(B) **Discretionary opportunities (***Ow***):** The set of *Ow* available in the study area is georeferenced using OpenStreetMap as a core data source. These comprise all the study areas' amenities apart from workplaces, schools, and other educational facilities. Therefore, they mainly include groceries, shopping facilities, healthcare facilities, leisure facilities and other services such as post offices and banks. We consider all *Ow* to have the same importance for all individuals for the *STA* computation. Additionally, we assume that all *Ow* need at least a 10-min stay to be considered in the *PPAs*.

To calculate *STTP*, it is necessary to estimate (A) the unitary value of travel time for both *Civttk a*,*a+*1 and *Covttk a*,*a+*1; (B) the unitary monetary cost for *Cmk a*,*a+*1; and (C) the Euclidean distances among fixed activities, i.e., *Da*,*a+*1. Even these components are implemented in ArcGIS through the Network Analyst extension by calculating different route analyses and described below in detail.

(A) **Unitary value of travel time (***VTT***):** *VTT* is estimated with the wage rate method [44]. According to this approach, the value of travel time outside working hours (called Off-The-Clock Travel Time) for the driver is empirically found to be approximately 60% of the wage rate, excluding benefits. This percentage tends to decreases to 45% for passengers (of cars and PT) and increases to 100% when considering any kinds of out-of-vehicle travel time (i.e., walk-access, waiting, and transfer times). These differences depend on the perceptions of disutility of travel time for different modes of transport. Generally, travel time by PT or as car passenger has a higher utility since it is possible to make a profitable use of that time (e.g., to read, work or relax). When focusing on travel time during working hours (called On-The-Clock Travel Time), a percentage of 100% is considered for any kind of in-vehicle and out-of-vehicle travel time. Since we do not have individual income data at our disposal, we rely on the average hourly wage rates registered in Austria in 2018 for four different categories of people relevant for our case study, i.e., full-time workers (€16.22/h), part-time workers (€13.78/h), pupils (€9.88/h) and pensioners (€8.89/h) [49]. Accordingly, *VTT* is calculated for each individual and transport mode as summarised in Table 4. Combining these values with the travel-time performances, we obtain the *Civttk a*,*a+*1 and *Covttk a*,*a+*1 figures for each individual.

**Table 4.** *VTT* values applied to the different modes of transport and categories of individuals.

(B) **Unitary monetary cost (***UMC***):** *UMC* is estimated for private cars and PT in two different ways. For private vehicles, we rely on the average kilometric Vehicle Operating Cost (VOC) for passenger cars in Austria. This includes the average cost of fuel and oil, maintenance and repair, tyres, and kilometric-dependent depreciation. According to the EU report by Infras [50] and the yearly values provided by ACEA for all EU countries, [51], a VOC of €0.42/km is assumed for Austria. This is multiplied by the distance travelled to obtain *Cmk a*,*a+*1 figures for each individual travelling by car. As

for PT, the transport operator of the city of Vienna offers different yearly subscriptions covering the whole urban transport system [52]. Given the age and mobility habits of individuals, three subscriptions are considered: the annual ticket for adults (€365/year), for seniors +65 (€235/year), and for students till 24 years old (€79/year). According to these fares, a *UMC* of €1/day, €0.64/day and €0.21/day is taken as *Cmk a*,*a+*1 for individual C, D and E, respectively.

(C) **Euclidean distances (***Da***,***a+***1):** The Euclidean distances are first measured for each couple of subsequent fixed activities and then summed up to obtain the total daily Euclidean distance (*IDD*). Each *Da*,*a+*1 value is obtained via GIS and then merged for each individual.

Table 5 presents the values of the components discussed above for the individuals A–E. Based on these components, Figure 4 displays the *STA* and *STTP* results. Figure 4 (left side) focuses on *STA* by showing the extension of the *DPPA* and the related *FOS* for each individual. For individuals B–E (who have a wide free-time span available for discretionary activities either in the morning or afternoon), results are divided into two clusters. The first includes the *DPPA* and *FOS* resulting from the time available between fixed activities occurring in different locations (*DPPAfa* and *FOSfa*). The second includes the additional *DPPA* and *FOS* deriving from the free-time span available between consecutive mandatory home stays (*PPAhs* and *FOShs*). Figure 4 (right side) shows the results of *STTP*. Each individual shows the *ITCk a*,*a+*1 and *Da*,*a+*1 segments on the map, plus the overall *IDTC* and *IDD* figures.

**Figure 4. Left**, results of the *STA* computation; **right**, results of the *STTP* computation.

**Table 5.** Components for the calculation of *STA* and *STTP* for individuals A–E.

**Notes:** \* The time span between the ending time of a fixed activity and the starting time of the following one. \*\* Subsequent fixed activities occurring at the same location (i.e., home place) with a free-time span in between. Travels that could be potentially performed between them are considered in the *STA* computation, but not in the *STTP* one. \*\*\* For the values regarding PT, the unit of measure is €/day and not €/km. † *PPA* and *Ow* are equal to 0 because there is less than 10 min at disposal to engage in discretionary activities.

#### *4.3. Discussion of Results*

The results of *STA* and *STTP* are summarised in Table 6. Since they are expressed in different measurement units, they are also converted in percentages (*rSTA* and *rSTTP*). The highest *STA* and *STTP* figures across the five individuals are 100.00%, while the other values are rescaled accordingly. The coefficient of variation (CV) is measured for both *STA* and *STTP* to point out their differences in terms of distribution across individuals. To better understand these differences in distribution, we take into account a set of time, space and transport variables, which have a relevant influence on *STA* and *STTP* (reported in Table 6). These include: the amount of constrained time in a day, i.e., the number of hours/day spent in fixed activities (*CT*); the density of discretionary opportunities available within the *DPPA* of each individual (*OD*); the average speed of the travels linking the subsequent fixed activities of each individual (*AS*); the average kilometric monetary cost (considering the travelled distance) incurred by individuals to travel among their fixed activities (*AKC*); the average travel-time cost to perform daily travels by all modes (*ATC*); the detour effect experienced by each individual expressed as the ratio between the travelled distance and the Euclidean distance (*DE*); and finally the preferred mode(s) of transport used by the individuals for their fixed activities (*PMT*). The first two variables are particularly relevant to explain *STA* results, while the others have a higher influence on *STTP*. The following two

paragraphs first discuss the overall accessibility differences registered by *STA* and *STTP*, and then explore the main reasons for these differences for each individual.

**Table 6.** Results of *STA* and *STTP* for individuals A–E.

**Overall accessibility differences:** Accessibility differences measured by *STA* are sensibly higher than those registered by *STTP* (CV equal to 153% and 19%, respectively). This is consistent with the different approaches of the two measures. The primary purpose of *STTP* is to isolate the individual accessibility differences that are directly related to the performance of the transport system by excluding other variables not affected by changes in the transport system. Accordingly, *STTP* varies depending on the travel-time and monetary costs incurred to travel between fixed activities (*ATC* and *AKC*). Moreover, it depends on the level of the detour (*DE*), since travel costs are weighed according to the Euclidean (and not travelled) distance among fixed activities. Accordingly, the individuals with the lowest *rSTTP* (B and C) register the highest average time cost (*ATC* = €0.18/min for individual C), monetary cost (*AKC* = €0.42/km for Individual B), detour effect (*DE* = 182% for individual B), and one of the lowest average speeds between fixed activities (*AS =* km11/h for individual C). In contrast, *STA* considers a wider range of factors, including the availability and distribution of discretionary opportunities across space and the individual amount of constrained and free time on a daily basis. These two factors play a crucial role in determining the higher differences registered by *STA*. Indeed, the three individuals scoring the lowest *STA* (E, A and C) also have the highest amount of daily constrained time (*CT* equal to h23/day and h20/day for individuals A and E); and the lowest density of discretionary opportunities within their *DPPAs* (*OD* equal to 14.9/km2 and 31.3/km2 for individuals E and C).

**Accessibility differences at the individual level:**

corresponds to about 50% of their daily travel time. This has great impacts on their *AS* and *ATC*.

#### *4.4. Added Value of STTP for STA and Its Limits*

According to the developed methodology and test, the main added value of *STTP* for *STA* consists in its capacity to focus explicitly (and exclusively) on the performance of the transport system. Although this allows *STTP* to point out the accessibility differences that are strictly linked to the transport system, it also makes individual differences less evident (as demonstrated by the test results). Indeed, other aspects such as the daily amount of free time, the distance daily travelled, and the availability of discretionary opportunities are excluded from the computation. This confirms that *STTP* should be seen as a complementary (and not alternative) measure to be used together with *STA* to deal with the broad topic of accessibility equality. On the one hand, *STA* measures individual accessibility from a broad perspective by taking into account spatial, transport, individual and temporal factors and by holding the potential dimension of accessibility. On the other hand, *STTP* narrows the focus down, by isolating the performances of the transport system in allowing individuals to carry out their schedule of daily fixed activities.

Beside this key added value of *STTP* for *STA*, it is important to mention also some limits of *STTP* that need to be addressed in future applications. First, *STTP* results highly depend on the estimation of *VTT*, which has to be as accurate as possible and performed at the individual level. However, to estimate *VTT* at the individual level with the wage rate method, personal income data has to be collected. This is not always feasible since people tend to be not willing to answer income-related questions [53]. An alternative may be to estimate *VTT* through stated and revealed preference methods [44]. However, this approach is very data demanding and time-consuming and it requires the availability of individuals to answer a lengthy questionnaire that should include (a) preliminary socioeconomic and demographic questions; (b) the travel diary for *STPA* computation; and (c) stated-preference questions to estimate *VTT*. Second, regarding the test, there are some

computational limits to be refined. First, the opening/closure time of the discretionary opportunities should be integrated to properly select those to be counted in *STA*. Second, discretionary opportunities could be weighed according to the importance assigned by individuals to different categories of opportunities such as groceries, shopping facilities, or post/bank offices. However, the inclusion of these elements in the computation highly depends on the data at disposal in the study area and the availability of individuals to answer longer questionnaires. Third, the walking speed assigned to individuals (km5/h in our test) could be differentiated in specific cases, e.g., for elderly people with physical hindrances that make them walk slower. These limits need to be addressed to highlight precisely accessibility difference issues at individual level (e.g., refs. [54–56]).

#### **5. Conclusions**

Considering that many accessibility differences are unavoidable and irremediable by transport policies [1], and that *STA* measures tend to incorporate a broad variety of factors, this study has introduced a transport performance measure isolating the role of the transport system in individual accessibility differences. As suggested by the test, the results obtained by *STTP* may be sensibly different from those of *STA*. On the one hand, individual differences tend to be smaller, according to the more narrowed and transport-specific approach of *STTP*. On the other hand, the individuals registering the highest *STA* do not necessarily correspond to those with the highest *STTP* and vice versa. Indeed, an individual might register some transport difficulties in running their daily schedule but at the same time have enough time to engage in several discretionary activities (like Individual D in Section 4). Even the opposite may apply: a person could easily reach their usual daily destinations but have little free time and few surrounding amenities so as to register a low space-time accessibility (like Individual E in Section 4).

These results highlight the complementary value of *STTP* for *STA*. Indeed, researchers and policymakers might gain relevant benefits from the combined analysis of these two measures since they may evaluate both the overall and transport-specific impacts of various transport policies on individual accessibility differences (e.g., refs. [57–59]). This would be particularly relevant to assess transport policies that are expected to trigger controversial impacts on individual accessibility differences. For instance, in the case of high-speed railways, autonomous vehicle applications and transport sharing services, which are often found to increase accessibility in general, but also the accessibility differences across (groups of) people (e.g., refs. [57,59,60]). At the same time, *STTP* might be used to discuss the individual accessibility impacts of growing mobility trends, such as the usage of individual slow mobility solutions (such as e-scooters), which are progressively replacing walking travels, especially for the first- and last-mile.

To prove the suitability of the combination of *STA* and *STTP*, it is necessary to refine the estimation of user transport costs on the one hand and extend the application of this methodology to a broader case study on the other. The former challenge is mainly related to reliable estimation of the value of travel time (*VTT*). This study relied on the wage rate method, given its popularity and ease of application. However, more articulated estimation approaches could be used (such as stated and revealed preferences) to differentiate better *VTT* values depending on, e.g., the travel purposes, length of the travel and transport modes [61,62]. The latter challenge implies collecting *STPA* information from a substantial sample of individuals and applying sound statistical distribution analyses to the results. The first aspect is problematic for many studies using space-time measures, and it is one of the main practical reasons for the low usage of this kind of measure compared with, e.g., gravity-based measurements [15]. To overcome this limit, recent studies have deployed multi-stage stratified random sampling approaches, reducing the survey sampling rates while maintaining high accuracy [12]. The usage of statistical distribution analyses is problematic for a conceptual reason, since they imply the focus on one or more equity typologies [63]. For instance, calculating the coefficient of variation (CV) over the whole sample is closely linked to an egalitarian point of view, since the CV measures how spread

the distribution of a good over a population is. Conversely, calculating the percentile ratio (PR) by comparing the accessibility values scored at the median (50%) with those scored at e.g., 10% is linked to the vertical-equity point of view, since it focuses on the individuals with the lowest accessibility values. To guarantee a scientifically solid distributional analysis, future applications of *STTP* and *STA* to a broader case study would require a methodological effort in selecting a broad set of statistical distribution analyses to apply to the results.

Despite these challenges, *STTP* provides an added value for *STA*, and it may be deployed to complement the analysis of individual accessibility and of the distributional implications of transport policies, which represent an increasingly relevant priority of policymakers and transport planners.

**Author Contributions:** Conceptualization, A.D., G.H.; methodology, A.D., G.H.; software, M.G.; validation, A.D., M.G.; formal analysis, A.D., M.G.; investigation, A.D.; resources, A.D.; data curation, M.G.; writing—original Draft Preparation, A.D.; writing—review and editing, A.D., M.G., G.H.; visualization, A.D., M.G.; supervision, G.H.; project administration, G.H.; funding acquisition, A.D., M.G., G.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded in whole or in part by the Austrian Science Fund (FWF) [I 5224-G Internationale Projekte]. For Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. The research leading to these results has received funding from the Department of Innovation, Research and University of the Autonomous Province of Bozen/Bolzano, within the framework of the FWF Joint Projects between Austria and South Tyrol, under Project number I 5224-G. The APC was funded by the Austrian Science Fund (FWF) [I 5224-G Internationale Projekte].

**Data Availability Statement:** Data used and developed in this study will be uploaded to an institutional repository in case of approval. In that case, details for data access will be provided in this section.

**Acknowledgments:** Open Access Funding by the Austrian Science Fund (FWF). The authors warmly thank Elisa Ravazzoli (Eurac Research, Institute for Regional Development) for her support to the conceptualisation and revision of the article and her contribution within the framework of the RAAV research project.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Analytical Model for Enhancing the Adoptability of Continuous Descent Approach at Airports**

**Emad A. Alharbi 1,\*, Layek L. Abdel-Malek 2, R. John Milne 3 and Arwa M. Wali 4**

**Featured Application: We present an analytical model, using a queueing theory framework, that identifies periods of time for air traffic controllers when they can permit the vast majority of approaching aircrafts to land using Continuous Descent Approach, thereby reducing noise, fuel consumption, and pollution, while enhancing air transportation sustainability.**

**Abstract:** Continuous Descent Approach (CDA) is the flight technique for aircraft to continuously descend from cruise altitude with an idle thrust setting and without level-offs, contrary to the staircase-like Step-down Descent Approach (SDA). Important for air transportation sustainability, using CDA reduces noise, fuel consumption, and pollution. Nevertheless, CDA has been limited to low traffic levels at airports, often at night, because it requires more separation distance between aircraft arrivals and, thus, could decrease throughput. Insufficient attention has been given to helping air traffic controllers decide when CDA may be used. In this paper, we calculate the probability that an aircraft arriving during a particular brief period of time (e.g., 15 min) will need to revert to SDA when the controller tentatively plans to permit CDA for all aircrafts arriving during that time period. If this probability is low enough, the controller may plan to permit CDA during that time period. We utilize an analytical approach and queueing theory framework that considers factors such traffic and weather conditions to estimate the probability. We also provide the number of aircrafts that can be accommodated within the airport's stacking space using CDA. This number provides insight into whether a particular aircraft may use CDA.

**Keywords:** green transport; continuous descent approach; optimized profile descent; climate change; terminal maneuvering area; environmental impact; applied queueing theory; air traffic management; air transportation sustainability

#### **1. Introduction**

The air transportation and aviation industry face several challenges due to projected increases in demand for air travel and freight accompanying limited airspace congestion and airport capacity. The International Air Transport Association expects 7.2 billion passengers to travel in 2035, almost doubling the 3.8 billion air travelers in 2016, with the U.S. as the second-fastest-growing market, after China, with 484 million additional passengers per year forecasted for a total of 1.1 billion passengers [1]. With increased pressure on the infrastructure of terminals, runways, airspace around airports, and air traffic control operations, the industry is struggling to cope with this demand, yet it has to limit the harm that aircrafts cause to the environment through carbon emissions and noise levels.

With regard to aircraft emissions, the U.S. Environmental Protection Agency finalized its determination that greenhouse gas emissions from certain types of aircraft engines,

**Citation:** Alharbi, E.A.; Abdel-Malek, L.L.; Milne, R.J.; Wali, A.M. Analytical Model for Enhancing the Adoptability of Continuous Descent Approach at Airports. *Appl. Sci.* **2022**, *12*, 1506. https://doi.org/10.3390/ app12031506

Academic Editor: Giovanni Randazzo

Received: 31 December 2021 Accepted: 26 January 2022 Published: 30 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

primarily engines used on large commercial jets, contribute to the pollution that causes climate change and endangers Americans' health and the environment [2]. Other countries are taking strict measures to limit emissions from aviation operations at airports by setting penalties for emissions levels above a specified limit. Under the European Union Emission and Trading System, all airlines operating in Europe, European and non-European alike, are required to monitor, report, and verify their emissions and to surrender allowances against those emissions that exceed certain levels from their flights per year [3]. Aircraft noise, on the other hand, is the biggest concern for airport officials at 29 of the 50 busiest U.S. airports [4]. Airports' support personnel who work in proximity to aircrafts idling on the ground or taking off and landing may suffer hearing loss. Residents of communities surrounding airports suffer sleep disorders and interference with speech, both of which may lead to reduced productivity in learning and work. Furthermore, recent studies have linked noise to non-auditory health effects, such as hypertension, heart disease, and stroke [5]. These issues represent critical challenges to air transportation and aviation industry sustainability, development, and prosperity.

The Continuous Descent Approach (CDA), also known as Optimized Profile Descent (OPD), is an advanced flight technique for aircrafts to descend continuously from cruising altitude to the Final Approach Fix (FAF) or touchdown without level-offs and with an idle, or near idle, thrust setting. Descending using the CDA procedure, an aircraft can stay as high as possible for a longer time than with a conventional descent, thereby expanding the vertical distance between the aircraft's sources of noise and the ground and thus, significantly reducing the noise levels for populated areas near airports. Furthermore, by descending with an idle, or near idle, engine setting, fuel burn is decreased, resulting in the reduction of fuel consumption and harmful emissions to the environment. A study that conducted flight trials of CDA at Kentucky's Louisville International Airport using an aircraft fleet of the United Parcel Service (UPS), an express package delivery company, quantified the benefits of CDA in terms of fuel savings by 400 lb. to 500 lb. per flight and noise level by 3.9 A-weighted decibels (dBA) [6]. Another study conducted at San Francisco International Airport estimated a reduction of CO2 emissions of between 700 lb. and 10,000 lb. per flight with CDA flights [7]. To cut down on aircraft emissions, airplane manufacturer Airbus recently has been working on unique ways used by birds and emerging concepts like tandem flying that could reduce fuel burn by up to 10% [8]. When compared with the widely used Step-down Descent Approach (SDA), in which the arrival aircraft descends in a step-like fashion, CDA reduces flight time by around two minutes [9]. FedEx, another express transport and delivery company with one of the largest civil aircraft fleets in the world, has been using CDA at their World Hub, Memphis International Airport. Their use of CDA at Memphis reduced flight time by 2.5 min for each flight, and this translated into cost savings of \$105 million based on their field study from 2006 to 2009 [10].

These operational, economical, and environmental benefits from CDA procedures have made it a cornerstone in some aviation modernization programs at the national (e.g., FAA's Next Generation Air Transportation System, "NextGen"), continental (e.g., EU's Single European Sky Air Traffic Management Research, "SESAR"), and international (e.g., United Nations' International Civil Aviation Organization, "ICAO", Continuous Descent Operations, "CDO", initiative) levels. Although considered as an effective Noise Abatement Procedure, CDA is not widely implemented, especially during high density operations [11,12]. Due to safety considerations [13–15], CDA procedures may require more separation between aircraft arrivals, which may affect the airport arrival rate and runway throughput [16,17]. The larger separation spacing for a CDA aircraft is mainly due to two reasons: the difficulty for air traffic controllers to predict the future position of an aircraft with significantly variable speed [6] and the inability of the pilot to quickly decelerate during descent [18]. Although CDA has been proven to be feasible and without increasing the required spacing between aircraft under light traffic conditions, such as night-time operations [6], aircrafts flying CDA are most likely to be spaced further apart under heavy traffic conditions.

Thus, CDA implementation has been limited to low to moderate traffic levels. During these low traffic conditions, CDA has been used at more airports. To increase the use of CDA, several studies in the literature have used various approaches, such as simulation [19], mathematical modeling [15,20], and flight trials [6,14], to quantify CDA's benefits and/or suggest solutions to the problem of increasing CDA's usage at airports through the analysis of sequencing and merging [21], merging and spacing [18], scheduling and conflict detection and resolution [16], time and aircraft energy management during descent [22], fuel and flight-path management [23,24], and ground-to-air air traffic network vulnerability [25]. Other literature has applied quantitative methods to improve aircraft operation [26,27]. However, insufficient attention has been given to developing a quantitative measure to enable air traffic controllers to make informed decisions on safely accepting more CDA operations.

The contribution of this work is the development of a model that addresses this gap in CDA research and that helps air traffic controllers determine brief periods of time (e.g., 15-min periods) in which the vast majority of arriving flights may land using CDA. These time periods are based on time of aircraft arrival into the TMA. An aircraft entering the TMA during one of those time periods may begin its continuous descent upon entering the TMA while completing its continuous descent during a later time period, in which then-arriving aircrafts are no longer using CDA. In fact, although the time to descend using CDA depends on several factors (e.g., aircraft weight), it may be longer than 15 min. Data from previous authors [28,29] implies the time to descend using CDA may be 20–30 min.

Special attention is dedicated to factors that have a significant impact on CDA implementation, such as airspace structure around airports, airport arrival rate, and distance requirements for longitudinal separation between approaching aircrafts. Analyzing airspace structure around an airport offers a systematic way of developing an analytical model that adequately captures the elements associated with descent and approach procedures.

In particular, we calculate the probability that an aircraft arriving during a particular brief period of time will need to revert to SDA under the initial modeling assumption that the controller will permit CDA for all aircraft arrivals during that period. If this calculated probability is low enough, the controller may be comfortable in planning to permit CDA for all arriving aircrafts during that time period, and otherwise, they will not permit any of them to use CDA. Our model utilizes an analytical approach and queueing theory framework that considers factors such traffic and weather conditions to estimate the probability. The non-queueing portion of our modelling provides the number of aircrafts that can be accommodated within the airport's stacking space when CDA is used for all aircrafts arriving during the time period. This number provides insight to the controller on whether to permit a particular aircraft to use CDA during the period when all (or nearly all) arriving aircrafts will be permitted to descend with CDA (due to the low probability an aircraft will need to use SDA instead). Through the use of this modeling, it is our hope that CDA will be used more often and, thus, reduce noise, fuel consumption, harmful emissions and, thus, provide greener and more sustainable air transportation operations. This paper should draw attention to the opportunity to systematically increase the use of CDA for aviation green operations and air transportation sustainability.

The paper is organized as follows. Section 2 describes the airspace around airports with respect to the terminal maneuvering area and describes descent and approach operations. In particular, two approach operations (CDA and SDA) are discussed and compared. In Section 3, we present the adoptability of CDA and the factors that impact aircraft landing time; the Base of Aircraft Data (BADA) Aircraft Performance Calculation (APC) is estimated and validated against actual landing times of flights operated at Nashville International Airport (BNA). Section 4 presents a background on the queuing theory and the main assumptions and fundamental components used to develop our model, while Section 5 presents the concept of the probability of an aircraft being denied CDA entry as a key output of the queuing model. In Section 6, we illustrate the calculation of the model probabilities

using standard industry data (e.g., separation distance requirements) and actual flight data from the BNA airport. Finally, Section 7 presents our main findings and conclusions.

#### **2. Preliminaries and Process Description**

We begin this section by describing the airspace around airports, then generally describe aircraft descent and approach operations at airports, and we conclude with a comparison between the two most-commonly used descent approaches: CDA and SDA.

#### *2.1. Structure of Airspace around Airports*

Terminal Maneuvering Area (TMA). TMA refers to the designated area of airspace managed by air traffic control services around major airports that have high volumes of traffic. Normally, TMA airspace is designed in a cylindrical configuration, including all altitudes centered around the geographical coordinates of the airport. Geographical positions that define the boundaries of the TMA, known as entry fixes, are considered as entry points to the TMA (although each fix includes all altitudes and thus may be conceptualized as a line), and the arriving aircraft enters the TMA airspace via entry or arrival fixes. When crossing the TMA boundary over one of these entry fixes, the responsibility for the separating aircraft will be handed over usually from a controller at the air traffic control center responsible for separating the en route aircraft (e.g., Air Route Traffic Control Center "ARTCC") to a controller at the air traffic control center responsible for separating the aircraft approaching an airport (e.g., Terminal Radar Approach Control "TRACON"). A simplified structure of a TMA is illustrated in Figure 1.

**Figure 1.** Typical structure of a TMA (top view).

As an arriving aircraft nears an entry fix, the air traffic controller may clear the pilot for the approach or, depending on traffic congestion and the separation and sequencing method used, may place the aircraft in a holding pattern. While aircraft separation aims to have the controller apply and maintain the separation distance requirements between

aircrafts for safety purposes, aircraft sequencing aims to have the controller organize a stream of aircrafts to provide an orderly sequence of continuous traffic flow towards the final approach path. In practice, there are a number of aircraft-sequencing methods for approach traffic management, but generally, all of them fall under two broad categories: procedural control (published procedures with altitude change and speed instructions) and radar vectoring (controller-generated instructions in terms of headings, altitude, and speeds to optimize traffic flow in order to maximize the number of aircrafts with the least average delay). Today, radar vectoring is one of the main methods to achieve efficient sequencing for aircrafts flying towards the final approach path.

Once an aircraft has been cleared by the controller to approach the airport or to leave a holding pattern, the aircraft approaches the merging fix. However, as the aircraft approaches the merging fix, it flies in the stacking space, the space that the controllers use from the available terminal airspace to stack arriving aircrafts, that is, orderly align aircraft arrivals for approach. In the stacking space, the controller manages air traffic and enhances airspace capacity by stacking arriving aircrafts using techniques such as minimal speed adjustments and path-stretching. This efficient management of air traffic flow enables the controller to bring together aircrafts that have crossed entry fixes from different directions to be stacked and merged at the merging fix. For instance, an aircraft may enter the TMA through one of about 12 entry fixes and then proceed to one of about four merger fixes as they get closer to the airport. The merging fix provides a transition for arriving aircrafts from the stacking space to approach, as it connects traffic from different directions into one merger fix to create one stream of aircraft arrivals to follow a standard published arrival procedure. This way, arrivals from several directions can be accommodated, and traffic flow is efficiently managed within a congested airspace. To safely merge arriving aircrafts, the controller synchronizes aircrafts based on joining window time on the air route leading to the merging fix considering sufficient spacing for other aircrafts to fit into the air traffic stream and while maintaining, at least, the minimum required separation between aircrafts.

#### *2.2. Description of the Aircraft Descent and Approach Process at Airports*

In this subsection, we first describe the aircraft descent operations. Then, we present SDA and finally introduce CDA and compare it with SDA.

#### 2.2.1. Descent and Approach Operations

Aircraft descent could be initiated to attain an optimal profile from the cruise altitude all the way down to landing to minimize fuel burn, emissions, and noise exposure. However, due to Air Traffic Control (ATC) restrictions and aircraft performance limitations, an optimal descent profile may not be attained all the time. For an aircraft operating at typical cruise altitudes, descent will normally initiate at 100 to 130 nautical miles (nmi) from the destination airport. This distance varies primarily due to ATC service restrictions, aircrafts' equipment and performance capabilities, and weather conditions. The controller may issue crossing restrictions during the descent, as part of a Standard Terminal Arrival Route (STAR) or as a requirement for traffic sequencing. These crossing restrictions are generally issued to the cockpit crew in terms of altitude over a fix, and they may include a speed restriction as well [30].

A stabilized descent requires minimum control adjustments by the pilot in maintaining the planned descent path; more specifically, excessive corrections or control inputs indicate that the descent was improperly planned. Thus, planning the descent from cruise altitude is important because descending early results in more of the flight at a low altitude with increased fuel consumption and noise impacts, and starting the descent late results in problems with controlling both airspeed and descent rates later in the approach phase.

Prior to flight, pilots need to compute the fuel, time, and distance required to descend from the cruising altitude to the approach gate (an imaginary point used by the controller to provide headings (i.e., vectoring) for aircraft arrivals to the final approach course), with the objective of determining the most economical distance from the airport to begin descent. This distance is referred to as the Top of Descent (TOD) point. The computations for the TOD point could be done manually prior to flight or automatically during flight using the Flight Management System (FMS). Conversely, in flight prior to the descent, pilots plan the descent from cruise by reviewing and verifying landing weather to include winds in their consideration, since tempestuous weather at the landing airport can cause slower descents. Furthermore, pilots need to know the cruise altitude and approach gate altitude (otherwise known as the initial approach fix (IAF) altitude), descent rate, and ground speed during descent.

Based on aircraft performance, approach constraints, aircraft weight, and weather data (such as winds, temperature, and icing conditions), the vertical component of the flight plan, which referred to as the Vertical Navigation (VNAV), is computed. Usually, the VNAV approach is computed from the TOD point down to the waypoint at which the descent ends, which is generally the runway or the Missed Approach Point. There are only two types of VNAV paths that the FMS uses: the performance path or geometric path. The performance VNAV path is computed using an idle or near-idle thrust from the TOD point to the first constrained waypoint, which is constrained by speed and/or altitude and represents a typical CDA. The geometric VNAV path is computed from point-to-point between two constrained waypoints or when a vertical angle is assigned, which may represent a typical SDA, as it is shallower than the performance VNAV path and is typically using a non-idle thrust. Detailed descriptions of SDA and CDA are presented in the following subsections.

#### 2.2.2. Step-Down Descent Approach (SDA)

In air navigation, if the aircraft flies under Instrument Flight Rules (IFR), which represents a set of rules governing the navigation of aircraft using instruments, then the instrument approach procedures (IAP) must be followed. The IAP consists of four approach segments along the aircraft flight path, namely the initial, intermediate, and final approach and, as a backup plan to use if needed, a segment for a missed approach. Typically, the initial approach segment starts at the en route (i.e., cruise) altitude from an IAF and ends when the aircraft joins the intermediate approach segment, where the later ends at the final approach fix (FAF).

SDA is the conventional arrival procedure that pilots and air traffic controllers have been accustomed to for many years. In SDA, an aircraft begins its initial descent at the TOD point and continues descending gradually in a series of steps along the descent path. This step-down descent occurs because the aircraft descends over a stair-like path from the current altitude to a new altitude, due to the controller instructions and/or airspace constraints. During the SDA, the aircraft gradually levels-off by transitioning from the initial to the intermediate to the final approach segments through predefined fixes that indicate the start and end of each approach segment. To fly from the fix that marks the end of the previous approach segment to the fix that marks the subsequent one, the aircraft must increase speed by employing thrust to maintain altitude [31]. Figure 2 illustrates the SDA profile and the approach segments of the IAP.

SDA also requires communication between the pilot and controller to inform and authorize air movement, which means more workload on both the aircrew and controller during a critical phase of flight that requires situational awareness and additional concentration. Once an aircraft has reached the fix or waypoint that marks the end of the previous approach segment and marks the subsequent one at the new altitude assigned by the controller, the pilot needs to utilize engine thrust to maintain altitude and prepare for further instructions from the controller with respect to approach. Air traffic may be expedited during periods of high demand at airports when using SDA through radar vectoring; however, the utilization of engine power increases fuel burn, which, in turn, increases emissions and noise levels at lower altitudes [31].

**Figure 2.** The vertical profile of SDA based on the IAP and approach segments.

#### 2.2.3. Comparison between CDA and SDA

In this subsection, we provide a comparison between CDA and SDA from an operational perspective.

Considering aircraft approach speed, if a pair of aircrafts are approaching an airport for landing heading for the same runway, both aircraft approach speeds may not be the same when CDA is used, even with the same aircraft type. This is due to the fact that during descent, pilots make efforts to stabilize their approaches by controlling and balancing several parameters such as rate of descent, approach speed, thrust, and the aircraft's attitude. With CDA, landing is conducted with idle thrust as the aircraft approach speed decreases just before touchdown [32]. With SDA, the pilot utilizes thrust and adjusts speed more frequently along the descent path, and the aircraft approach speed increases just before touchdown. This comparison is illustrated in Figure 3 below. Table 1 highlights some of the differences between CDA and SDA operations.

**Figure 3.** The vertical profile of CDA compared with SDA.

**Table 1.** Summary of the Differences between CDA and SDA.

#### **3. CDA Adoptability and Aircraft Descent Times**

This section introduces the factors that influence our model and then estimates and validates the time aircrafts take to land under CDA and SDA operations. The estimation and validation are essential for developing our model. In our model, we assume that during a given brief period of time, say 15 min or 30 min, for example, the air traffic controller will enable all arriving aircrafts to use CDA or not permit any aircrafts to use CDA. This assumption simplifies the controller's duties and avoids the complexity associated with a significant number of aircrafts within the TMA using CDA and a significant number using SDA. That being said, it remains possible for the controller to plan on permitting all aircrafts arriving in the brief period of time to use CDA, if suggested by the model, and yet on a case-by-case basis, decide whether to deny CDA for a particular aircraft. The case-by-case basis analysis is beyond the scope of our queueing model, but it is considered by the maximum number of aircrafts that may reside in the stacking space at any given time, as we determine much further below.

#### *3.1. Factors Impacting CDA Adoptability and Aircraft Descent Time*

Before we present the details of our model [33], we briefly discuss the concept of acceptance, and rejection, in the context of landing operations at an airport and, particularly, with CDA operations. In general, our queueing model assumes that at a given airport, the air traffic controller will either accept all CDA requests from aircraft arrivals to approach and land using CDA over a specified brief time period, say 15 min, or reject them all. Before the queueing model details are calculated, we first calculate the CDA Adoptability Factor (CDA\_AF). This factor is a function of *λss*, the average arrival rate of the aircraft that requests CDA at an airport (which our model assumes is all the aircrafts arriving at

the TMA's stacking space due to the advantages of continuous descent), and *AAR*, the Airport Arrival Rate, which is defined as the dynamic parameter that specifies the number of arriving aircrafts that an airport can accept during any consecutive 15-min period of time [34]. As shown from the equation below, CDA\_AF represents the ratio of *λss* to *AAR*:

$$\text{CDA\\_AF} = \frac{\lambda\_{\text{ss}}}{AAR} \tag{1}$$

If the value of CDA\_AF during the brief time period is high (e.g., over 100%), then there is no need to continue the analysis. It is obvious in that case that CDA will not be permitted during that time period. Conversely, if the value of CDA\_AF is low (e.g., under 10%), then it is obvious that CDA will be permitted during the time period. The queueing calculations are performed only for those periods of time when the value of CDA\_AF does not make it obvious whether or not CDA should be permitted during the time period.

#### Factors Impacting CDA Adoptability and Aircraft Descent Times

There are a number of factors that could impact the nature of aircraft arrivals at airports. Such factors could be operational, meteorological, planning, technological, or related to airspace structure and procedures design. We discussed some of these factors in Section 2 and discuss others briefly in the following subsections. Technology factors (e.g., the level of Air Traffic Management automation at an airport) are beyond the scope of this work. Other factors, however, such as traffic at neighboring airports and wind speed and direction, can be managed by reducing aircraft stacking space and increasing the minimum separation distance between aircrafts.

The Airport Arrival Rate (AAR) states the hourly capacity of airplane arrivals at an airport, and thus, it is critical to our model.

The aircraft fleet mix, or more generally fleet mix, refers to the ratio of various aircraft types that, based on wake turbulence categories, make up the total arrival traffic that operates at an airport. Fleet mix is essential in airport planning to determine the likely average landing speed and separation requirements on final approach, which are important factors that affect the AAR and, in turn, our model. Generally speaking, and from the perspective of runway capacity, which is defined as the expected number of landings that can be performed per hour on a runway, a relatively homogenous fleet mix, consisting of two dominant aircraft classes, is more favorable than a heterogeneous fleet mix.

The aircrafts' separation requirements determine the maximum number of aircrafts that can navigate each part of the airspace or can use a runway system per unit of time. The separation requirements for an aircraft landing on the same runway specify the minimum separation in longitudinal distance, or time, that must always be maintained between two aircrafts operating consecutively on the runway. These requirements are also specified for every possible pair of classes and every possible sequence of movements [35]. Table 2 exhibits the ICAO's minimum wake turbulence separation standards [36], and apparently, the larger the separation required, the lower the AAR. Furthermore, the more heterogeneous the fleet mix at an airport, the more influence there will be on AAR and our model. These separation distances are based upon SDA being used. If CDA is used, then the minimum separation distances are the same when the leading and trailing aircrafts are from the same weight turbulence category but longer than with SDA when the aircraft weight classes differ. Furthermore, the air traffic controller will be inclined to use longer minimum separation distances with CDA because of the greater challenge of controlling aircrafts using CDA.

**Table 2.** ICAO Minimum Wake Turbulence Separation Standards.

Among the usually considered weather conditions at airports, such as cloud ceiling and visibility, wind speed and direction are the most influential conditions on ATM operations in general and on approach operations, in particular. The two components of the wind, headwinds and tailwinds, have a significant impact on AAR. In fact, wind speed and direction dictate the availability and orientation of runways at any given time. Adverse wind conditions can reduce AAR due to the increased complexity of merging arrival traffic streams and separating aircrafts as they descend and change heading under intense or varying winds. Specifically, winds aloft may result in a phenomenon called compression, in which the separation between pairs of arriving aircrafts decreases rapidly as they descend to the final approach [37]. The results from applying our model indicate it captures the effect of wind speed.

In general, airport and airspace constraints refer to limitations that hinder airport capacity by creating difficulties for arrival aircrafts, largely due to airspace consideration. Often, such constraints are contingent on the original airspace design, which gradually became less efficient due to increasing demand and fluctuating traffic patterns, or airspace redesign, which necessitates consideration of nearby restricted airspace. On the other hand, a restricted airspace, which is an area of airspace typically used by military operations, could be close to an airport and would impose a specific airspace design that affects the pattern of the arriving aircraft. Other airspace constraints include the topographical nature and terrain (e.g., an airport close to a mountainous terrain). Airspace constraints, collectively as a single factor, are beyond the scope of this work. While estimating the effect of this factor is beyond the scope of this work, our model's behavior reflects its ability to capture such effect.

Growth in air traffic at airports within close geographical proximity likely will create congestion, especially if these airports are in a large, busy metropolitan area. The impact of air traffic at neighboring airports comes from systems of airports commonly referred to as *metroplexes*. Operationally, air traffic that flows into and out of airports within a metroplex airport system needs to be coordinated between airports in such systems to maintain efficient air traffic and individual airports' throughput, while contributing little (if any) impact to the AAR of an airport over another in such a system [38,39] and, therefore, limiting or even preventing the use of our model. The FAA is having ongoing efforts to accommodate CDAs within metroplexes, with plans to deploy during a later phase of NextGen.

#### *3.2. Estimation of Aircraft Descent Time*

In this section, we estimate the time an aircraft takes to descend, starting from the TOD point at cruise altitude down to the runway, under CDA and SDA operations, using version 3.11 of Base of Aircraft Data's (BADA) Aircraft Performance Model (APM) [40]. Estimating aircraft descent time under the two distinct approach operations is a fundamental step towards developing our model.

BADA is an APM developed and maintained by the European Organization for the Safety of Air Navigation, commonly known as EUROCONTROL, through active cooperation with aircraft manufacturers and operating airlines. To estimate aircraft landing time at airports using BADA, we used BADA's web-based Calculation Tool, the Aircraft Performance Calculation (APC), to calculate aircraft performance for the descent phase of flight. Essentially, BADA's application software provides access to an online implementation of BADA APM, which consists of a database of aircraft operational performance files and formulas derived from the Total-Energy Model that EUROCONTROL relied on to model aircraft performance in categories such as aircraft, aerodynamics (e.g., drag), and engine thrust [41], as follows:

#### 3.2.1. Aircraft Velocity and Lift Model

For a straight-and-level flight at cruise altitude, the aircraft speed (velocity) is given by

$$\mathbf{V\_{TAS}} = \mathbf{a\_o} M\_{cruise} \sqrt{\frac{T}{T\_o}} \tag{2}$$

where VTAS is aircraft's true airspeed (TAS) in nautical miles per hour (knots), ao is the speed of sound at sea level in knots, *Mcruise* is the aircraft's Mach number at cruise altitude, and *T* and *To* are the temperatures at cruise altitude and at sea level, respectively. The lift coefficient, *CL*, can be calculated using the classical formula for the lift force, *L*:

$$L = \mathbb{C}\_L \frac{1}{2} \rho V^2 \text{S} \tag{3}$$

where *ρ* is the density of air in kilograms per meter cubic, *V* is the aircraft speed in meters per second, and *S* is the aircraft's wing area in square meters.

In cruise flight, the lift force, *L*, in Newtons, may be assumed to be equal to the aircraft's weight in kilograms, *m*. Combining this relationship with Equation (3) and rearranging terms results in

$$\mathcal{C}\_L = \frac{2mg}{\rho V^2 S} \tag{4}$$

where *g* is the acceleration due to the earth's gravity. Assuming a no-wind scenario and that the flight path's angle in degrees is γ, then the relationship between ground speed and true airspeed is given by

$$\mathbf{V\_{ground}} = \mathbf{V\_{TAS}} \cdot \cos \chi \tag{5}$$

#### 3.2.2. Drag Model

Drag is the aerodynamic force acting on an aircraft body in terms of air resistance to aircraft motion through air. Similarly, to the lift force, the aerodynamic drag, *D*, is the product of the dynamic pressure and drag coefficient, as follows:

$$D = \mathbb{C}\_D \frac{1}{2} \rho V^2 \mathbb{S} \tag{6}$$

The drag coefficient is given by the sum of zero-lift, *CDo*, and induced drag, *CDi*, coefficients, where the latter is a quadratic function of the lift coefficient, as follows:

$$\mathbf{C}\_{D} = \mathbf{C}\_{Do} + \mathbf{C}\_{Di}\mathbf{C}\_{L}^{2} \tag{7}$$

Typically, *CDo* and *CDi* are functions of the aerodynamic configuration of the aircraft flight phase. Generally, drag coefficients are functions of the aircraft's Mach number and the Reynolds number (*Re* = *ρVL*/*μ*, where *μ* is the absolute viscosity coefficient of air). For each aerodynamic configuration, BADA models these coefficients as constants to provide computations for altitude and speed profile thresholds at pre-determined flight phases (i.e., takeoff, initial climb, clean, approach, and landing).

3.2.3. Thrust Model

BADA uses a general formula to calculate the maximum climb thrust, *Thr*max,climb, at a standard atmosphere for three different types of engines: jet, turboprop, and piston engines. For jet engines, the general equation is given as

$$Thr\_{\text{max,climb}} = \mathcal{C}\_{\text{Tc},1} \times \left(1 - \frac{H\_p}{\mathcal{C}\_{\text{Tc},2}} + \mathcal{C}\_{\text{Tc},3} \times H\_p^2 \right) \tag{8}$$

Since BADA uses this maximum climb thrust for both take-off and climb phases, the descent thrust is then calculated from the maximum climb thrust using adjustment coefficients for cruise, approach, and landing configurations [41], respectively, as follows:

$$\text{Thr}\_{\text{des,low}} = \text{C}\_{\text{Tdes,low}} \times \text{Thr}\_{\text{max,climb}} \tag{9}$$

$$\text{Thr}\_{\text{des,app}} = \text{C}\_{\text{Tdes,app}} \times \text{Thr}\_{\text{max,climb}} \tag{10}$$

$$Thr\_{\rm des,ld} = \mathcal{C}\_{Tdes,ld} \times Thr\_{\rm max,climb} \tag{11}$$

where *CTc*,1, *CTc,*2, *CTc,*3, *CTdes,*low, *CTdes,*app, and *CTdes,*ld are aircraft-specific coefficients, and *Hp* is the geo-potential pressure altitude, in feet. The rate, in feet per minute, at which an aircraft's altitude changes with respect to time when descending and approaching the runway for landing is the Rate of Descent (ROD). ROD is given by

$$ROD = \frac{dh}{dt} = \frac{(Thr\_{des} - D)V\_{TAS}}{mg} - \frac{V}{g}\frac{dV}{dt} \tag{12}$$

where *dV/dt* is the aircraft's vertical speed, in feet of descent per minute. Given that the typical target of a flight path is about 3 degrees, the flight path angle, *γ*, in degrees for a 3-degrees flight over the descent path is

$$\gamma = \sin^{-1}(\frac{ROD}{V\_{app}}) \tag{13}$$

where *Vapp* is the aircraft approach speed, in knots. The distance, in nautical miles, that the aircraft covers over the descent path is given as follows:

$$\text{Distance} = \frac{(\Delta h \div 100)}{\gamma} \tag{14}$$

where Δ*h* is the difference between the altitude that the aircraft is currently flying at and the altitude that the aircraft will descend to, in feet. Finally, the time, in minutes, that the aircraft takes to descend and land can be estimated by dividing the difference in altitude, in feet, by the rate of descent, in feet per minute, as follows:

$$\text{Aircraft Landing Time} = \frac{\Delta h}{ROD} \tag{15}$$

#### *3.3. Evaluation of Aircraft Estimated Descent Time*

To evaluate the calculations outputs of BADA APM, Figure 4 shows a comparison between the estimated landing times computed by BADA APC and actual landing times for an aircraft with CDA operated at Nashville International Airport (BNA) on 17 June 2015. There is a slight variation observed across the compared values between the estimated landing times and actual landing times. For example, with a CRJ9 aircraft that has estimated and actual landing times of 38 min and 27 min, respectively, there is an error of almost 29%, while for a CRJ7 aircraft with estimated and actual landing times of 20 min and 19 min, respectively, there is an error of 5.3%. On average, BADA APC have estimated the landing time for an aircraft with CDA operations to be 20 min. When compared with the actual

average landing time for an aircraft with CDA at BNA airport, which is 21 min, an error of 4.7% was generated from this estimation.

**Figure 4.** Evaluation of aircraft landing times with CDA at BNA airport.

Similarly, Figure 5 shows a comparison between the estimated landing times computed by BADA APM, using BADA APC, and actual landing times for an aircraft with SDA operated at BNA. It shows that for a B737 aircraft with estimated and actual landing times of 32 min and 36 min, respectively, BADA APC produced an error of about 11%, with an error of about 8% for an E135 aircraft with estimated and actual landing times of 39 min and 36 min, respectively. However, there are SDA instances where BADA APC was able to match the estimated landing time with the actual landing time, such as with the MD88 aircraft, or provide close to a match, such as with the FA50 aircraft. On average, BADA APC have estimated the landing time for an aircraft with SDA operations to be 21.7 min. When compared with the actual average landing time for an aircraft with SDA at BNA airport, which is 24 min, an error of 9.6% results from this estimation.

**Figure 5.** Evaluation of aircraft landing times with SDA at BNA.

#### **4. Model Development**

#### *4.1. Background on Queueing Theory*

In this subsection, we briefly discuss the fundamentals of queueing theory. Queues, or waiting lines, are common in people's daily lives. Queueing theory is the field of study within operations research (OR) that concerns the study of queueing models to represent the different types of queueing systems (systems that involve some sort of queue) that appear in real-world applications. Thus, these queueing models are helpful for determining how to operate a queuing system [42].

The basic process of most queueing models is that customers requiring service are generated over time by an input source (also known as a calling population). The arrival pattern by which customers are generated from the input source is statistically defined to accommodate the randomness of the customer arrival pattern. A common assumption is that customers arrive according to a Poisson process, that is, customers arrive at random but at a fixed mean rate, or equivalently, the time between consecutive customer arrivals, that is, interarrival time, follows an exponential distribution. These customers enter the queueing system and form a queue to wait for the required service.

Queues could be infinite or finite according to the maximum permissible number of customers that they can contain. At certain times, a customer is selected from the queue for service according to some defined rule referred to as the queue discipline (usually first-come-first-serve, shortly known as FCFS, or some priority-based rule). The service is then provided to the selected customer by a service mechanism that may consist of one or more service facilities, each of which contains one or more servers. The time elapsed from the commencement to the completion of service for a customer is referred to as the service time. Collectively, characteristics of queueing systems include arrival patterns of customers, service patterns of server(s), the number of servers, system capacity, queuing discipline, and the number of service stages, if more than one service stage exists [43].

A convenient notation for summarizing the basic characteristics of the queueing systems was developed by D. G. Kendall and is known in the literature as the Kendall notation. It follows the notation of (a/b/c), where a = customer arrivals distribution, b = service time distribution, and c = number of servers [44]. For instance, the queuing model (M/D/5) uses Markovian (or Poisson) arrivals (or equivalently, exponential interarrival time distribution), deterministic (constant) service time, and five parallel servers.

Generally, there are three basic measures of performance for queuing systems: the waiting time that a typical customer endures, the number of customers that may accumulate in the queue or system, and the idle time of the servers. Since most queuing systems follow random processes (i.e., stochastic processes), these measures are represented as random variables, and thus, their probability distributions need to be defined. Depending on if the main objective of modeling a queuing system is whether to determine some measure of effectiveness for a given process or to design the optimal system based on some defined criterion, the measures of performance could include the expected number of customers in the system, expected number of customers in the queue, expected waiting time in the system, expected waiting time in the queue, and expected number of busy servers.

Beyond the previously mentioned measures of performance, there is a measure of performance of particular interest that indicates the percentage of time the service facility within the queuing system is being utilized. This measure of performance represents the traffic intensity or utilization factor, which is the expected arrival rate of the customers to the queuing system, divided by the expected service rate, assuming one server in the service facility. If more than one server is available, then the number of servers must be multiplied by the expected service time. The utilization factor is an important performance measure of the queuing system.

#### *4.2. Adopting Queueing Theory to Our Model*

In this section, we introduce the fundamental parameters and essential conceptual elements for developing our model. In our model, aircrafts arriving at the TMA are viewed as customers of a queuing system. The aircraft within the stacking space are modeled as the customers waiting for the service and being served. Aircrafts leaving the queueing system are viewed as customers completing service at a single server.

4.2.1. Assumptions and Parameters of the Model

Our model assumes that the number of aircraft arrivals over the period of time considered follows the Poisson probability distribution. This distribution has high variability and, thus, is likely to lead to the model results being conservative. Moreover, the fleet mix is assumed to be homogeneous, that is, dominated by two aircraft wake turbulence classes. The following parameters represent the fundamental components of our model: the space available to stack aircraft arrivals, the minimum allowable horizontal separation distance between a pair of consecutive same-weight-class aircraft arrivals, and the number of aircrafts that can be stacked for the approach. Figure 6 illustrates these components in our model. In this regard, while stacking space can be viewed as three dimensional, we model it as one dimensional, reflecting the longitudinal separation of stacked aircrafts as if the aircrafts within the space are all positioned in a single line.

**Figure 6.** Parameters of our model for aircrafts approaching airports with CDA.

4.2.2. Capacity of the Stacking Space for Aircraft Arrivals

To maximize airport capacity, especially during periods of high demand, the controller longitudinally aligns and separates approaching aircrafts (i.e., positions arriving aircrafts in the queue) for landing on the same runway in a predetermined airspace, according to a predefined requirement for minimum separation between aircrafts that typically operates under IFR [36].

Optimal spacing refers to the efficient implementation of separation requirements by the controller, such that spacing delivers seamless and efficient air traffic control services while maintaining safety. As the controller often emphasizes sequencing (ordering of aircrafts approaching based on their sizes), this should not be the case with CDA operations. During CDA operations, the optimal spacing between aircrafts is more important than optimal sequencing [45]. Thus, we principally assume that the separation distance (mapped as the horizontal distance in Figure 6) between two, same-weight-class, consecutively

arriving aircrafts conducting CDA is *greater* than when these two consecutive arriving aircrafts are conducting SDA, thus

$$d\_{\rm CDA} > d\_{\rm SDA} \tag{16}$$

where:

*dCDA* = minimum separation distance between aircrafts conducting CDA; and

*dSDA* = minimum separation distance between aircrafts conducting SDA.

Assuming that the space available to stack aircraft arrivals (i.e., the maximum number of aircrafts in the queuing system) at an airport is *Sp*, and the minimum allowable horizontal separation distance between a pair of same-weight-class aircraft arrivals is *d*, then the number of aircrafts stacked for approach, *k*, must fit safely within the allowable stack space, as follows:

$$k \le \frac{\mathcal{S}\_p}{d} \tag{17}$$

The largest integer value of *k* that satisfies Equation (17) is a key output of our modeling. When CDA is used, that largest integer value of *k* is the maximum number of aircrafts that can fit within the stacking space under the CDA assumption. The air traffic controller may be able to compare this largest integer with the number of CDA aircrafts presently in the tracking space to ascertain whether there is available stacking space to permit the next arriving aircraft to use CDA or not.

Assuming that the aircraft approach speed, measured in knots, on average, is *Vapp* and that the distance the aircraft covers during descent from the TOD point to touchdown, measured in nautical miles, is *ddes*, then the *average* descent time, *tdes*, could be estimated as

$$t\_{des} = \frac{d\_{des}}{V\_{app}}\tag{18}$$

We assume that an airport's nominal capacity, *AAR*, is sufficiently large to handle all aircrafts that can fit safely within the stacking space. Therefore, when implementing CDA, this assumption is represented as follows:

$$AAR \times t\_{des} \ge k \tag{19}$$

Essentially, stacking space is a contained airspace with predefined boundaries based on traffic and/or obstacles limitations with the purpose to stack aircraft arrivals up to a certain capacity. As the separation distance between aircrafts increases, the stacking space capacity, in terms of the number of aircrafts that could be stacked, *k*, will decrease. Moreover, as the airport arrival rate increases, typically during periods of high demand when many airport staff are working and the airport operates at near capacity, stacking space capacity may decrease as well. This is due to the high level of traffic causing stress and cognitive pressures on the air traffic controllers who, thus, may decide to increase the minimum separation distance between aircrafts as a safety buffer to reduce stress and the possibility of a safety error.

Furthermore, we assume that almost all aircraft arrivals at the airport are expected to successfully land on a runway, regardless of their descent profile type. To attain this operationally, the runway, as a critical element in ATM and airports operations, is assumed to have an arrival capacity that is at least as large as the *AAR*. The maximum runway arrival hourly capacity is calculated by dividing the average aircraft ground speed, *GS*, in knots, crossing the runway threshold by the longitudinal separation distance, *d*, in nautical miles, required between successive arrivals, as follows:

$$RwyCap = \frac{GS}{d} \tag{20}$$

Observe above that the stacking space capacity, *k*, was determined above based on the minimum allowable separation distances between a pair of aircrafts of a similar weight class. Thus, the value of *k* represents a bound on the capacity of aircrafts that may safely fit within the stacking space. Consequently, an upper bound of *k* should be determined based on the worst-case sequencing of aircrafts within the stacking space. That worst case can be determined by assuming a sequence in which the lightest aircraft scheduled to land that day is followed by the heaviest aircraft scheduled that day followed by the lightest aircraft scheduled and so forth. Following these calculations, the air traffic controller may be provided with the lower and upper bounds of the stacking space capacity under the assumption that all aircrafts arriving during that time period use CDA. When a particular aircraft arrives during the period, the controller may compare the number of aircrafts presently in the system versus the lower and upper bounds. If the number in the system is less than the lower bound, then that is a favorable indicator that the arriving aircraft may be admitted using CDA. If the number is above the upper bound, then that indicates that CDA should be denied. If the number of aircrafts within the stack is as much as the lower bound or greater and yet below the upper bound, then the controller will need to consider other factors in reaching a decision on whether CDA is safe for that arriving aircraft. Even if the number in the system is below the lower bound, those other factors may need to be considered by the controller to ensure there is sufficient separation distance between the arriving aircraft and the aircraft it follows most closely within the stacking space. Providing the controller with lower and upper bounds on stacking space is an optional tactic. Doing so depends on whether it would be too much additional information for the, often busy, controller to absorb.

#### **5. The Applied Queueing Model**

In this section, we present our model and its key output, the Probability of CDA Blocking, and by blocking, we mean that an aircraft would be denied conducting CDA by the controller. Therefore, the probability of CDA blocking is the probability that (assuming all aircrafts arriving during the brief period of time considered (e.g., 15 min) are assumed to use CDA) an aircraft would need to revert to SDA even though the initial plan was for all aircrafts arriving in that time period to use CDA. However, we first discuss how the concept of traffic intensity, which is borrowed from the queuing theory, applies in the context of our model.

#### *5.1. Traffic Intensity*

Queuing theory presents a key parameter known as the traffic intensity, also referred to as the utilization factor, which is denoted by the Greek letter *ρss* ("rho"), which is defined here as the average hourly demand rate of the stacking space divided by the average hourly capacity (or *service*) of the stacking space. If the average demand rate (the rate at which aircrafts arrive at the stacking space, i.e., the aircraft arrival rate) is denoted by *λss* and the average service rate is denoted by *μss*, then the *utilization of airspace factor*, *ρss*, for the stacking space within the TMA is as follows:

$$
\rho\_{\rm ss} = \frac{\lambda\_{\rm ss}}{\mu\_{\rm ss}} \tag{21}
$$

where the demand rate is expressed in terms of the number of aircrafts that arrive per hour at the stacking space, and service rate is expressed in terms of the number aircrafts per hour that may enter the stacking space. The value of the service rate, *μss*, is conceptually equivalent to the airport arrival rate (AAR). However, because *λss* is expressed in our examples per 15-min time period, the value of the service rate, *μss*, represents the number of aircrafts that can be processed (served) per 15-min time period, and thus, it is one fourth of the value of AAR. The symbol *μss* is typically used in publications on queueing theory, while AAR is commonly used in air traffic management. Observe that the service rate, *μss*, will be lower when CDA is assumed than when SDA is assumed due to the longer separation distances required between aircrafts using CDA.

#### *5.2. Probability of Aircraft Blocking*

In a queueing system of finite capacity, the probability of "blocking" is the probability that an arriving customer arriving at the queue finds it full and thus exits this system. In our context where aircrafts are the customers, the interpretation of the probability of blocking depends on whether CDA or SDA is assumed for all aircrafts during the brief time period being analyzed. If CDA is assumed for the time period, then a full queue suggests that CDA may not be used, and thus, SDA will be used instead. If SDA is assumed for the time period, then a full queue suggests that the aircraft will enter a holding pattern until the queue has available space to accommodate it. The probability of blocking is the percentage of time an aircraft's request to embark on CDA (or SDA) is denied principally due to safety and because the stacking space within the TMA is busy and congested. This probability is denoted by *Pk* and could be specified for an airport and its TMA to define a threshold beyond which CDA is unsafe to implement, or in the case of SDA, it is the probability that an aircraft will need to enter a holding pattern. Since the approach operations would be limited to the two profiles, namely CDA and SDA, then *Pk* should be determined for these two approach profiles. Theoretically, *Pk* is expressed based on the *M/M/1/k* queuing model, in which the arrival process is Poisson with rate λs and the service process is Poisson with rate μs, a single server (that is, the stacking space), and finite system capacity at *k* aircraft, as follows:

$$P\_k = \frac{1 - \rho\_{\rm ss}}{1 - \rho\_{\rm ss} k + 1} \rho\_{\rm ss}{}^k \tag{22}$$

Because the Markov (Poisson) process distribution has high variability and is assumed for both arrivals and service, the resulting probability is likely to be higher than the value experienced in practice, and thus, the Markov assumption may be viewed as conservative.

#### **6. Numerical Results to Illustrate the Model**

This section illustrates the application of our model through the use of industry standard data (e.g., minimum separation distance rules) and a stream of aircrafts arriving for landing at a mid-sized international airport during an afternoon level of demand. In particular, we used actual flight data from flights operated at Nashville International Airport (BNA) from 1200 to 1759 local time, on 17 June 2015.

Using BNA flight data and standard industry data, we calculated the probability of blocking for each type of descent profile, namely, CDA and SDA. These probabilities are denoted as *PkCDA* and *PkSDA*. *PkCDA* is the probability of blocking if all the aircrafts in the stacking space will conduct CDA, and *PkSDA* is defined as the probability of blocking if all the aircrafts in the stacking space will conduct SDA. As previously mentioned, the probability of blocking is the percentage of time an aircraft request to embark on CDA is denied for safety considerations and due to the stacking space being congested and busy and similarly the faction of time an aircraft landing with SDA would need to enter a holding pattern.

The relevant parameters in building the model are described as follows. The rate of aircrafts arriving per time period, *λss*, is determined based upon the actual number of arrivals at BNA within each of the 24 15-min time periods analyzed. The stacking space, *Sp*, was estimated by visually examining the data and assuming its value as a constant value throughout the six hours. The wind speed, *Ws*, is the average value at BNA during each time period. The aircraft approach speed, *Vapp*, is determined based on averages, across all arriving aircrafts, of their initial approach velocity and final approach velocity. The fleet mix of heavy-, medium-, and light-weight aircrafts arriving in each time period and their sequence of arrivals is determined from what actually occurred in each time period.

The minimum separation distances under SDA and CDA assumptions, *dSDA* and *dCDA*, respectively, were chosen based on ICAO's wake turbulence application [36] and matrix

model to calculate the separation distance between a mix of aircrafts proposed in [35] in each time period. As mentioned previously, these distances vary based on the wake turbulence categories of the leading and trailing aircrafts and, thus, depend on the fleet mix in each time period. Furthermore, the values of *dSDA* and *dCDA* are identical when the leading and trailing aircrafts have the same weight class and differ otherwise.

Figure 7 shows the values of the aircraft arrival rate, *λss*, over time for BNA.

**Figure 7.** The number of aircrafts arriving in each time period at BNA airport.

Consistent with Equation (17), we calculated the number of aircrafts that can fit in the stacking space if CDA is used, *kCDA*, and the number of aircraft that can fit in the stacking space if SDA is used, *kSDA*, as follows:

$$k\_{\rm CDA} = S\_p / \mathbf{d}\_{\rm CDA} \tag{23}$$

$$k\_{\rm SDA} = \mathbf{S}\_p / \mathbf{d}\_{\rm SDA} \tag{24}$$

Those values of *kCDA* and *kSDA* for BNA are shown in Figure 8. This figure may be provided as systematic output for the air traffic controllers, thus enabling them to know the bounds on the maximum number of aircrafts that may be permitted within the stacking space for each descent method. Because the minimum separation distances for CDA are longer than with SDA, the value of *kCDA* is always lower than *kSDA*, while the difference between the two varies due to the varying fleet mix and arrival sequences in each period.

Using Equation (18) to determine *Tdes*, we determined the service rate, μ*CDA* and μ*SDA*, under the CDA and SDA conditions in the following manner, using a calculation similar to Equation (19), described earlier:

$$
\mu\_{\rm CDA} = k\_{\rm CDA} / \text{Tdes}\_{\rm CDA} \tag{25}
$$

$$
\mu\_{\rm SDA} = k\_{\rm SDA} / \text{Tdes}\_{\rm SDA} \tag{26}
$$

Because CDA requires greater minimum separation distances between aircrafts than SDA, this reduces the rate at which CDA arrivals can be processed through the stacking space and, thus, results in μ*CDA* being lower than μ*SDA*.

**Figure 8.** Capacity of the TMA's stacking space *k*.

Using the above parameters and Equation (22), we calculated the values of the probabilities of blocking, *PkCDA* and *PkSDA*, for CDA and SDA, respectively, and show the results in Figure 9.

**Figure 9.** Probability of blocking of the two descent methods.

Observe in Figure 9 that the probability of CDA blocking (i.e., CDA requests being denied), *PkCDA*, is consistently less than the probability of an SDA request requiring the aircraft to enter the holding pattern, *PkSDA*. By looking at graphs such as Figure 9, the air traffic controller can see those periods of time when the vast majority of aircrafts will be able to use CDA, i.e., when the probability of CDA blocking, *PkCDA*, is sufficiently low. For example, except for the late afternoon periods between 15:00 to 15:15 and from 15:30 to 16:45, there is less than one percent probability of CDA blocking. Aside from those late afternoon exceptions, the other time periods would be favorable for permitting CDA arrivals for all (or nearly all) arriving aircrafts. Even during the late afternoon time

periods, the probability of CDA blocking is low enough that the air traffic controller may be able to permit many of the aircrafts to land using CDA. Different air traffic controllers will have different probabilities at which they will be comfortable with using CDA. Their thresholds in such decision-making may change over time as they gain experience using the model. Overall, the information should be helpful to the air traffic controllers by focusing their attention on those opportunities to increase the use of CDA and thus lead to more sustainable air transportation operations.

After deciding on the periods of time when CDA may be used for all (or nearly all) arriving aircrafts, knowing the bounds on the number of aircrafts that may fit safely in the stacking space, *kCDA* and *kSDA*, as shown in Figure 8, may help the air traffic controller to decide on an aircraft-by-aircraft basis whether to admit a particular aircraft's descent using CDA. For instance, if an aircraft arrives during a period of time when the controller plans on permitting CDA and when the actual number of aircrafts within the stacking space upon a particular aircraft's arrival at the TMA is less than *kCDA*, then the controller knows it is likely fine to accept that particular aircraft's request to use CDA, and otherwise, it is not.

#### **7. Conclusions**

Based on the analysis of the parameters that govern CDA implementation during high traffic levels, such as the terminal maneuvering area (TMA) and the size of stacking space to arrange aircraft arrivals, an analytical model has been developed that aims at addressing the accommodation of more CDA operations than is presently done. Our analysis shows that the parameters that have significant impacts on CDA usage include airport arrival rate, capacity of the stacking space, and the minimum separation distance between aircraft arrivals. Although CDA usage is also affected by other parameters, such as wind speed, types of arriving aircrafts, and traffic levels at contiguous airports, we were able to capture the underlying relationship between these parameters and CDA usage, potentially helping air traffic controllers to decide on whether to adopt more CDA more often and using more quantitative information. In particular, we calculated the probability that an aircraft arriving within a brief period of time (say 15 or 30 min) would be denied CDA as a function of airport conditions. This may enable controllers to identify those periods of time when CDA should be anticipated, in other words, when the controller should plan on permitting CDA. This may lead to an increased use of CDA and, thus, result in lower noise, fuel consumption, and pollution. Furthermore, we established bounds for the maximum number of CDA descending aircrafts would fit within the stacking space, providing insight to the controllers on whether to permit a particular aircraft to use CDA or not. Finally, we illustrated our model using actual data from flights operated at Nashville International Airport (BNA).

Future research opportunities include better support for air traffic controllers in analytically determining which arriving aircraft may be able to use CDA for a portion of their descent and when they should switch from SDA to CDA and vice versa. Another research possibility would be to analytically identify opportunities to put arriving aircrafts into a holding pattern for a short while if so doing would be result in it being able to use CDA after holding. Calculations could be performed to identify whether the additional fuel burned from holding (or adjustments to en route speed) would be more than compensated by the saved fuel from using CDA. In addition to the work presented in this paper, these research opportunities and others should be explored to improve aviation green operations and ensure air transportation sustainability.

**Author Contributions:** Conceptualization, L.L.A.-M., E.A.A. and R.J.M.; methodology, L.L.A.-M., E.A.A. and R.J.M.; software, E.A.A. and A.M.W.; validation, L.L.A.-M., R.J.M. and E.A.A.; formal analysis, E.A.A., R.J.M. and A.M.W.; investigation, E.A.A., R.J.M. and A.M.W.; resources, E.A.A.; data curation E.A.A. and A.M.W.; writing—original draft preparation, E.A.A. and R.J.M.; writing—review and editing, R.J.M.; visualization, E.A.A. and A.M.W.; supervision, L.L.A.-M.; project administration, E.A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Mode Choice Effects on Bike Sharing Systems**

**Matthias Kowald \*, Margarita Gutjar, Kai Röth, Christian Schiller and Till Dannewald**

Department of Architecture and Civil Engineering, RheinMain University of Applied Sciences, 65197 Wiesbaden, Germany<EMAIL_ADDRESS>(M.G<EMAIL_ADDRESS>(K.R<EMAIL_ADDRESS>(C.S<EMAIL_ADDRESS>(T.D.)

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Bike-sharing systems (BSS) are offered in many cities and urban municipalities and urban areas without such systems are thinking about their introduction. In addition, many studies on BSS are available; however, neither mode nor route choice parameters are available for station-based BSS, which are required for the implementation of BSS in local and regional transport demand models. As a result, this makes it impossible to simulate demand model-based effects of these systems on other transport modes and e.g., calculate scenario-guided modal shifts. The paper presents results obtained from a survey study, which aims to estimate BSS-related choice parameters. The study combined computer-assisted telephone interviews (CATI) for a collection of revealed preferences (RP) on the use of BSS with a follow-up paper-and-pencil survey on stated preferences (SP) of 220 BSS users and non-users from the Rhine-Neckar area in mid-west Germany. Considering the three transport modes BSS, public transport (PT), and private motorized transport (PMT), results from this choice experiment and, according to behavioural parameters, allow integration of BSS in transport demand models and a simulation of modal shifts. Survey design, mode-choice experiment, and choice models are presented in this paper.

**Keywords:** bike-sharing system (BSS); mode choice; stated choice experiment; multinomial logit model; transport demand model

#### **1. Introduction**

The first bike-sharing systems (BSS) were introduced around five decades ago. Over the past two to three decades, the number of BSS has increased, and such systems are nowadays available in many cities around the globe. It is, however, surprising, that parameters for neither BSS-related mode nor route choices are currently available. This results in a lack of knowledge of behavioural patterns. Amongst other purposes, such parameters are needed for the implementation of BSS as a transport mode in transport demand models and to calculate, e.g., modal shifts.

To estimate such parameters, a survey study was conducted in the field in Germany and collected information on mode- and route choices from around 220 participants in an existing station-based BSS. This BSS was introduced in 2012, and is located in the Rhine-Neckar area in mid-west Germany, including 20 municipalities in total; 4 of them are major cities (Mannheim, Ludwigshafen, Heidelberg, Kaiserslautern), 11 are mid-size municipalities and 5 are smaller towns. The survey study combined computer-assisted telephone interviews (CATI) for a collection of revealed preferences (RP) on the use of BSS with a follow-up paper-and-pencil survey on stated preferences (SP) for BSS users and non-users. The choice experiment considers the three transport modes: BSS, PT, and PMT.

This effort resulted in a rich data set, which allows an analysis of behavioural patterns in terms of BSS-related mode and route choices and a quantification of the needed parameters; with that, the study closes a knowledge gap and allows the implementation of station-based BSS in local or regional transport demand models and according to simulations with these tools.

**Citation:** Kowald, M.; Gutjar, M.; Röth, K.; Schiller, C.; Dannewald, T. Mode Choice Effects on Bike Sharing Systems. *Appl. Sci.* **2022**, *12*, 4391. https://doi.org/10.3390/app12094391

Academic Editors: Giovanni Randazzo, Anselme Muzirafuti, Dimitrios S. Paraforos and Stefania Lanza

Received: 16 March 2022 Accepted: 25 April 2022 Published: 27 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The paper focuses on mode choices exclusively. Section 2 presents results from literature analysis and aims to identify attributes of relevance for choices pro or against BSS-use. Section 3 introduces the study area and an existing BSS, that was used to recruit survey participants and collect information on BSS use. Furthermore, the recruitment strategy, survey protocol, and experimental design for the choice experiment are presented. Next, descriptive statistics on respondents' socio-demographics and their choices are provided in Section 4 together with the model formulation. Section 5 presents results on model development and the final multinomial logit models on choices between the alternatives BSS, public transport (PT), and private motorized transport (PMT). The models are estimated for mandatory and leisure trips and model results are accompanied by interpretations. Finally, conclusions and an outlook on future research are drawn in Section 6.

#### **2. Literature Review**

BSS were introduced in many cities around the globe in the last decade. In parallel, the number of studies on BSS has increased as well (for comparative meta-studies see e.g., Refs. [1–5]). Most of these studies indicate that BSS-use substitutes sustainable modes such as walking and PT; however, some report that BSS-use also reduces trips by car and other PMT means. The effect on PMT is closely related to the synergetic effects of multiand intermodal combinations of BSS with PT and promoting cycling in general [5]. In order to incorporate BSS into transport demand models and thus estimate more comprehensively the potential of reducing car trips, it is necessary to understand the mode and route choice behaviour of (potential) BSS users; so far, only a few studies focused on mode and route choice behaviour of BSS-users see Refs. [6–9], while much more studies exist for cycling with private bikes. Filling this gap is the aim of the survey, which is presented in the following sections.

Several research studies investigated the influence of different attributes on cycling. Buehler and Dill [10] reviewed the effects of cycling infrastructure; among other things, they found that cyclists tend to prefer separated bike lanes, lower speed limits and volumes of motorized traffic, trees along the route, and routes with fewer intersections; further, they tend to avoid routes with on-street parking and many variations in altitude.

Other studies investigated the effects of the built environment to enhance walking and cycling levels [11,12]. Their main findings highlight the importance of short distances to destinations, mixed land use with high densities of population and facilities for groceries, retail, service, and recreation), charges for car parking, and a network of convenient cycling infrastructure for increased shares of bike-use. What cyclists perceive as convenient highly depends on the study location, but amongst other factors, they prefer segregation or protection from motor traffic, little or only small detours, avoidance of intersections with motor traffic, and bike parking facilities.

Studies have also investigated how the built environment affects the use of bikesharing stations [13,14]. It was found that high densities and proximity to cycling-friendly routes and to PT stations play a crucial role; furthermore, a study from Lisbon described an algorithm-based approach for the identification of optimal locations for stations and fleet dimensions for BSS by taking into account user demand, renting-costs, and a mixed fleet of regular and electric bikes [15].

In addition, there are studies, which explicitly investigated the mode choice behaviour of cyclists on both private and shared bikes: Hamre and Buehler [16] studied the mode choice behaviour of around 4.600 commuters in Washington; their result is those bike parking facilities, non-free car parking, and showers at work increase the utility of commuting by bike. In another study, cycling was compared with bus riding and driving with respect to travel time reliability [17]; it was found that for habitually repeated trips, travellers rate reliability higher than travel time. Campbell et al. [6] investigated the factors influencing the choices for bike-sharing (conventional bike and e-bike) in Beijing [6]; they found that trip distance, rain, temperature, and poor air quality negatively impact the choice for non-electric BSS on the one side. On the other side, they reported that users'

socio-demographic characteristics only play a minor role. A study from Switzerland [18,19] compared several mode-specific effects on choices between PMT, PT, cycling, and walking under the inclusion of individuals' and area-specific characteristics, whereby for walking and cycling only the effect of travel time was considered as a mode-specific attribute; they found that car availability, younger age, low fuel, and parking costs, and low parking search times increase the utility of PMT, while low access and egress times, low ticket costs, and a low utilized capacity increase the utility of PT. An investigation on the Dutch mobility panel with almost 2000 participants focused on characteristics that affect choices between PMT, PT, cycling, and walking [20]. Among others, these characteristics include individual and household characteristics (such as socio-demographics and mobility ownership), weather, trip characteristics (such as distance and travel time), effects from the built environment, and work characteristics. Results indicate that, among other things, higher education, transit subscription, cycling to high school, weekdays, and certain trip purposes increase the utility of cycling, while owning a company car and travelling in larger groups decrease its utility. A recent study compared shared modes in Zurich, namely station-based BSS, e-bike sharing systems (e-BSS), and e-scooters [7]; they found that station density and morning hours increased the utility of BSS, while variation in topographical altitude and night hours decreased its utility. Ilahi et al., (2021) undertook an extensive survey with more than 5000 participants from the Greater Jakarta area in which they also incorporated less-established modes such as urban air mobility, including currently developed electricbased aircraft or autonomous vertical take-off and landing vehicles, on-demand transport, and bus rapid transit [21]; they found that motorcycles have the highest baseline utility, while bikes have the second-lowest.

In addition, numerous studies have focused on the route choices of cyclists. Although this paper is primarily focused on mode choices, it can be expected that route choice effects in general also affect mode choices. A recent study with 662 participants from Greece and Germany investigated the effects of cycling infrastructure, speed limit, surface, on-street parking, trees, and travel time on route choices [22]; they found that in both countries protected bike lanes are preferred over other forms of infrastructure. Furthermore, asphalt is preferred over cobblestone, while the utility of a speed limit depends on the country. Other attributes that were incorporated in older studies are the number of car lanes [23], stop signs and crowding of cyclists [24], number and type of crossings [25], the width of bike lanes and traffic volumes [26], as well as sharing space with pedestrians and the availability of secure parking and showers at the destination [27].

With reference to the presented studies, it can be assumed that relevant attributes for cycling with private bikes are relevant for BSS, too. Furthermore, additional attributes, such as renting costs, access and egress times, to renting stations are relevant in the case of BSS. Evaluating which effects are of relevance for BSS and quantifying their influence is the aim of our survey study. The employed survey design and choice experiment are introduced in the following section. The study aims to provide an overview of the most relevant effects to allow the implementation of BSS in multi-modal transport demand models, and, with that, to provide a basis for forecasts on urban transport, which consider BSS as an alternative transport mode.

#### **3. Survey Design and Choice Experiment**

In 2020, the transport association Rhine-Neckar (VRN) decided to evaluate the performance of its BSS named VRNnextbike and especially focus on users and their behavioural patterns such as e.g., origins and destinations of rental bike trips, trip purposes, average renting times, and distances. Figure 1 provides an overview of the supply area of VRNnextbike, which lies in Mid-West Germany; it includes 20 municipalities in total; 4 of these municipalities are major cities (Mannheim, Ludwigshafen, Heidelberg, Kaiserslautern), 16 are minor cities with 11 mid-size municipalities and 5 smaller towns.

**Figure 1.** The supply area of VRNnextbike.

Figure 2 provides an overview of the absolute development of bike rents between 2015 and 2020; it documents a positive development trend and repeating temporal patterns between annual seasons. Furthermore, it shows the effect of the first Corona-Lockdown in the second quarter of 2020 and the quick recovery of the system in the third quarter.

**Figure 2.** Quarterly development of the absolute number of rents.

Evaluating the BSS VRNnextbike and analyzing user behaviour in terms of, e.g., sociodemographics made it necessary to design a survey study. This provided the opportunity to include items on the effects of mode and route choices in terms of a BSS and to quantify mode and route choice parameters. Collecting data on BSS-related mode and route choices; however, made it necessary to extend the survey framework and include a stated choice experiment. In addition, the target population had to be extended. While the VRN-survey wanted to focus on BSS users exclusively, the choice experiment made it necessary to include non-users as well, to understand differences in the perception between these two groups and allow a later simulation of, e.g., modal shifts. For this reason, a hybrid recruitment strategy and a specific survey protocol for BSS users on the one side and non-users on the other side were employed and a stated preference experiment was developed and included in the survey.

The following descriptions and data analyses focus on the mode choice experiment exclusively. The route choice experiment and recording results will be presented in the future. Readers who are interested in the results are encouraged to contact the research team.

#### *3.1. Recruitment Strategy*

Table 1 presents an overview of the frame population and recruitment strategy of the survey study, which was split and specifically designed for BSS users and non-users. BSS users, on the one side, were recruited electronically either before or after renting a bike from VRNnextbike. During the electronic check-in or -out of the rented bike in the VRNnextbike smartphone app, they have presented an invitation to participate in a computer-assisted telephone interview (CATI) on their travel behaviour, bike-rent habits, and the BSS-trip they performed either before or after the recruitment. To participate, they were asked to mention their preferred daytime for a 30-min telephone interview within the next week and, in addition, to report their age, gender, and city of residence in an electronic recruitment questionnaire. Questions on socio-demographics aimed to keep control over the distribution of socio-demographic characteristics in the CATI sample. Participation in the electronic recruitment questionnaire took about two minutes on a smartphone. Accompanying the questions, information on data protection and the aim of the research project was provided on linked websites and an incentive of EUR 20 for participation in the CATI was mentioned. After participants completed the CATI, they were recruited for the subsequent paper-and-pencil questionnaire, which was sent via postal mail to the respondents. Enhancing convenient participation was the aim of this study, ensured by sending an addressed and postpaid mail-back envelope together with the questionnaire, including additional information on the study and data protection.

#### **Table 1.** Frame population and recruitment strategy.

BSS non-users, on the other side, were recruited from a sample of randomly generated phone numbers for the supply area of VRNnextbike. These phone numbers might in some cases have resulted in interviews with BSS-users; however, this approach was chosen as only 2.9% of all inhabitants in the supply area are BSS-users and sampling a user of VRNnextbike was for this reason rather unlikely; furthermore, a control questions whether respondents are BSS users was added to allow the identification in the analysis. Recruitment of this subsample was done via telephone by asking for gender, age, and city of residence to keep control over the distribution of socio-demographic characteristics. In addition, the telephone recruitment aimed to provide information on the study, and data protection issues and to discuss potential respondents´ questions. In addition, an incentive of EUR 20 was offered for a filled-out survey instrument. Like in the sample for BSS users, the printed paper-and-pencil questionnaire was sent via postal mail to the respondents, which included an addressed and postpaid mail-back envelope.

#### *3.2. Revealed and Stated Preferences: Survey Protocol*

Choices on, e.g., transport modes and routes can be observed either in real-life situations or in hypothetical choice situations. Real-life observations result in information on revealed preferences (RP) whereas observations of hypothetical choices result in data

on stated preferences (SP). RP data have the advantage of representing peoples' actual behaviour; they, however, also include disadvantages such as little variation in attributes, which could be used to explain choices (e.g., travel times by bus on a specific route), and issues of multicollinearity (e.g., travel times, distances, and costs are often highly correlated for a specific transport mean). In addition, future effects, demands, and supplies cannot be addressed with RP data. SP and according to hypothetical choices overcome these issues. Here, an experimental design is employed, that focuses on selected and potentially future attributes. It asks respondents to exclusively consider these selected effects when making their choices. Attribute variation is controlled by an experimental design, which allows overcoming the challenge of multicollinearity. The disadvantages are, however, the hypothetical character of the choice tasks and the reduction of complexity (for a more detailed discussion on RP- and SP choices see, e.g., Refs. [19,28,29]).

In transport planning, RP and SP data are often combined to overcome the mentioned limitations of the SP approach. One way to increase the reliability of SP choices is to employ an individual´s RP decisions as the basis for her or his SP-choice situations [30] (for a discussion of combined RP–SP studies see Ref. [19]). This means, on the one hand, an increased complexity for the fieldwork, as choice situations are individually tailored for each participant of the SP survey. On the other hand, the RP–SP combination increases the quality of a survey as the choice situations are based on former choices of a respondent, transport familiarity and thus allow an easy imagination of the choice situation under observation. The more realistic and familiar a choice situation is, the less effort it takes to be contextualized resulting in more reliable respondents' answers (for choice situations see Ref. [31]; for a more general discussion on response burden see Ref. [32])

In the CATI for BSS-users, information on mobility-tool ownership, trip characteristics of the BSS-use at the time of recruitment, attitudes on BSS, and socio-demographics were collected. During the interview, the chosen route of the rental bike trip was traced electronically by employing an online routing tool [33] to gather additional information for the trip, such as travel time and road surface. The collected information and RP data were employed as a basis for the mode choice experiment. Based on these BSS attributes, trip characteristics for the alternative modes PT and PMT were collected using an online routing provider [34] and an electronic PT-schedule service [35]. The choice experiment itself was designed as a follow-up survey and presented to those CATI participants, who agreed in filling out the paper-and-pencil questionnaire.

As RP data were not available for BSS non-users, aggregated RP characteristics on BSS usage were employed as the basis for the SP experiment. The aggregated figures for travel time were calculated on the automatically recorded data from the BSS VRNnextbike by discriminating between short, middle, and long trips for both major and minor cities (on average trips of the length of 0.8, 1.5, and 3.2 km for major cities, and 0.7, 1.4, and 4.4 km for minor cities), while averages for access and egress times were obtained from the BSS user-survey. In this case, data on mode alternatives were based on aggregated figures from the national travel survey in Germany [36], taking into account differences between major and minor cities. To design an individual questionnaire for this subsample, firstly, each respondent was assigned to a town size group based on his or her postal address. Secondly, every participant was sequentially assigned to a short, middle, or long trip distance and a trip purpose, either a leisure or mandatory activity at the trip destination. The resulting RP-values for each BSS non-user were employed as the basis for SP-experiment and its variations of attributes.

The recruitment procedure of both subsamples is visualized in Figure 3.

**Figure 3.** Schema of survey protocol.

*3.3. Experimental Design and Choice Situations*

Attributes of the mode choice experiment were taken from former studies on mode choices and studies on selected transport modes such as bikes, PMT, and PT (see Literature Review in Section 2). Furthermore, they were discussed with external academic partners and practitioners from transport planning offices.

As described above, RP information (for BSS users) or aggregated empirical figures (for BSS-non-users) were employed and empirical values for the alternative modes were collected. Next, an individually tailored SP questionnaire was created by varying the mode-specific characteristics in accordance with a predefined experimental design. An overview of the attributes and variation of attribute levels is provided in Table 2.

**Table 2.** Stated preference experiment: transport modes, attributes and variation.

To reduce the number of possible combinations of the presented variation levels, an efficient design [37] was generated with the software Ngene [38]; it resulted in 60 combinations to design the choice tasks, which were split into six blocks (the experimental design is available upon request). Each participant was assigned to one block and the empirical values were varied accordingly. Finally, each participant was asked to complete ten choice

tasks in the paper-and-pencil questionnaire. Participation in the study was restricted to adults (18 years and older) owning a driver's license to make the alternative PMT realistic.

The individually tailored paper-and-pencil questionnaires were created, printed and sent within one week after recruitment to avoid fatigue effects. To increase reliability in terms of PT utilized capacity, an illustration accompanied the questionnaire (see Figure 4; for more details on reliability see Ref. [19]).

**Figure 4.** Illustration of capacity utilization (illustrations taken from Weis et al. [19]).

Both the survey protocol and instrument followed the suggestions by Dillmann [39]. After four weeks of non-response, reminders were sent with a new copy of the questionnaire. An exemplary choice situation is shown in Figure 5.

**Figure 5.** Example of a choice task.

#### **4. Descriptive Statistics and Modelling Approach**

The survey was in the field from September 2021 to February 2022. After data cleaning, information from 220 respondents, who filled out and returned the questionnaire, was collected. On average, respondents answered 9.93 (median = 10) mode choice tasks, which resulted in a total of 2184 observations for the analysis. 27 respondents (12.3%) showed non-trading behaviour, meaning they chose an identical transport mode in all presented choice tasks.

#### *4.1. Descriptive Statistics*

Respondents from the subsample recruited via randomly generated phone numbers (see subsample 2 in Table 3), who indicated to use a BSS, are considered BSS-users in the following analytical procedure (*n* = 11). Information on the distribution of selected socio-demographic characteristics and the frequency of chosen transport modes in the choice experiment for both subsamples and the whole sample are presented in Table 3.

**Table 3.** Relative frequency distribution of selected sample characteristics.

Around 58% of all participants were BSS users and 42% are non-users. Users were more often males (64.1%) than non-users (41.3%). For the whole sample, the gender proportion was more balanced with 54.5% males and 45.5% females. BSS users belonged remarkably more often to younger age groups than non-users. Again, the proportion between young adults (18–30 years; 47.3%) and middle-aged persons (31–65 years; 41.8%) was more balanced for the whole sample. There are only a few observations of people in the retired age group (66–94 years): 0% for BSS-users, 26% for non-users and around 11% for the whole sample. Furthermore, around 89% of the user-sample lives in cities, 9% in larger towns and around 2% in small municipalities. This fits well with the automatically tracked renting numbers of VRNnextbike [40]. The non-user sample includes more respondents from larger towns (25%) and small municipalities (around 11%). In summary, there is socio-demographic variation in the data, and it can be assumed that evaluations from people with different socio-demographic characteristics are considered in the analysis.

Concerning mode choice situations, respondents from the user sample most often chose the BSS (around 60%), followed by PT (around 32%) and PMT (9%). Non-users also preferred the BSS (64%), however, followed by PMT (37%) and PT (22%).

Covariates in the behavioural experiment are based on RP-data for subsample 1, respondents recruited during the CATI, and on aggregated empirical figures for subsample 2, respondents recruited from the random phone number sample. Table 4 presents the empirical distribution of these covariates as included in the experiment.

**Table 4.** Empirical distribution of covariates in a choice experiment.

In terms of the BSS, access and egress time has a minimum of 1 min, a median of 6 min, a mean of around 6 min and a maximum of 49 min. This distribution is comparable to access and egress for PT. BSS trips are short with a median travel time of 10 min and 15 min for the 3rd quartile. A few trips, however, are long with a maximum of 108 min. Travel costs are low, with EUR 1.80 for the 3rd quartile.

The overall travel time (including parking search time) of PMT is substantially higher than the travel time for BSS and PT. The minimum travel time is 6 min, 1st quartile at 12 min, median at 15 and 3rd quartile at 19 min. The maximum travel time, however, is 46 min and substantially lower than the maximum travel times for BSS and PT. Fuel costs for the trip show a range between EUR 0.10 for a very short trip and EUR 6.20. Parking costs lay between EUR 0.60 and EUR 4.80 with a median of EUR 3.20.

Access and egress times and travel times for PT are overall comparable to BSS. In terms of travel costs, PT shows moderate values between BSS and PMT.

#### *4.2. Model Formulation*

Discrete choice data, where respondents choose between a limited number of alternatives, are commonly analyzed by applying random utility maximization theory. The theory assumes rational behaviour in which respondents choose the alternative with the highest utility [29,41–43]. Namely, an individual *n* faced with *J* alternatives in *T* choice tasks associates an indirect utility *Unjt* for an alternative *j* in a choice task *t* and chooses the alternative with the highest utility. The utility of an alternative *j* is therefore decomposed as

$$
\mathcal{U}\_{\rm njt} = V\_{\rm njt} + \varepsilon\_{\rm njt} = \mathfrak{x}'\_{\rm njt}\mathcal{B} + \varepsilon\_{\rm njt} \tag{1}
$$

where *Unjt* is not observed, but *Vnjt* is the deterministic utility of alternative *j*, and *εnjt* is a random component not included in *Vnjt*. The deterministic utility *Vnjt* can be specified by the term *x njt*, where *x* is a vector of explanatory variables (e.g., attribute levels), and *β* is the corresponding coefficients to be estimated.

For each alternative, a utility function (*Vnjt*) is specified, whereby the alternativespecific attributes, characteristics of the respondent or the choice situation are included as explanatory variables. When specifying the utility function, it is important to understand that only the differences in utility matter, while the scale of utility is arbitrary [29] (p. 19). Therefore, to capture the differences in the utility of the alternatives, *J*-1 alternative-specific constants (ASC) are specified, whereby the estimated ASCs are interpreted relative to the omitted alternative, which is normalized to zero [29,43]. For the categorical attributes, street type, surface type, and utilized capacity, the *L* levels of each attribute were transformed into *L* − 1 dummy variables. This means, the utility for one level per attribute is normalized to zero and serves as a reference category, while the parameter estimates for the *L* − 1 dummy variables capture the utility differences to this reference category [28,29,43].

#### **5. Results**

The 2184 observations (choice tasks) were analyzed by estimating multinomial logit models (MNL) [44] in R [45,46], whereby BSS was chosen as reference alternative when specifying the equations for estimation. Firstly, an initial MNL was estimated by including exclusively effects of attributes from the choice experiment (see Table 2; for a documentation of this work see Ref. [47]). With reference to previous studies on mode choice [18–21] effects of socio-demographics (age, gender, education, student status, car availability, PT season ticket availability), home municipality, and season (winter vs. autumn) were expected. Consequently, as recommended in methodological literature [29,44] the initial model was sequentially built up by including these effects as alternative-specific attributes in maximum *J*-1 alternatives (one alternative as reference category), testing the hypotheses, and comparing the models (restricted vs. unrestricted) to omit parameters without significant effects and/or substantial improvement in the model fit. Further, it was assumed that the effects of travel time and travel costs depend on household income and the distance of the trip, and this is why corresponding continuous interactions were specified [18,19]; however, these interactions neither had a significant effect nor made a substantial improvement of the model and thus are not presented. All analytical steps along with estimated models can be made available on request. Table 5 provides an overview on model fit between the initial model, which exclusively included effects from attributes of the choice experiment, and the extended, final model, which is presented below. The likelihood ratio-test indicates a significantly better fit for the final model, which is supported by the increase in adjusted Rho-square, and by the decrease in AIC and BIC (for evaluation of model fit indices and model comparison, please review methodological literature, Refs. [29,44]).

**Table 5.** Model fit comparison between the initial and the final model.

Employing the estimated parameters in transport demand models at a later stage of the project requires a distinction between mandatory and leisure trips. Mandatory trips are those with destinations for purposes such as education, work, business, or home. Leisure trips are those with destinations such as shopping, private activities and tasks, or any leisure activities. Usually, people have more degrees of freedom in destination choice for leisure than for mandatory activities. Therefore, the trip purpose was included as alternativespecific attribute in the final model on the total sample. In addition, segregated models were estimated on a subsample for mandatory and a subsample for leisure trips. The results of all three models, the overall (total) model on all observations, and the segregated model on mandatory and leisure trips, are presented in Table 6.

All parameters for the final model show the expected sign and reasonable differences in parameter values. For all modes (BS, PMT, and PT), the estimated parameters for travel time and time for access and egress show a negative effect. Hereby the negative effect is stronger for access and egress, which was expected as ride-times in or on a vehicle are often considered less negatively than waiting times or access and egress-times [19]. Travel costs demonstrate a negatively associated utility for all modes. In addition, parking costs and fuel costs for PMT are negative, too.

For BS, the data do not support any significant difference in utility for the street type; however, with reference category arterial road, the cycleway has a higher positive estimated utility (β = 0.195, t-value = 1.339) and the side street has a negative utility (β = −0.013, t-value = 0.089). This negative utility of side streets can be explained with a detour-association in comparison to the probably more direct and thus shorter route on an arterial road. Relatively to macadam surface, cobblestones do not show differences in utility (β = 0.004, t-value = 0.028), while asphalt is a more preferred surface type; however, the effect is also not significant (β = 0.239, t-value = 1.634).

For PMT and PT, the estimated ASCs show the differences in utility of a given alternative from the reference BS when everything else is equal [44]. The utility of PMT is higher than for BS (β = 0.669, t-value = 1.059), whereby the direction of the effect changes when comparing mandatory trips (β = −1.677, t-value = 1.389) to leisure trips (β = 0.980, t-value = 1.233). This can be explained with the high share of commuters and students mainly using the system for trips to work and education. For these people, BS has a higher utility as PMT. This interpretation is also supported by the negative sign for mandatory trips in the overall (total) model (β = −0.608, t-value = −3.739). In addition, PT has a higher positive utility than BS, too (β = 0.756, t-value = 1.552), whereby there is no change in sign between mandatory and leisure trips. Influences from the spatial typology are limited to PMT, where the utility for PMT decreases with an increasing size of the home municipality. For PT, a mode-specific effect results from capacity utilization. An increasing utilization results in a decreasing utility for PT.

**Table 6.** Results of MNL models for all observations (total) and trip specific models.

In terms of socio-demographics, the effect of age and age-squared shows a u-shaped distribution of utility for both, PMT and PT (see Figure 6). Choosing PMT has a negative utility from 18 to 64 years, whereby the smallest value is reached between 32 and 33 years. From this age on the utility of PMT increases again. A somehow similar picture is observed for PT, where PT has a negative utility in comparison to BS between 18 and 55 years. The lowest utility is calculated for an age of 28 years. From this age on the utility of PT increases in comparison to BS.

For women, PMT has a higher utility than BS (β= 0.745, t-value= 4.976). This effect is different for PT, where the utility for women is negative (β= −0.109, t-value= 0.840). This pattern fits the results of other studies, which show that women appreciate the privacy of cars (for a general discussion on car use and gender see, e.g., Ref. [48]) and perhaps BSS in comparison to PT.

Furthermore, in comparison to BS, having a car always available increases the use of PMT (β = 0.627, t-value = 3.056), while owning a PT season ticket increases the utility of PT (β = 0.433, t-value = 3.241) and decreases the utility of PMT (β = −0.494, t-value = −2.897). In winter, both, PMT (β = 0.360, t-value = 2.230) and PT (β = 0.643, t-value = 4.322) are more preferred than BS.

**Figure 6.** Example of a choice task.

#### **6. Conclusions**

The survey resulted in behavioral parameters, which show the expected signs and allow a straightforward interpretation. It has to be kept in mind that the survey was in the field between September 2020 and February 2021. In this rather cold season of the year, BSS-using figures are low, and it can be assumed that the share of experienced users is overrepresented, whilst occasional users are underrepresented in comparison to the warmer season. This, however, does not necessarily lead to bias in the data.

In addition, our study has a regional character. Topographically seen, the supply area of VRNnextbike is rather flat with some hills. Mountains and large altitudinal differences are rare if present at all. Even though altitude was not considered in the choice experiment, there is a correlation with travel time and with travel time related costs; this has to be considered when statistical results are employed in other regions.

In general, results can be used to implement BSS in transport demand models. The main empirical findings are:

Analyses, however, are not finished yet. Future work will be on a calculation of willingness to pay values (WTP) as well as values for travel time savings (VTTS). These values will allow a comparison to similar studies for PT and PMT and will show to what extent the above presented results are similar and reasonable. In addition, parameters for route choices have to be estimated. Once this is done, BSS-parameters will be implemented in an existing regional transport demand model and three scenarios will be simulated:

4. Estimation of route-choice parameters, implementation of BSS in a transport demand model and calculation of modal shifts along the above-mentioned scenarios will be documented later and published elsewhere. The present work, however, represents one necessary next step for a better understanding of a good established transport mode in cities and urban areas. In terms of data collection and analysis, it would be good to combine survey data on cycling in general with sensor-based data on, e.g., cycling safety [49].

**Author Contributions:** Conceptualization and methodology: M.K., T.D., C.S.; writing: M.K.; data acquisition: K.R., M.G., M.K.; data analysis: M.G.; literature review: K.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the state of Hessian and the House of Logistics (HOLM) in the program "Innovations in logistics and mobility" of the Hessian Ministry for Economic Affairs, Energy, Transport and Housing, grant number HA-No. 1013/21-15. Open Access funding provided by the Open Access Publication Fund of RheinMain University of Applied Sciences.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The survey data can be obtained from the corresponding author. Interested researchers are asked to send a data request via e-mail.