated choice interviews that included the attributes of crowding and reliability based on the real data of the local public transport operator. The analysis of the revealed preference survey showed, in addition to the mobility behavior of respondents, that respondents had ambiguous opinions on the issue of establishing a ropeway in Graz, Austria, while also having a clear personal familiarity and sense of safety about the use of a ropeway. Therefore, the investigation of safety perception did not show statistical significance in our models. The results of the model estimation showed that an ML model reached a higher McFadden R² compared with classic multinomial logit or nested logit models.

Crowding and reliability were estimated as alternative specific variables. Crowding showed a statistically significant influence on mode choice. In comparison, only reliability for traditional public transport showed a statistically significant influence because of the sample size. Crowding has greater influence on mode choice than reliability. Crowding is perceived to be more annoying in ropeways than in traditional public transport. Limited cabin size (35 passengers versus up to 210 passengers per vehicle in buses and trams) and height (up to 150 ft above ground) may justify this observation. Furthermore, the general personal attitude toward urban ropeways is statistically significant according to the choice experiments. Respondents with a negative opinion about ropeways, either based on bad experiences with touristic ropeways or on personal fears, refuse to use it despite a higher utility of the ropeway. The mode-specific constant for ropeways usage is slightly negative and for traditional public transport positive. This indicates a higher unobserved influence for traditional public transport compared with a ropeway, which could be because of the general opposition to a ropeway by some respondents who are probably project opponents.

Future Work

The current model estimation does not include walking and bicycling as additional alternatives, although these modes are relevant considering the size of the city of Graz, Austria. Future work will include these modes by extending the survey work. Additional surveys will also consider the COVID-19 impact on the attitudes toward public transport and the changes in crowding perception.

The model estimation showed that the personal attitudes of the respondents have an influence on choice behavior and reduce the unobserved influence of the mode-specific constants. Future work will include some latent variables concerning personal attitude, such as “fear of heights,”“negative previous experiences with ropeways,” or “refusing the use of a ropeway,” to reduce this unobserved influence even further. An application of the estimate model is planned in the future. This will include value of time calculations and variations of attributes (crowding, reliability).

Finally, the sample size with 129 respondents is sufficient for reliable results; however, a larger and more representative sample size for further experiments would be desirable. Thus, an integration of more sociodemographic attributes into the model estimation is possible.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: K. Hofer, M. Haberl, and M. Fellendorf; data collection: K. Hofer; analysis and interpretation of results: K. Hofer; draft manuscript preparation: K. Hofer, M. Haberl, and M. Fellendorf. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Karl Hofer

Michael Haberl

Martin Fellendorf

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