Comparing Light Rail and Bus Semirapid Transit on a Level Playing Field: A Model Oriented to Ex Ante Evaluation Under Uncertain Conditions

Abstract

Light Rail Transit (LRT) and Bus Semirapid Transit (BST) are two different forms of semirapid, medium-capacity transit systems. Over recent decades, there has been an ongoing, unresolved debate on which of these two technologies brings about a higher net contribution to a society’s welfare. This study seeks to shed light on this topic through the design, development, and computational execution of a model specifically devised for forecasting transport-related outcomes that would result from the implementation of either an LRT or BST system in a given corridor. This model dynamically systematizes the mutual interactions between travel demand prognoses, the supply attributes of a typical set of modal alternatives, the valuation of those modal alternatives from travelers’ perspectives, and travelers’ consequent choices, taking into account the specific differences between LRT and BST. Furthermore, the model incorporates a methodological treatment of uncertainty through the application of Monte Carlo random simulation techniques. In practice, the model is applied to a case study based on artificial data representative of usual conditions seen in corridors with enough ridership to consider these transit systems. The specific results indicate that LRT generates a moderately higher benefit for travelers in these circumstances, but this turns into a very slight advantage for BST when the investment costs are deducted. Ultimately, this research will contribute to better-informed decision making when selecting a semirapid, medium-capacity transit system, leading to more efficient budget allocation.

1. Introduction

1.1. Context and Motivations

One of the most pressing challenges that today’s cities and metropolitan areas must face is meeting the mobility needs of their population and visitors in accordance with a context currently marked by aspirations to improve sustainability, involving economic, social, and environmental issues. It is widely recognized that public transit (PT) networks currently and will continue to play—in the short, medium, and long term—a key role in the accomplishment of this goal.

Concerning the provision of collective PT services in cities and metropolitan areas, it is relatively common to find corridors (or axes, or trunk or arterial routes) that gather medium PT ridership volumes. In this regard, medium PT ridership volumes are understood to, on the one hand, make conventional bus services in mixed traffic insufficient or unable to meet the demands of the potential ridership volume satisfactorily, i.e., without downgrading the level of service of public transit services. On the other hand, medium PT ridership volumes appear to be clearly insufficient to justify—with a minimal reasonable efficiency—the introduction of urban/metropolitan mass rapid transit systems such as heavy rail, metro/subways, or full BRT (as originally conceived in Latin America), given their very high investment costs and “hard” introduction into the urban layout. In practice, corridors with medium PT ridership volumes are often found in medium-sized cities (approximately 200,000–800,000 inhabitants in a European context) in one or a few of the structural, trunk axes of their urban transport networks, but also in big cities and metropolitan areas in the form of feeder routes.

When the construction of a new urban/metropolitan PT system for this kind of corridor is under consideration (usually as a replacement for a pre-existing service rendered by conventional buses in mixed traffic), planning administrations and PT authorities are faced with the selection of one of the PT modes that are classified generically as medium-capacity transit systems (broadly equivalent, in practice, to semirapid transit systems). The principal decision is a choice between the two basic types of medium-capacity transit systems: light rail modes and bus semirapid transit systems with exclusive right-of-way. Although the specific terminology used for these systems varies significantly around the world, in the first group, we include Light Rail Transit (LRT) and “modern” (contemporary) tramways (that is, with exclusive right-of-way). In the group of bus semirapid transit (BST) systems, we can include systems termed as Buses with High Level of Service, or BHLS (with this term restricted to the highest degrees of dedicated infrastructure, that is, “full BHLS”), as well as many of the systems commonly—but imprecisely—designated as Bus Rapid Transit or BRT (i.e., excluding from this category high-capacity “full BRT” systems, as are typically found in Latin American and Asian metropolises, which are indeed mass rapid—not medium-capacity semirapid—transit systems).

In general, there is not a sufficiently broad and accepted consensus on which type of medium-capacity transit system yields a higher net contribution to the overall welfare of society, as can be seen in the literature review we provide in Section 2. This fact further strengthens the necessity to apply, to each specific case, technically sound methods of appraisal and selecting alternatives, such as Cost–Benefit Analyses. Additionally, the appropriate application of these techniques to an ex ante evaluation (that is, with prospective purposes prior to implementing the plans or projects under assessment) is critically conditional upon the validity, reliability, and accuracy of the future values of a very wide set of transport and transport-economic variables, which must be obtained from a prognostic exercise. At the same time, a rational, consistent prognosis necessitates indispensably the analytical modeling of the system under study (here, a certain portion of the transport network) along with its evolution through the different scenarios that result from every alternative project or plan.

Accordingly, the first objective of this study is the design, development, and computational implementation of a model specifically devised for forecasting the effects on urban/metropolitan transport caused by the hypothetical introduction—into a corridor with given characteristics—of either a light rail medium-capacity transit system (LRT/tramway) or a bus semirapid transit system (BST), placing a comprehensive, detailed focus on the particular features and qualities of each of these PT systems and on their respective impacts. The effects on transport will be quantified in the model by means of a set of variables including, among others, changes in trip volumes, operational parameters of PT service, traffic conditions of private motorized travel, and trip attributes (transformed into respective travel costs). In addition, the design of the model should allow for the incorporation of the uncertainty inherent to any forecasting exercise, linked both to the data or input variables and to the modeling itself. Ultimately, the set of variables resulting from the transport model calculations will be available for eventual use as inputs into quantitative evaluation methods such as Cost–Benefit Analyses.

The second aim of this research is to put into practice the developed model by applying it to a case study based on a set of artificial data that have been carefully designed to illustrate some typical conditions in corridors with medium PT-ridership volumes. Besides testing and checking the functionality of the model, the results of this exercise should contribute to shed light on the decision between rail-based and bus-based medium-capacity transit systems, although without neglecting the limitations in the scope of applicability of this study’s conclusions, since they are drawn from a single, specific set of data.

The remainder of this paper is organized as follows: Section 1.2 provides a brief overview of the key characteristics of medium-capacity transit systems; Section 2 provides a review of the relevant literature on this topic; Section 3 provides a description of the model’s development from a methodological perspective, with Section 4 presenting its practical application in an illustrative artificial case study with a discussion of the most meaningful results; and Section 5 summarizes the principal conclusions extracted from this research.

1.2. Some Notes on Medium-Capacity Transit Systems

The concept of medium-capacity transit systems has been introduced in Section 1.1, in which we define them as PT systems that cover the range between the upper limit of adequacy of conventional buses in mixed traffic and the lower limit of socioeconomic efficiency of mass rapid transit systems. The quantitative determination of these limits is a contextual issue, i.e., it depends strongly on local factors, so there are no “one-size-fits-all” figures that can be generalized and accepted as valid in all situations. Nevertheless, it could be said that medium-capacity transit systems are usually the most suitable option for peak hour volumes of passengers (pphpd) ranging from 1200–1500 passengers per hour and direction (prs/h-dir) to around 10,000 prs/h-dir. However, as explained before, these figures must be taken with caution.

Medium-capacity transit systems—either rail-based or bus-based—are also characterized by some infrastructural features that shape the usual operating environment for these systems. These infrastructural features are in fact typical of the semirapid transit category, which emphasizes the similarities between both concepts. These three common features can be summarized as follows:

• These transit systems are conceived as on-surface modes (i.e., running at ground level), which entails the regular presence of at-grade crossings with other intersecting traffic, crosswalks, etc. There may be some specific grade-separated crossings along the route, but there should only be few.
• The PT systems in this category operate—at least for the vast majority of their route—on a right-of-way specifically reserved for transit use at all times, preferably with longitudinal physical obstacles such as curbs and green strips. This degree of reservation of the right-of-way is technically known as category B according to the classification stated by [1] (pp. 5–6), or as an exclusive operating environment according to the terminology of the ‘Transit Capacity and Quality of Service Manual’ [2] (pp. 2.31–2.35).
• These PT modes must be provided with some level of Transit Signal Priority (TSP) system that gives priority to transit vehicles at intersections over general crossing traffic by altering traffic signal timing when necessary, in order to favor a non-interrupted circulation of the transit vehicle from a station or stop to the next.

Clearly, the three basic features noted above are insufficient to fully characterize medium-capacity transit systems, as many other factors should be considered. Although the in-depth examination of all of these features is beyond the scope of this article, a discussion of those factors, along with the comparative advantages and disadvantages of LRT and BHLS/BRT systems, can be found in [3].

A disparity between bus- and rail-based medium-capacity transit systems that should be noted, due to its later impacts on some model calculations (particularly in relation to transit operations, service scheduling, and derived service attributes), is the difference in the static capacity of the vehicles (or transit units, TU) typically employed. In LRT/tramway systems, the vehicle capacity (measured for a standing passengers density of 4 sps/m² as the maximum acceptable comfort limit) usually ranges from 120 sps/veh (in compact trams 22–24 m long) to around 320 sps/veh (for light rail vehicles 45 m long), with the opportunity to couple more than one vehicle into a compound transit unit if the line’s infrastructure is adapted to this. On the other hand, the typical capacity of buses employed in BST (also with 4 sps/m²) varies around 64–68 sps/veh for rigid regular buses 12 m long, around 98–115 sps/veh for articulated buses 18 m long, and from 120 to 150 sps/veh for bi-articulated buses (24–28 m long). These differences clearly impact the service frequency (and thus the headway) required to achieve the same scheduled line capacity.

2. Literature Review

Comparative analyses between rail- and bus-based urban and/or metropolitan transit modes have a history spanning several decades. However, previous research is strongly heterogenous in terms of approach, scope of analysis, and methodological framework, which has led to noticeably diverse results. Therefore, the best way to survey the literature on this broad topic is by grouping previous studies according to their different kinds of approach.

Many previous studies address this topic from a more or less general approach, sometimes even through qualitative estimations. D. A. Hensher and W. G. Waters, as authors of [4], are often regarded as the experts who triggered the debate on the excessive use of LRT systems instead of bus priority systems, concluding that the latter can transport comparable passenger volumes at a lower cost than LRT. Over the years that followed, D. A. Hensher has stimulated and revitalized this debate with several contributions [5,6,7]. The most recent of them, Ref. [8], remarks the recurrent lack of serious consideration of BRT as an alternative to light rail, particularly in several Australian cities. Some studies taking a general approach have been based on case studies in which the deployment and impacts of new transit systems of one or both types have been analyzed, either focusing on a specific location, region, or country [9,10], or taking a wider perspective [11,12]. Many other studies that have dealt with this topic with a general approach have been based on a mix of the authors’ own experience and background, knowledge gained from thorough collection and examination of academic and/or empirical information, reviews of available technical data, and other literature surveys [3,13,14,15,16,17]. This is also the case for [18], which presented a systematic comparison of Light Rail and Bus Semirapid Transit (BST) in order to identify their relative advantages and disadvantages and to define the optimal domains of each, and [19], in which the author argues again in favor of the term Bus Semirapid Transit (BST) instead of the more ambiguous BRT and summarizes the superiorities of LRT or BST in relation to several characteristics. Sometimes, rail- and bus-based transit modes are compared by means of a meta-analysis [20], considering costs, capacity, and land use impacts. Finally, there are other studies in which the comparative analysis is focalized on extracting conclusions from the features adopted and the results of a successful real-life case of BHLS/BRT implementation [21], or through the virtual replacement of an actual LRT with a notional BRT [22].

Another category of research dealing with the comparative analysis between rail- and bus-based transit modes consists of studies that focus their attention on the demand potential of these systems and their distinct ability to attract travelers. Many of these research efforts aim to elucidate and quantify the hypothetical existence of an inherent preference of PT riders and other potential PT users for one of the two types of systems (usually rail-based modes). One of the first studies that aimed at this goal was Ref. [23], which analyzed a survey program performed in the city of Dresden (Germany) when some tram lines were replaced with bus services, revealing the presence of a weak but consistent preference for rail-based transport (“rail bonus”). Nevertheless, Ref. [24] examined the possibility of a preference for rail over bus travel through the estimation of discrete choice models among alternative travel modes, but it concluded that there was no evident preference for rail over bus if quantitative service characteristics are equivalent. With relatively similar objectives, discrete choice models have also been used in [25,26,27], as well as in [28], which explored travelers’ preferences for BRT or LRT systems in developing countries. Moreover, among the variety of methodological approaches and scopes investigated, we also find the use of a trip attribute approach for examining the relative passenger attractiveness of BRT compared to on-street bus, light rail, and heavy rail systems [29]; a qualitative study of travelers’ attitudes toward several public transport modes and private cars [30]; a synthesis of research literature, documented experience from a series of studies, and results of an international bus expert Delphi survey [31]; the use of focus groups and an attitudinal survey [32]; a multiple linear regression model to explore possible differences in the ridership drivers of BRT and LRT lines [33]; and the use of fixed-effects panel regression models to investigate the ridership effect of implementing new LRT and arterial BRT in corridors already well-served by local bus routes [34].

The third main category of research on the comparison and informed choice between rail- and bus-based transit modes comprises studies that tackle detailed analyses of the costs entailed by both classes of systems and/or that attempt to advance toward a comprehensive evaluation of such transit modes.

The first kind of approach adopted in studies within this category consists of analyzing the costs (mostly producer costs such as initial investments, operation and maintenance costs, etc.) commonly occasioned by the implementation and operation of one or both types of transit technology. In this line of work, the authors of Ref. [35] developed a parametric cost model to provide both average and marginal cost estimates and to compare the annual operating costs for LRT and BRT. Furthermore, Ref. [36] presented a tool to assess the most suitable public transit technology for urban and inter-urban corridors by means of a model that calculates total social cost. This model was updated and extended years later in [37], by incorporating the effect of endogenous demand. Another cost estimating model is found in [38], which provides the total and annualized capital costs, operating and maintenance costs, and cost per passenger-mile both for LRT and BRT. Also, Ref. [39] developed a model to assist with choosing between BRT and LRT by computing the annualized capital and operating costs over a wide range of demand for systems with characteristics specified by the user, along with local energy-related emissions for both technologies. Exhaustive, detailed comparisons of implementation costs (capital costs), and operating and maintenance costs, of an LRT/tramway system and a similar-quality BRT have been contributed by [40] in Germany, and by [41,42] in the UK.

Another methodological line advancing toward the comparative appraisal of both PT systems is based on the development of optimization models intended to lead to the selection of the most appropriate transit technology for a corridor or a network. This is the approach taken in [43], with the development of a model that compares three public transport systems—light rail, heavy rail, and BRT—in an urban network of radial lines, with the objective of minimizing the total cost of public transport service provision, taking into account both operator and user costs; in [44], where the authors proposed a model for a linear corridor that aims to maximize the society’s welfare derived from transit services by determining the optimal combination of line and service parameters in conjunction with the choice of transit technology (including BRT, LRT, and metro); and in [45], where a model to select a transit technology (BRT or metro) for a many-to-many travel demand in an urban area by optimizing a society’s welfare function for different levels of population density. Optimization models are also the methodological framework adopted in Ref. [46], which presented extensions to a base optimization model of a transit line able to evaluate technology choices (buses in mixed traffic, BRT, LRT, and heavy rail) with the adding of optimal stop spacing and transit unit length, crowding cost, and multiperiod generalization, but with fixed demand. In Ref. [47], the assumption of elastic demand was added, whereas Ref. [48] improved the representation of the temporal and spatial variability of demand. Moreover, Ref. [49] formulated a new optimization model for technology selection and transit line design through the development of spatially aggregated (for selection) and spatially disaggregated (for design) models.

Another approach that aims for a comparative assessment of investments in rail- and bus-based transit modes is the development or application of Cost–Benefit Analyses (CBA). In this area of research, Ref. [50] developed a simplified, parametrical Cost–Benefit model with the aim of determining the set of conditions in which light rail can represent a more worthwhile option than bus systems (however, it is important to note that this study considers conventional bus routes in a corridor, but not a BRT system). There are also some examples of specific applications of CBA, either ex ante or ex post, to case studies of rail- and bus-based alternatives. An example of ex ante application is found in [51], which modeled and compared, through a simple CBA, some alternative public transport options (busway, LRT, and elevated rail) for a congested corridor in Beijing. Ref. [52] also used CBA to conduct an ex post assessment of the substitution of a bus line by a modern tramway on a Paris boulevard in 2006, detecting a negative net present value.

Another methodological framework for evaluating plans and projects involving rail- or bus-based transit mode selection comprises multicriteria techniques, which enable the comparison of non-homogeneous criteria, both qualitative and quantitative. Although these methods are less relevant to the goals of this article, research that applies these methods can be found in References [53,54,55,56,57].

In addition to the main categories expounded above, there are minority approaches that supplement this literature review on the topic of rail- and bus-based urban/metropolitan transit system analysis. For example, Ref. [58] investigated the environmental benefits, in terms of air pollution, generated by modal shift from existing car users if a tram system and two levels of BRT were introduced in some illustrative urban areas of South Korea. In [59], a model was developed to estimate users’ time benefits (in terms of travel and access time) from implementing a median busway in a mixed-traffic bus service, which, in fact, would be the key component for the conversion to BRT. Taking a broader perspective, Ref. [60] studied the preferences of communities (not only users and potential users) in the choice between BRT and LRT in eight Australian cities, whereas [61] extended this approach to other geographical areas. In a similar line, Ref. [62] examined how citizens’ preferences for BRT or LRT change with the different roles they might play (an altruistic resident, a self-interested resident, a tax-payer, or a voter). Finally, some studies, such as [63,64,65], focus on assessing the impact of medium-capacity transit systems, either LRT or BRT, on land value and real estate prices.

Among the most recent research concerning comparative analyses of rail- and bus-based medium-capacity transit systems, some relevant references can be identified and discussed in more detail regarding the methodological frameworks they propose and their notable results and conclusions. As a first assessment approach, the efficiency of public transport in several metropolitan areas in South Korea, as well as of some types of medium-capacity transit systems (light rail, tramways, bimodal trams, and BRT), was compared in [66] by employing data envelopment analysis (DEA). In relation to construction costs, this analysis ranked tramways first, bimodal trams second, and BRT and light rail third, according to their Variable Returns to Scale (VRS) efficiency scores. On the other hand, as regards operation costs, BRT was ranked first, tramways second, and bimodal trams and light rail third. On the subject of the environmental and economic sustainability of rail- and bus-based medium-capacity transit systems, a comprehensive life cycle assessment of greenhouse gas emissions and expenditures of BRT and Very Light Rail (VLR) was performed in [67] by analyzing two real case studies from the UK—the Coventry Very Light Rail project and the Cambridgeshire Guided Busway. These specific assessments concluded that the BRT system is not only less expensive but also more effective in terms of reducing greenhouse gas emissions. Also from the point of view of environmental performance (CO₂ emissions), but analyzing energy costs too, Ref. [68] explored the best options for optimizing a public transport corridor in a peri-urban area of a Portuguese medium-sized city, where a bus line and a railway line operate partially in parallel, offering alternative transport options. This study’s conclusions place focus on the implementation of innovative, complementary services able to adapt to demand variability while optimizing existing infrastructure, as well as on the potential for emissions reduction by means of electric buses, minibuses, or even by a BRT system instead of the railway line. In the field of multicriteria methods, Ref. [69] proposed a multicriteria group decision-making (MCGDM) framework with the aim of selecting the most suitable public transit system (trams, LRT, metro/subways, BRT, commuter trains, or conventional public buses) in urban contexts, without being restricted to a particular city. To that purpose, the method, based on 11 selection criteria, found the following priority sequence: investment costs, number of accidents, vehicle capacity, CO₂ emissions, frequency, number of passengers per departure, operating costs, operating speed, journey time, energy consumption, and noise. In regard to other complementary approaches, Ref. [70] explored the type of relationship between bus services and light rail transit in Seattle by applying quantile regression. The authors concluded that the relationship in this case can be regarded as public transit congestion substitution, as LRT does not replace bus services in areas where bus ridership is low, while the substitution is significant in areas where bus ridership was high. Finally, another supplemental approach is found in [71], which tackles the matter of which segments of a bus line should be upgraded to a BRT such that the number of newly attracted passengers is maximized. To answer this question, the authors developed and solved a bi-objective problem to quantify the trade-off between the number of attracted passengers and the investment budget. Their conclusions showed that the resulting trade-off depends both on the origin–destination demand and on the passengers’ responses to upgrades. In summary, a review of the most recent research on this topic reveals that the same degree of diversity in approaches, scopes of analysis, methodological frameworks, and, thus, heterogeneity of results, is still present, which emphasizes the need to address the research gaps presented in the following paragraph.

In light of this literature review, several research gaps can be identified concerning issues such as the scarcity of studies taking a comprehensive, integral approach that would be able to overcome the limitations of more fragmented or restricted scopes of analysis, found in most of the studies discussed. Other issues include the scarce application of models with thorough integration of mutual, endogenous effects between demand behavior and trip attributes offered by different transport modes; the scarcity of multimodal approaches incorporating the modal attributes not only of the public transit systems but also of other trip alternatives such as private motorized vehicles, and including the assessment of possible changes in the user costs of these alternatives; the weak adoption of multiperiod analyses in order to capture the influence of the full range of demand levels occurring over different hourly/daily periods; the lack of consideration of the negative impacts that the construction phase of new PT systems has on travel costs during that stage; and the almost exclusive focus on deterministic approaches (only sometimes supplemented with basic sensitivity analyses), thus neglecting in most cases the actual existence of important uncertainty effects as well as their impacts on the evaluation and selection of alternative transit systems. Besides the major objectives of this article, this study aims to tackle these research gaps.

3. Methodology: Model Description

The model developed consists of two hypothetical scenarios in which each of the main types of medium-capacity transit systems would be respectively implemented (i.e., two ‘with project/alternative’ scenarios, named Scenario R for the hypothetical LRT construction and Scenario B for the notional BST), along with a baseline scenario in which neither of these two new modes would be implemented (‘without project’ scenario, here abbreviated as Scenario 0).

As a starting point for all of the scenarios, it is assumed that, in the base year, there is a public transport line with the same route, same stop locations, and similar zonal coverage as the hypothetical new LRT or BST line, but operated by means of the most usual transit mode of lower capacity and inferior level of service (namely, conventional buses in mixed traffic). The baseline scenario (Scenario 0) is therefore defined by the assumption that the operation and service of this conventional bus line will be maintained throughout the whole assessment period or horizon. Therefore, the general design of the model is based on the premise that the final aim would be to evaluate the possible replacement of an existing conventional bus line in mixed traffic—presumably subject to demand volumes that are relatively high for this mode—with either an LRT or a BST line with an equivalent route.

Over the assessment period, which, in these cases, usually extends over more than 30 years, the model distinguishes explicitly, for each scenario, different phases in accordance with the distinct circumstances of transport supply and demand that will occur during the implementation and subsequent service operation of public transport systems. Thus, for each of the two scenarios (R and B) in which the proposed medium-capacity transit systems would be deployed, the model defines and analyzes the following phases successively: an implementation phase for the new public transport mode (corresponding to the stages of project design, construction works, test running, etc.) in which the public transit service must be provided still by means of the pre-existing mode, i.e., buses in mixed traffic; a phase of introduction and growth of the new public transport system (over the first few years after start-up, marked by a progressive readjustment of the demand to the new service attributes rendered by the new mode); and a phase of service maturity (the longest stage in the commercial life cycle, commonly with more consolidated and stable demand behavior patterns). For the baseline scenario (0), the model assumes throughout the assessment period that the conventional bus service in mixed traffic is in its maturity phase.

Although the main focus of the model is on public transit modes, it must approach mobility in the analyzed corridor from a multimodal perspective, as the changes in supply and demand brought about by the introduction and service of the new medium-capacity transit modes also affect trip volumes in other transport modes, as well as their respective travel attributes (this kind of relation is also reciprocal among the various modal alternatives). Furthermore, the inclusion of other modal alternatives in the model is necessary to be able to assess possible changes in the users’ surplus of these transport modes, as well as to make it possible to quantify, in later evaluation stages, variations in the external costs generated (for example, as a result of changes in the trips volume made by automobile). Therefore, in addition to the respective public transit modes (LRT, BST, and conventional bus in mixed traffic), the model includes other modal options regarded as the most relevant to urban mobility. Specifically, the private automobile and the motorcycle/moped are incorporated into the modeling as two typical private motorized transport options. In addition, the pedestrian mode (walking trips) and a conjoined alternative of bicycle or/and other personal mobility vehicles (PMVs) are also included as representative modes of non-motorized travel and micromobility (although with limitations, the model manages these modal options of non-motorized travel and micromobility at least as alternatives incorporated into the formulation of the modal split). In summary, each scenario contains, in every phase, five modal alternatives (the respective mode of public transit and the four alternatives stated above).

The developed model allows one or several corridors or routes to be defined in which the hypothetical implementation of a medium-capacity public transit mode would be under consideration, each with its own specific characteristics and data, but a limitation in this regard is that possible interactions or network effects between different corridors are out of the modeling scope (i.e., if there were more than one corridor defined, the model calculations would be independent for each of them). The model also allows for three types of lines to be specified in accordance with their spatial configuration and running directions: conventional lines (longitudinal routes) with two-way running, circle lines with one-way running, and circle lines with two-way operation. Therefore, the model must necessarily differentiate the dissimilar conditions of travel demand and transport supply attributes for each of the two travel directions—when applicable—in every corridor or route.

The model defines and processes separately the different conditions related to demand, supply, travel costs, etc., that may occur in a series of distinguishable time periods corresponding to regular hourly, daily, or weekly patterns, such as peak hours, off-peak hours, intermediate intervals, weekend/holiday periods, or as many others as deemed appropriate. This capability to distinguish several time periods is especially convenient, since analyzing only the situation foreseen for one specific time period (usually the peak hour) and trying to expand or extrapolate the results of that period to the whole PT service span could lead to substantial distortions in the assessment of the project’s benefits.

With regard to long-term evolution, the total duration of the assessment period in each scenario is split by the model into single years as a discretization unit for the purposes of forecasting the progression of the series of future values of the transport and mobility variables over time.

Regarding the set of data that can be entered into the model, a remarkable feature is the wide range of input variables considered, which contributes to enriched opportunities in the analysis of the factors that could potentially influence the results of medium-capacity transit system implementation projects. The sets of input variables subject to potential modification comprise matters such as the schematic configuration of the public transport line; the characteristics of the PT vehicles; the design criteria to be applied in the scheduling, operation, and pricing of the transit service; basic parameters involved in the operating performance of the transit systems; specifications of the initial public transit demand; the assessment period and its split into phases or stages; the mobility characteristics and modal split in the corridors under study; the street/highway capacity and traffic conditions for vehicles in mixed traffic; other features related to trips in private motor vehicles; the variety of unit costs related to travel time; energy consumption and its prices for private motor vehicles; other possible changes in modal costs applied as exogenous measures; etc. Further details about the full list of the model’s data and input variables are provided in Appendix A (

Table A1. Full list of model data and input variables.

Data or Input Variable	Type of Data (a)	Levels of Data Distinction (b)
General data
Number of corridors/PT-lines to be analyzed [-]	FV	Common value for the whole model
Number of time periods corresponding to distinct hourly/daily/weekly patterns [-]	FV	C/L
Configuration of the public transit lines
Type of PT line by spatial configuration and running directions [-]	FV	C/L
Line length [km]	FV	C/L
Number of stops or stations in each PT line [-]	FV	C/L
Distance from the origin terminal to each stop/station along the PT line [km]	FV	C/L, STO
Ratio of off-line stops over the total number of stops [-]	FV	C/L, DIR
Assessment period and division into phases or stages
Total length of the assessment period [yr]	FV	Common value for the whole model
Average speed of line’s infrastructures implementation for the new medium-capacity PT modes [km/yr]	PD	C/L, SCE (except 0)
Duration of the introduction and growth phase of the new PT service [yr]	PD	SCE (except 0)
Characteristics of the PT vehicles or Transit Units
Density of standees used as reference for capacity of vehicles or TUs [sps/m2]	FV	Common value for the whole model
Static capacity of the vehicles or TUs [sps/veh or sps/TU]	FV	PTM, VET
Number of seats in the vehicles or TUs [-]	FV	PTM, VET
Most restrictive number of door channels either for boarding or alighting [-]	FV	PTM, VET
Average acceleration of the vehicles or TUs [m/s2]	FV	PTM (except conv. bus), VET
Service deceleration of the vehicles or TUs [m/s2]	FV	PTM (except conv. bus), VET
ID of the type of vehicle assigned to each line for each PT mode [-]	FV	C/L, PTM
Percentage of vehicles or TUs for reserve and on maintenance and repair [%]	PD	PTM
Design criteria to be applied in the scheduling, operation, and pricing of the transit service
Annual number of hours in each time period [h/yr]	FV	C/L, TPE
Minimum headway [min]	FV	C/L, TPE, PTM
Maximum or policy headway [min]	FV	C/L, TPE, PTM
Load factor or capacity utilization coefficient on the maximum load section [-]	FV	C/L, TPE, DIR, PTM
Programmed speed for each stop-to-stop section in reserved right-of-way [km/h]	FV	C/L, SBS, DIR, PTM (except conv. bus)
Price per trip by fare type [CU]	FV	PTM, FAT
Fraction of PT rides paid by each fare type [-]	FV	FAT, C/L, TPE, DIR
Basic parameters influencing the operating performance of the transit systems
Individual passenger service time for boarding/alighting (without crowding effects) [s/prs]	PD	C/L, TPE, DIR, PTM
Door channels’ efficiency factor due to uneven boarding/alighting volumes through different door channels (c) [-]	PD	PTM, VET
Balance factor of boarding and alighting passengers service time (d) [-]	PD	C/L, TPE, DIR
Door opening and closing time [s]	PD	PTM, VET
Terminal time coefficient as a fraction of operating time on the line [-]	PD	C/L, TPE, PTM
Initial public transit demand on the analyzed lines
Initial trip volume in public transit (base year, bus) [prs/h]	FV	C/L, TPE, DIR
Coefficient of relative concentration of passenger volume on the maximum load section over total boardings along the line (reciprocal of the coefficient of passenger exchange) (e) [-]	FV	C/L, TPE, DIR
Coefficient of relative uniformity of the passenger volume profile along the line (reciprocal of the coefficient of flow variations) (f) [-]	FV	C/L, TPE, DIR
Peak-hour coefficient (reciprocal of peak-hour factor) [-]	FV	C/L, TPE, DIR
Basic characteristics of the journeys and modal split in the corridors
Initial portion of total trips made by mode-captive users (base year) [-]	FV	C/L, TPE, DIR, MOA
Initial modal shares (base year) [-]	FV	C/L, TPE, DIR, MOA
Fraction of business/work trips in the mobility composition by journey purpose [-]	FV	C/L, TPE, DIR
Fraction of commuting trips in the mobility composition by journey purpose [-]	FV	C/L, TPE, DIR
Average annual variation in the portion of total trips made by mode-captive users [perc. points]	PD	C/L, TPE, DIR, MOA
Average rate of annual variation in the total trip volume due to exogenous factors (not related to travel costs) [%]	PD	C/L, TPE, DIR
Street/highway capacity and traffic conditions for vehicles in mixed traffic in the corridor
Initial street/highway capacity for mixed traffic (base year) [PCE/h]	PD	C/L, DIR
Street/highway capacity for mixed traffic after full implementation of new medium-capacity PT system [PCE/h]	PD	C/L, DIR, SCE (except 0)
Average travel speed for automobiles at zero traffic volume in the corridor [km/h]	PD	C/L, DIR
Average travel speed for motorcycles/mopeds at zero traffic volume in the corridor [km/h]	PD	C/L, DIR
Average travel speed for conventional buses (mixed traffic) at zero traffic volume in the corridor [km/h]	PD	C/L, DIR
α parameter in the BPR formulation (volume-delay function) for vehicles with ≥4 wheels (automobiles and buses) [-]	PD	C/L, DIR
α parameter in the BPR formulation (volume-delay function) for 2-wheel vehicles (motorcycles/mopeds) [-]	PD	C/L, DIR
β parameter in the BPR formulation (volume-delay function) for vehicles with ≥4 wheels (automobiles and buses) [-]	PD	C/L, DIR
β parameter in the BPR formulation (volume-delay function) for 2-wheel vehicles (motorcycles/mopeds) [-]	PD	C/L, DIR
Passenger-car equivalents for bus vehicles [-]	PD	C/L, DIR
Passenger-car equivalents for motorcycles/mopeds [-]	PD	Common values for the whole model
Other characteristics related to trips in private motor vehicles
Ratio of average travel length on the corridor (in private motorized transport) to average passenger travel length on the PT line [-]	PD	C/L, TPE, DIR
Contribution of through trips (E-E) in the corridor’s volume-to-capacity ratio [-]	PD	C/L, TPE, DIR
Initial average vehicle occupancy rate for automobiles [prs/veh]	PD	C/L, TPE, DIR
Average vehicle occupancy rate for motorcycles/mopeds [prs/veh]	PD	Common values for the whole model
Average annual variation in automobiles’ occupancy rate [prs/veh]	PD	C/L, TPE, DIR
Compliance rate with yield-to-bus law in off-line stops [-]	PD	C/L, TPE, DIR
Unit costs related to travel time
Value of in-vehicle time for commuting trips in public transport (without crowding effects) [CU/h]	PD	Common values for the whole model
Ratio of value of in-vehicle time for business/work trips in public transport to value for commuting trips [-]	PD	Common values for the whole model
Ratio of value of in-vehicle time for other trips in public transport to value for commuting trips [-]	PD	Common values for the whole model
Ratio of value of in-vehicle time for commuting trips in private motorized transport to value in public transport [-]	PD	Common values for the whole model
Ratio of value of in-vehicle time for business/work trips in private motorized transport to value in public transport [-]	PD	Common values for the whole model
Ratio of value of in-vehicle time for other trips in private motorized transport to value in public transport [-]	PD	Common values for the whole model
Average annual growth rate of value of time (at constant prices) [%]	PD	Common values for the whole model
Waiting ratio in public transport (ratio of value of waiting time in stops to value of in-vehicle time) [-]	PD	PTM
Lateness ratio for public transport (ratio of value of average lateness to value of regular in-vehicle time) [-]	PD	C/L, TPE, DIR
Reliability ratio for private motorized transport (ratio of value of SD of travel time to value of travel time) [-]	PD	C/L, TPE, DIR
Unit costs related to energy consumption in private motor vehicles
Initial ratio of veh-km traveled by electric-powered automobiles to the total veh-km traveled by automobiles (base year) [-]	PD	Common values for the whole model
Initial ratio of veh-km traveled by gasoline automobiles to the total veh-km traveled by gasoline and diesel automobiles (base year) [-]	PD	Common values for the whole model
Yearly variation in the ratio of veh-km traveled by electric-powered automobiles to the total veh-km [perc. points]	PD	YEA
Yearly variation in the ratio of veh-km traveled by gasoline automobiles to the total veh-km by gasoline and diesel [perc. points]	PD	YEA
Initial ratio of veh-km traveled by electric-powered motorcycles/mopeds to the total veh-km traveled by motorcycles/mopeds (base year) [-]	PD	Common values for the whole model
Yearly variation in the ratio of veh-km traveled by electric-powered motorcycles/mopeds to the total veh-km [perc. points]	PD	YEA
Average energy consumption for electric-powered automobiles [kW·h/km]	PD	Common values for the whole model
Average energy consumption for electric-powered motorcycles/mopeds [kW·h/km]	PD	Common values for the whole model
Relative reduction in average fuel consumption (per distance unit) of gasoline automobiles expected by the end of the assessment period [%]	PD	Common values for the whole model
Relative reduction in average fuel consumption (per distance unit) of diesel automobiles expected by the end of the assessment period [%]	PD	Common values for the whole model
Relative reduction in average fuel consumption (per distance unit) of gasoline motorcycles/mopeds expected by the end of the assessment period [%]	PD	Common values for the whole model
Initial retail price of gasoline (base year) [CU/l]	FV	Common value for the whole model
Initial retail price of diesel fuel (base year) [CU/l]	FV	Common value for the whole model
Initial retail price of electric energy employed for EV charging (base year) [CU/kW·h]	PD	Common values for the whole model
Average annual variation in the retail price of gasoline (in real value) as a fraction of the initial price [%]	PD	Common values for the whole model
Average annual variation in the retail price of diesel fuel (in real value) as a fraction of the initial price [%]	PD	Common values for the whole model
Average annual variation in the retail price of electric energy for EV charging (in real value) as a fraction of the initial price [%]	PD	Common values for the whole model
Possible changes in other modal costs
Modal bonus of LRT and BST compared with conventional bus in mixed traffic [generalized min]	PD	PTM (except conv. bus)
Yearly variation (at constant prices) in other modal costs out of the scope of model’s endogenous calculations [generalized CU]	PD	C/L, TPE, DIR, YEA, MOA (except PT)
Additional data for calibration of demand model parameters λ and β
Portion of total trips made by mode-captive users in previous years used as calibration reference [-]	FV	C/L, TPE, DIR, MOA
Modal share of public transit in previous years used as calibration reference [-]	FV	C/L, TPE, DIR
Changes in generalized cost of travel from previous years used as calibration reference to the base year [generalized CU]	PD	C/L, TPE, DIR, MOA
Ratio of β parameter to λ parameter in the demand model [-]	PD	C/L, TPE, DIR
Numerical parameters for model computation
Number of random simulations [-]	FV	Common value for the whole model
Absolute convergence tolerance in iterative calculations of modal shares [-]	FV	Common value for the whole model
Absolute convergence tolerance in iterative calculations of total trip volumes [prs/h]	FV	Common value for the whole model
Coefficient of relative weighting between two consecutive iterations [-]	FV	Common value for the whole model

(a) FV: fixed value; PD: probability distribution. (b) C/L: corridor or PT line; DIR: travel direction; FAT: fare type; MOA: modal alternative; PTM: public transit mode; SBS: section between consecutive stops; SCE: scenario; STO: stop/station; TPE: time period; VET: type of PT vehicle; YEA: year. (c) The door channels’ efficiency factor ($e_{DC}$) is specifically defined by the model’s formulation as $e_{DC}=\left(100/p_{BDC}\right)/N_{DC}$, where $p_{BDC}$ is the percentage of passengers through the busiest door channel, and $N_{DC}$ stands for the number of door channels. (d) The model’s formulation defines specifically the balance factor of boarding and alighting passengers service time ($b{f}_{BA}$) as $b{f}_{BA}=1-\left(t_1^b+{\displaystyle {\sum }_{n=2}^N\left|t_n^b-t_n^a\right|}+t_{END}^a\right)/\left(t_1^b+{\displaystyle {\sum }_{n=2}^N\max \left\{t_n^b,t_n^a\right\}+t_{END}^a}\right)$, where $t_n^b$ is the maximum boarding passengers service time of all door channels at the stop or station where the n-th interstop section starts, $t_n^a$ is the maximum alighting passengers service time of all door channels at the stop or station where the n-th interstop section starts, N is the total number of sections between stops/stations, and $t_{END}^a$ is the maximum alighting passengers service time of all door channels at the end terminal (depending on the travel direction) of the line. Note that this formulation assumes implicitly that the alighting and boarding of passengers at line terminals are performed separately for each terminal-to-terminal trip, not simultaneously. (e) The model’s formulation specifies the coefficient of relative concentration of passenger volume on the maximum load section over total boardings along the line ($\sigma$) as $\sigma =P_{max}/{\displaystyle {\sum }_{n=1}^N{b}_n}$, where $P_{max}$ is the maximum passenger volume of all sections along the line (maximum load section), $b_n$ is the volume of boarding passengers at the stop or station where the n-th interstop section starts, and N is the total number of sections between stops/stations. This variable coincides with the reciprocal of the coefficient of passenger exchange [1] (pp. 40–43) for those lines that have only one point (stop/station) at which the boarding and alighting curves intersect, and therefore, there is no relative maximum in the passenger volume curve other than $P_{max}$ on the maximum load section. (f) The coefficient of relative uniformity of the passenger volume profile along the line ($\delta$) is specifically defined by the model’s formulation as $\delta ={\displaystyle {\sum }_{n=1}^N{P}_n{l}_n}/\left(P_{max}L\right)$, where $P_n$ is the passenger volume on the n-th interstop section, $P_{max}$ is the maximum passenger volume of all sections along the line (maximum load section), $l_n$ is the length of the n-th interstop section, L is the line length, and N is the total number of sections between stops/stations. This variable is equivalent to the reciprocal of the coefficient of flow variations [1] (pp. 39–40).

).

Another question to be considered in parallel to the definition of the input variables is the treatment of the level of uncertainty predictably associated with each class of data. Depending on their expected degree of uncertainty, a distinction is made in the model data between those for which the specification of a single or fixed value is deemed appropriate (on the assumption that they can generally be known with a sufficient level of certitude and precision) and those considered to be usually subject in practice to a substantial level of uncertainty (it is therefore more proper to treat them as a random variable from the outset of the model). For the latter class of input variables, the model must take as data the parameters specifying their respective probability distributions. In this regard, the model developed makes use of triangular distributions, so these parameters are the mode, lower limit, and upper limit values.

Regarding the main calculation sections, the core of the model represents mathematically, for each of the scenarios and in each stage of the assessment period, the mutual interactions and interdependencies between the following classes of processes:

• Travel demand prognosis: This is aimed at forecasting trip volumes (trips/hour) made by each of the modal alternatives, along with the sum or total trip volume for the entire set of alternatives in the analyzed corridor.
• Dynamic forecasting of the full set of supply characteristics: This process consists of calculating values for all of the variables involved in the sizing, scheduling, and operation of the public transport service, as well as those representing the features or attributes that the other modal alternatives offer to their potential users. The model incorporates the substantial impact that the trip volume forecast for each modal option has on the values of the supply-side variables (chiefly through the scheduling, headway and resulting waiting time at stops, operating speed, and crowding costs in the public transit systems, and via several congestion costs for the private motorized transport).
• Valuation of the modal alternatives: On the basis of the attributes offered by the modal alternatives and the relative value that travelers place on each of these attributes, a comprehensive valuation is performed for each modal option (via the concept of generalized cost of travel), as well as an overall valuation of the full set of available modal alternatives (by means of the composite cost of travel).
• Estimation of aggregate travelers’ choices: The valuation of each modal alternative (with the generalized cost of travel for each of them) is used as a basis to forecast changes in the modal split (incorporating considerations of the existence of captive users of any specific mode who lack the opportunity to choose). Moreover, the composite cost of travel for the whole set of alternatives influences, through the trip distribution stage, the expected total trip volume in the corridor under analysis. The results of this process must be returned to the travel demand prognosis in order to check whether they are consistent with the initial forecast, and, if not, they are used to compute a new approximation continuing the loop.

Figure 1 displays a chart that shows the relations between the categories of processes within the core of the model, and also situates this core within the general framework of the model.

The development of the model’s sections intended to forecast travel demand and aggregate travelers’ choices is based on the theoretical reference framework of a gravitational, synthetic model of trip distribution and modal split. A general formulation of this kind of models is commonly specified as shown in Equation (1) (e.g., [72] (pp. 211–212), originally attributed to [73]):

$$T_{ij}^{kn}=\stackrel{T_{ij}^n={\displaystyle {\sum }_k{T}_{ij}^{kn}}}{\overbrace{A_i^n{O}_i^n{B}_j{D}_j\exp \left(-{\beta }_n{K}_{ij}^n\right)}}\stackrel{P_{ij}^{kn}\left|{\displaystyle {\sum }_k{P}_{ij}^{kn}}=1\right.}{\overbrace{{\displaystyle \frac{\exp \left(-{\lambda }_{n}G{C}_{ij}^{kn}\right)}{{\displaystyle {\sum }_m\exp \left(-{\lambda }_{n}G{C}_{ij}^{mn}\right)}}}}}\hspace{1em}0\le {\beta }_n\le {\lambda }_n$$

(1)

where $T_{ij}^{kn}$ is the trip volume between origin i and destination j made by travelers of segment or type n by using modal alternative k (so $T_{ij}^n$ represents the whole trip volume from i to j made by travelers of segment n, whichever modal alternative they choose); $O_i^n$ is the total trip volume with origin in zone i made by persons of type n; $D_j$ is the total trip volume with destination in zone j; $A_i^n$ and $B_j$ are balancing factors, respectively, for origin i (with regard to trips made by travelers of segment n) and for destination j, which result from enforcing as model conditions ${\displaystyle {\sum }_j{T}_{ij}^n}=O_i^n$ and ${\displaystyle {\sum }_{in}{T}_{ij}^n}=D_j$; $G{C}_{ij}^{kn}$ is the generalized cost of traveling from zone i to zone j by mode k as perceived by persons of segment n; $K_{ij}^n$ is the composite cost of traveling from i to j for persons of type n; ${\lambda }_n$ is a parameter that controls among travelers of segment n the sensitivity of the modal split to the differences between the generalized cost of the modal options (λ is actually inversely proportional to the dispersion in mode choice); ${\beta }_n$ is another parameter that regulates the sensitivity of destination choice (in the trip distribution) to the accessibility or ease of access (measured as inversely proportional to the composite cost) between origins and destinations for persons of type n; and $P_{ij}^{kn}$ is the modal share of trips from i to j made by modal alternative k among the group of travelers of segment n.

Thus, the generalized cost of travel for the different modal alternatives is the main variable governing the behavior of the demand model. The generalized cost of travel is a quantitative measure in which the main attributes associated with the disutility of making a trip via a certain transport mode (i.e., the set of several disincentives or deterrent factors that an individual faces in making that journey) are combined additively in proportion to their relative importance as perceived by the travelers [72] (pp. 177–178). Therefore, the generalized cost is usually modeled as a linear function of those attributes, weighted by coefficients that represent the relative value that travelers place on them. Thus, the generalized cost converts and adds the different nature and value of this set of attributes (such as the time spent in each trip stage, money spent, other possible disincentives like discomfort, etc.) to a single, common measure, which is usually expressed in terms of equivalent monetary units (sometimes equivalent time). A typical generic specification for the generalized cost of travel may be given by Equation (2):

$$G{C}_{ij}^{kn}={\alpha }_1^{kn}{c}_{1,ij}^k+{\alpha }_2^{kn}{c}_{2,ij}^k+\dots +{\alpha }_M^{kn}{c}_{M,ij}^k+{\delta }_{ij}^{kn}$$

(2)

where $c_{h,ij}^k$ denotes the h-th cost element—or attribute—of the generalized cost of traveling from origin i to destination j via mode k; ${\alpha }_h^{kn}$ is the coefficient that weights the relative value that persons of segment n place on the h-th attribute when traveling via mode k; and ${\delta }_{ij}^{kn}$ is a modal penalty—or “bonus” if it diminishes the generalized cost compared to other alternatives—associated with traveling via mode k from i to j, as valued by travelers of type n (in fact, this modal penalty is assumed to encompass all other possible attributes not explicitly included as $c_{h,ij}^k$).

The composite cost $K_{ij}^n$ is a measure that values (in the same units as the generalized costs of the modal alternatives) the general disutility perceived by persons of segment n to make a trip from origin i to destination j, given the full set of modal options they could choose. In this regard, the composite cost of travel is, as advanced above, an inverse measure of the accessibility or ease of access to a certain destination zone from a given origin. The correct mathematical specification of the composite cost of travel is given by Equation (3) (e.g., [72] (p. 213), originally attributed to [74]):

$$K_{ij}^n=-{\displaystyle \frac{1}{{\lambda }_n}}\ln \left[{\displaystyle {\sum }_k\exp \left(-{\lambda }_{n}G{C}_{ij}^{kn}\right)}\right]$$

(3)

Building on the framework of the gravitational, synthetic modeling of trip distribution and modal split, incremental formulations have been developed and applied successively in the model, resulting in a kind of model that falls under so-called pivot-point modeling. In practice, an advantage of this kind of modeling is the opportunity to forecast future or hypothetical travel demand on the basis of its current or actual levels (e.g., total trip volume and modal shares of the different alternative modes). To do so, it suffices to consider only the expected changes in the cost-attributes or service-level variables of the modal alternatives between the current or actual circumstances and the future or hypothetical situation (i.e., the predicted changes in the generalized cost for each transport mode). This feature of pivot-point models makes it possible to ignore the values of all cost-attributes which can be assumed to not vary from the baseline situation or scenario to the others (in fact, the absolute levels of all of the attribute-variables can remain unknown too, as, in practice, only differences matter).

The incremental formulations for the total trip volume from i to j made by travelers of type n and for the modal split can be expressed, respectively, as shown in Equations (4) and (5):

$${T^{\prime }}_{ij}^{ n}={\displaystyle \frac{{A^{\prime }}_i^{ n}{O^{\prime }}_i^{ n}{B^{\prime }}_j{D^{\prime }}_j}{A_i^n{O}_i^n{B}_j{D}_j}}{T}_{ij}^n\exp \left(-{\beta }_n\Delta K_{ij}^n\right)$$

(4)

$${P^{\prime }}_{ij}^{ kn}={\displaystyle \frac{P_{ij}^{kn}\exp \left(-{\lambda }_n\Delta G{C}_{ij}^{kn}\right)}{{\displaystyle {\sum }_m{P}_{ij}^{mn}\exp \left(-{\lambda }_n\Delta G{C}_{ij}^{mn}\right)}}}$$

(5)

where the variables marked with the prime symbol refer to the values of such variables in a subsequent or hypothetical situation after a change $\Delta G{C}_{ij}^{kn}$ in the generalized cost of at least one modal alternative, and the variables without the prime symbol relate to the state regarded as original (i.e., before/without the changes).

Let us define a growth rate $F_{ij}^n$ as the proportional increase from the original state to a later situation of the total trip volume from origin i to destination j made by travelers of segment n due to factors not related directly to the travel cost between i and j (such as population growth over time, employment changes, income changes, age distribution changes, overall mobility increase, location/relocation of activities attracting trips, etc.). Thus, this growth rate can be expressed as shown in Equation (6):

$$F_{ij}^n={\displaystyle \frac{{A^{\prime }}_i^{ n}{O^{\prime }}_i^{ n}{B^{\prime }}_j{D^{\prime }}_j-A_i^n{O}_i^n{B}_j{D}_j}{A_i^n{O}_i^n{B}_j{D}_j}} \Rightarrow {\displaystyle \frac{{A^{\prime }}_i^{ n}{O^{\prime }}_i^{ n}{B^{\prime }}_j{D^{\prime }}_j}{A_i^n{O}_i^n{B}_j{D}_j}}=1+F_{ij}^n$$

(6)

Then, Equation (7) results from Equations (4) and (6):

$${T^{\prime }}_{ij}^{ n}=\left(1+F_{ij}^n\right)T_{ij}^n\exp \left(-{\beta }_n\Delta K_{ij}^n\right)$$

(7)

and from Equations (7) and (5) results Equation (8):

$${T^{\prime }}_{ij}^{ kn}={T^{\prime }}_{ij}^{ n}{P^{\prime }}_{ij}^{ kn}=\left(1+F_{ij}^n\right)T_{ij}^n\exp \left(-{\beta }_n\Delta K_{ij}^n\right){\displaystyle \frac{P_{ij}^{kn}\exp \left(-{\lambda }_n\Delta G{C}_{ij}^{kn}\right)}{{\displaystyle {\sum }_m{P}_{ij}^{mn}\exp \left(-{\lambda }_n\Delta G{C}_{ij}^{mn}\right)}}}$$

(8)

where the change in composite cost $\Delta K_{ij}^n$ (i.e., ${K^{\prime }}_{ij}^{ n}-K_{ij}^n$) can also be computed through an incremental form, as shown in Equation (9):

$$\Delta K_{ij}^n={K^{\prime }}_{ij}^{ n}-K_{ij}^n=-{\displaystyle \frac{1}{{\lambda }_n}}\ln \left[{\displaystyle {\sum }_m{P}_{ij}^{mn}\exp \left(-{\lambda }_n\Delta G{C}_{ij}^{mn}\right)}\right]$$

(9)

As the demand forecasting model employs an incremental formulation, it is necessary for the model to compute the variations in the generalized cost of the modal alternatives over time (i.e., from one year to another), and to subsequently calculate the differences in these generalized costs between scenarios.

Consequently, for the different modes of public transport, the model computes changes in the following constituents of the generalized cost: the fare paid per trip; the base cost associated with the in-vehicle time in public transport; the potential increase over the base cost of in-vehicle time due to the discomfort derived from the level of crowding of passengers; the cost of the average waiting time at stops or stations; and the additional cost linked to possible deficiencies in the reliability of the public transport service on account of lack of adherence to schedules, potential delays, uncertainty about arrival time, etc. For the medium-capacity transit systems of new implementation, the model also includes a potential reduction in the generalized cost of travel due to the valuation of the modal bonus attributed to either LRT or BST relative to conventional buses.

For the modal alternatives of private motorized transport, the model computes changes in the following components of their generalized cost of travel: the cost of the in-vehicle time in private motor vehicle, including potential increases in the cost per time unit due to unpleasant travel conditions resulting from high road congestion; the cost assumed by the traveler as a result of the variability, unreliability, or unpredictability of travel time via private motor vehicle; the private cost incurred per traveler on account of the vehicle’s energy consumption, in the form of fuel and/or electric power, depending on the type of vehicle; and other possible modal costs involved in the use of private motorized travel (e.g., parking costs, possible urban/metropolitan tolls, effect of other additional restrictions on car use, etc.), which, from the model’s point of view, are considered as exogenously set (i.e., as input variables to be determined by the analyst).

As regards non-motorized and micromobility modes (pedestrian mode, and bicycle and/or other PMVs), the way the model treats changes in the generalized cost of these alternatives is circumscribed to reflecting the value placed by the traveler on the impact of exogenous measures (therefore out of the scope of the model’s internal calculations), so these generalized cost changes must be input as external variables with values expected or known by the analyst. Anyway, the model assigns common values for the three scenarios to each kind of exogenous cost change, so as not to unbalance the equality of external conditions in which the comparative evaluation of public transport systems should be carried out.

Thus, the core of the model developed consists mainly of a calculation stream configured in accordance with the bases described above. In each year of the assessment period, this calculation stream must be sequentially computed for each combination of corridor (if more than one is specified), time period (hourly, daily, or weekly demand pattern), and travel direction.

The calculation stream starts by computing (either as an initial approximation or with the outputs from the previous iteration) the trip volume (trips/hour) for each modal alternative. The trip volume for the public transport mode (LRT, BST, or conventional buses, depending on the scenario and phase or stage) allows to derive the design passenger volume of the transit line to be derived, which is a key parameter for scheduling the service. This step essentially consists of determining the most appropriate headway—rounded down to a clock headway if appropriate—ranging within an interval whose upper endpoint is the policy headway and whose lower endpoint is linked to the capacity limits of the transit system. In the model, this is followed by calculations on the density of standing passengers (prs/m²), both on the maximum load section and average over the line, as a measure of PT crowding.

Then, the model proceeds with some basic calculations concerning the traffic intensity in mixed traffic, with the volume-to-capacity ratio as the final output. This ratio will influence not only the travel conditions for private motor vehicles but also the operating conditions of conventional buses in mixed traffic. It should be noted that the model allows different street/highway capacities to be set before and after the insertion of the new transit system with reserved right-of-way; thus, the street/highway capacity for mixed traffic can differ between scenarios (substantially between scenarios R or B and 0, and slightly between R and B).

The next procedure consists of computing a series of intermediate variables that lead to the operating or travel speed of each of the public transport modes. The operating time used for this calculation includes, for LRT, the sum of running times (with consideration of reduced effectiveness of Transit Signal Priority systems when frequencies are near the TU line capacity), aggregate passenger service times at stops/stations (longer with higher densities of standing passengers), and aggregate door opening and closing times. The operating time of the BST follows a similar structure but adds to the dwell times an increase factor on account of the possibility of stops failure (if actual headway is near the station headway, a bus arriving at a stop could find the loading area full, exceeding the stop capacity). The operating time for conventional bus is composed of the sum of its running time (computed as a vehicle running on mixed traffic, thus depending on the volume-to-capacity ratio), aggregate passenger service times (influenced by the density of standing passengers), door opening and closing times, and reentry delay for off-line stops (with the sum of the latter three components affected by a stops failure increase factor as the actual headway approaches the station headway).

The operating speed of each public transit mode, along with the average distance that passengers travel on the line, allows one to find the average in-vehicle time for PT users. This in-vehicle time is augmented by a time multiplier that takes into account the inconvenience that passengers experience due to crowding, so it is computed as a function of the density of standing passengers. Next, the model estimates the average waiting time for passengers at stops/stations depending on the service headway, but taking into account a fraction of passengers who will attempt to adjust their arrival to the transit stop to the timetables or real-time predictions in order to reduce their waiting time. Following this, the model proceeds with an indicator of the travel time reliability of the public transit service by estimating the mean lateness for each PT mode. For conventional buses in mixed traffic, it is assumed that the travel time reliability will depend mainly on the volume-to-capacity ratio along the route, decreasing the reliability (increasing the mean lateness) with higher ratios. For transit systems with reserved right-of-way and Transit Signal Priority (that is, LRT and BST), the model assumes that the travel time reliability will diminish for very short headways as the service headway approaches the minimum headway of the line related to line capacity.

Then, the model proceeds to calculate the changes in the generalized cost of the public transport modes according to the specification of the generalized cost of travel $G{C}_s^{kn}$ shown in Equation (10) for the average trip length on a line, when it is made by travelers of segment n using PT mode k in scenario s (where the PT mode will be bus in mixed traffic, LRT, or BST, depending on the scenario and its phase or stage):

$$G{C}_s^{kn}=f^{kn}+\left(M{C}_s^{kn}{t}_{vs}^k+W{R}^{kn}{t}_{ws}^k+L{R}^n{t}_{ls}^k-B{n}^{kn}\right)VO{T}_P^n+C_P^n$$

(10)

where f is the fare paid per trip; $t_v$ is the in-vehicle travel time; $t_w$ is the waiting time at stops/stations; $t_l$ is the mean lateness (cf. ([75] (p.15)), ([76] (pp. 79–80))); Bn is the modal bonus for LRT or BST (set to 0 for conventional buses) measured as generalized in-vehicle time; MC is the time multiplier accounting for PT crowding [77,78,79]; WR is the waiting ratio, i.e., how many minutes of in-vehicle time are cost-equivalent, from the passenger’s perspective, to a minute of waiting ([75] (p. 9)), [80,81,82]; LR is the lateness ratio, i.e., how many times greater is the cost of a minute of lateness, as valued by the passenger, compared to a minute of regular in-vehicle time ([75] (p. 15)), ([76] (pp. 79–80)), [82]; $VO{T}_P$ is the value of in-vehicle time for public transport; and $C_P$ represents all other modal costs (penalties) linked to public transport use (assumed to be constant over time during the assessment period and equal between scenarios).

As regards the modes of private motorized transport (automobile and motorcycle/moped), the model calculations are resumed by computing the average travel speed for each of these modes on the corridor under analysis. This is based on the widespread BPR formulation—with adapted parameters—as a volume–delay function, so the calculated speeds capture the influence of the volume-to-capacity ratio. These speeds, along with the average distance on the corridor for the trips in which private motorized modes compete with the public transit line, allow to compute the in-vehicle travel time for private motorized modes. Furthermore, the model computes a rate of incremental cost for congested traffic conditions in addition to the regular value of in-vehicle travel time, with an increasing rate as the volume-to-capacity ratio exceeds two-thirds. Next, the model calculates an estimation of the standard deviation of the travel time for private motorized modes as a measure of journey time variability, which diminishes the reliability or predictability of traveling via these modes and thus results in an increased travel time cost. Moreover, an estimation of the average cost per trip due to the vehicle’s energy consumption—fuel and/or electric power—is computed by the model. In this regard, the model introduces the dependence of the fuel consumption on the average speed by following mainly the guidance of [83] (pp. 54–80).

The calculations described in the paragraph above allow for the changes or variations in the generalized cost of the private motorized modes to be computed, with the specification of $G{C}_s^{kn}$ shown in Equation (11) for the average travel distance along the corridor (where k is, in this case, either automobile or motorcycle/moped):

$$G{C}_s^{kn}=\left[\left(1+AC{R}_s^n\right)t_{\mathit{vs}}^k+R{R}^n{\sigma }_{\mathit{ts}}^k\right]VO{T}_M^n+{\displaystyle \frac{E_s^k}{o^{kn}}}+C_M^{kn}$$

(11)

where $t_v$ is the in-vehicle travel time on the corridor or route; ${\sigma }_t$ is the estimated standard deviation of the in-vehicle travel time ([75] (pp. 13–14, 30–31)), [84,85,86]; ACR is the rate of additional travel time cost for congested traffic conditions (cf. [76] (pp. 65–66)); RR is the reliability ratio for private motorized transport, i.e., how many minutes of travel time are cost-equivalent, from the passenger’s perception, to a variability of one minute of standard deviation ([75] (p. 14)), ([76] (p. 80)), [87,88,89,90,91]; $VO{T}_M$ is the value of the in-vehicle time for private motorized transport; E is the average energy consumption cost along the corridor per vehicle and trip; o is the average occupancy per vehicle; and $C_M$ represents other modal costs (penalties) of private motorized transport modes (assumed to be subject to potential changes over time, but always equal between scenarios).

At the end of the calculation stream, the changes in the generalized cost of the public transport mode and of the private motorized alternatives from a prior year—commonly the immediately preceding—to the analyzed one, along with the respective changes in non-motorized and micromobility modes, enters the calculation of the change in the composite cost of travel (Equation (9)), which then allows for the new trip volume via each modal alternative (Equation (8)) to be computed, which can be disjoined into the total trip volume (Equation (7)) and modal split (Equation (5)).

The series of coupled equations formed from the calculation stream described in the previous paragraphs composes a large, non-linear system of equations, in which the basic variables for solving it (such as the future trip volumes for each transport mode or, alternatively, the future variations in the generalized cost of travel for each of these modes) are some of the unknowns of the problem. Finding solutions for this equation system requires iterative procedures for any year of the assessment period after the base year (i.e., for the model’s forecasting of future values) to be employed. These procedures are performed in the model by means of a set of iterative calculation modules.

The methodological treatment of the uncertainty involved in any forecasting exercise, as well as in the modeling process itself, has been incorporated into the model from the beginning of its development. This uncertainty arises from a combination of limitations in the available information (uncertainty about the reliability or accuracy of the values to be used as input data and, especially, about the future evolution of some of these data) and in the methodological modeling (related to simplifications, accepted assumptions, or other potential sources of inaccuracy). In order to address this issue methodologically, all of the variables that are reasonably expected to be subject to a considerable level of uncertainty have been modeled as random variables, each of them following its own probability distribution. In this regard, the model assumes the use of triangular distributions [92] (pp. 338–339) to simulate, in practice, the probabilistic behavior of this kind of variable. In addition, it is necessary to bear in mind the foreseeable existence of statistical correlations between some of the model’s variables that are subject to randomness (for example, different input variables that are all linked to travelers’ income or socioeconomic level, the evolution of the price of different fuel types such as gasoline and diesel fuel, etc.), so a reasonable degree of correlation between this kind of variables has been introduced in the preparatives of the randomization process.

Finally, Monte Carlo simulation techniques, based on repeated random sampling, are applied to the model. The method applied in this case consists of the computational implementation of multiple simulations or executions of the model, each time by using as inputs different sets of random variates that were previously sampled or drawn from the probability distribution of the respective variable according to its probability density function. By performing all of these simulations, the method generates a synthetic sample of multiple values (with a sample size equal to the number of random simulations that have been carried out) for each of the model’s output variables. This sample of potential results for each output variable can be statistically processed and thereby characterized by parameters such as its mean value, standard deviation, percentiles, etc., as well as with histograms of relative frequencies.

4. Application in an Artificial Case Study

As a case study, the model developed in this article was applied to an illustrative set of data which, although artificially originated, were carefully designed to be representative of relatively common conditions in corridors carrying medium PT-ridership volumes—mainly in the context of medium-sized European cities. Thus, some type of medium-capacity transit system could be reasonably proposed for such a corridor, and that proposal should necessarily involve an assessment of the convenience of its implementation.

The code developed to compute the model with the complete set of data used for this artificial case study and the set of raw results obtained from its execution are available in the ‘Supplementary Materials’.

4.1. Main Data

This numerical application example involved the analysis of a conventional 10 km long (longitudinal) public transit line with 2 terminals and 21 intermediate stops (see Figure 2), with a total annual ridership of 10,000,000 pax/year (5 million per travel direction) in the base year (with bus services in mixed traffic). The initial PT modal shares ranged between ca. 14% and 25%, depending on the time period. The assessment period was set for 40 years after the base year, and 2500 random simulations were performed.

The following tables detail the most relevant data—in addition to the main characteristics stated above—adopted to apply the model. In particular, the tables show the division of the assessment period into its different phases (

Table 1. Main input data concerning the division of the artificial case study’s assessment period into phases.

		Scenario
		Scenario R	Scenario B
Average speed of implementing the line’s infrastructures for the new medium-capacity PT modes [km/year]	Minimum	1.33	2.00
	Maximum	2.67	3.00
	Mode	2.00	2.50
Duration of the introduction and growth phase of the new PT service [years]	Minimum	2.00	2.00
	Maximum	4.00	4.50
	Mode	3.00	3.25

); the main vehicle features of the three PT modes (

Table 2. Main characteristics of the PT vehicles used as input data for the artificial case study.

	Bus	LRT	BST
General description	18 m articulated bus	32–37 m LRV/tram	24 m bi-articulated BRT vehicle
Number of seats	37	68	52
Vehicle capacity (seats + 4 standees/m2) [sps/veh]	104	212	140
Acceleration [m/s2]	n/app.	1.25	1.08
Service deceleration [m/s2]	n/app.	1.25	1.18

); the key design criteria applied in the scheduling, operation, and pricing of the transit service (

Table 3. Principal design criteria applied in the artificial case study to the scheduling, operation, and pricing of the transit service.

		Time Period Corresponding to Hourly/Daily/Weekly Patterns (P)
		P1	P2	P3	P4	P5	P6
Annual number of hours [h/year]		875	1000	875	1000	750	2070
Minimum headway [min]	Bus	2.00	2.00	2.00	2.00	2.00	2.00
	LRT	2.33	2.33	2.33	2.33	2.33	2.33
	BST	2.00	2.00	2.00	2.00	2.00	2.00
Maximum or policy headway [min]	Bus	15	25	20	15	30	30
	LRT	15	20	15	15	25	20
	BST	15	20	15	15	25	20
Average fare [€]	Bus	0.619	0.700	0.627	0.633	0.768	0.786
	LRT	0.643	0.737	0.652	0.661	0.815	0.833
	BST	0.638	0.724	0.644	0.655	0.798	0.812

); the major parameters defining the initial public transit demand in the line (

Table 4. Main parameters defining the initial public transit demand in the PT line of the case study.

	Travel Direction (D) and Time Period Corresponding to Hourly/Daily/Weekly Patterns (P)
	D1						D2
	P1	P2	P3	P4	P5	P6	P1	P2	P3	P4	P5	P6
Initial trip volume in PT (base year, bus) [prs/h]	1700.00	516.67	800.00	1050.00	281.11	500.00	1125.00	558.33	866.67	1433.33	307.50	500.00
Coefficient of passenger exchange (a)	1.563	2.174	1.587	1.786	2.439	2.000	1.724	1.923	1.852	1.515	2.222	2.222
Coefficient of flow variations (b)	1.587	1.449	1.639	1.449	1.351	1.515	1.471	1.613	1.408	1.563	1.389	1.429
Peak-hour coefficient	1.23	1.33	1.27	1.28	1.38	1.42	1.25	1.30	1.29	1.31	1.36	1.45
Average passenger travel length on PT line [km]	4.032	3.174	3.843	3.864	3.034	3.300	3.944	3.224	3.834	4.224	3.240	3.150

(a) See [1] (pp. 40–43); (b) see [1] (pp. 39–40).

); the main characteristics of the journeys and modal split in the corridor (

Table 5. Basic characteristics of the journeys and modal split in the corridor of the case study.

		Travel Direction (D) and Time Period Corresponding to Hourly/Daily/Weekly Patterns (P)
		D1						D2
		P1	P2	P3	P4	P5	P6	P1	P2	P3	P4	P5	P6
Initial modal shares (base year)	PT (bus)	0.232	0.254	0.200	0.190	0.153	0.135	0.205	0.237	0.198	0.211	0.158	0.142
	Automobile	0.450	0.396	0.453	0.472	0.596	0.460	0.490	0.425	0.460	0.439	0.585	0.458
	Motorcycle/moped	0.039	0.032	0.044	0.044	0.031	0.048	0.042	0.034	0.043	0.046	0.032	0.045
	Bicycle and/or PMVs	0.018	0.025	0.023	0.019	0.015	0.035	0.015	0.025	0.024	0.021	0.015	0.035
	Walking	0.261	0.293	0.280	0.275	0.205	0.322	0.248	0.279	0.275	0.283	0.210	0.320
Portion of total trips made by captive PT riders		0.139	0.140	0.115	0.114	0.115	0.093	0.123	0.130	0.114	0.127	0.119	0.099
Annual variation in the fraction of total trips made by captive PT riders [percentage points]	Minimum	−0.20	−0.15	−0.15	−0.20	−0.12	−0.11	−0.20	−0.15	−0.15	−0.20	−0.12	−0.11
	Maximum	0.20	0.15	0.15	0.20	0.12	0.11	0.20	0.15	0.15	0.20	0.12	0.11
	Mode	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Fractions of trips by journey purpose	Business/work (a)	0.08	0.06	0.06	0.09	0.04	0.02	0.10	0.06	0.07	0.08	0.04	0.03
	Commuting	0.72	0.27	0.53	0.68	0.32	0.12	0.75	0.25	0.50	0.66	0.35	0.10
	Others	0.20	0.67	0.41	0.23	0.64	0.86	0.15	0.69	0.43	0.26	0.61	0.87
Annual growth rate of the total trip volume due to exogenous factors [%]	Minimum	−0.20	−0.15	−0.20	−0.15	−0.15	−0.10	−0.15	−0.15	−0.20	−0.20	−0.15	−0.10
	Maximum	1.15	1.45	1.10	1.30	1.60	1.75	1.25	1.45	1.20	1.25	1.60	1.75
	Mode	0.55	0.75	0.50	0.65	0.80	0.90	0.65	0.75	0.55	0.55	0.80	0.90

(a) Journeys made on employers’ business, in the course of paid work, etc.

); the street/highway capacity for mixed traffic in the corridor (

Table 6. Basic data of street/highway capacity for mixed traffic in the corridor of the case study.

		Scenario and Travel Direction (D)
		Scenario 0		Scenario R		Scenario B
		D1	D2	D1	D2	D1	D2
Initial capacity for mixed traffic (base year) [PCE/h]	Minimum	1585	1450	1585	1450	1585	1450
	Maximum	1915	1750	1915	1750	1915	1750
	Mode	1750	1600	1750	1600	1750	1600
Capacity for mixed traffic after the new medium-capacity PT system has been fully implemented [PCE/h]	Minimum	n/app.	n/app.	1365	1300	1295	1245
	Maximum	n/app.	n/app.	1635	1550	1575	1505
	Mode	n/app.	n/app.	1500	1425	1435	1375

); the values of in-vehicle time and waiting time at stops or stations (

Table 7. Values of in-vehicle time and waiting time at stops or stations used in the case study.

		Minimum	Maximum	Mode
Value of in-vehicle time for commuting trips in public transport (VOTcp) [€/h]		8.87	11.99	10.43
Value of in-vehicle time for business/work trips in public transport (VOTbp) [€/h]		2.08·VOTcp	2.96·VOTcp	2.52·VOTcp
Value of in-vehicle time for other trips in public transport (VOTop) [€/h]		0.70·VOTcp	0.98·VOTcp	0.84·VOTcp
Value of in-vehicle time for commuting trips in private motorized transport (VOTcm) [€/h]		1.18·VOTcp	1.60·VOTcp	1.39·VOTcp
Value of in-vehicle time for business/work trips in private motorized transport (VOTbm) [€/h]		1.06·VOTbp	1.44·VOTbp	1.25·VOTbp
Value of in-vehicle time for other trips in private motorized transport (VOTom) [€/h]		1.18·VOTop	1.60·VOTop	1.39·VOTop
Annual growth rate of value of time (at constant prices) [%]		0.22	1.55	1.11
Waiting ratio (public transport)	Bus	1.75	2.45	2.10
	LRT	1.60	2.30	1.95
	BST	1.65	2.35	2.00

); the value of travel time reliability (

Table 8. Data used in the case study regarding the value of travel time reliability.

		Travel Direction (D) and Time Period (P)
		D1						D2
		P1	P2	P3	P4	P5	P6	P1	P2	P3	P4	P5	P6
Lateness ratio for public transport	Minimum	2.28	1.66	2.00	2.25	1.69	1.39	2.36	1.63	1.98	2.20	1.73	1.38
	Maximum	3.22	2.40	2.85	3.17	2.44	2.05	3.32	2.37	2.82	3.11	2.49	2.04
	Mode	2.75	2.03	2.42	2.71	2.06	1.72	2.84	2.00	2.40	2.66	2.11	1.71
Reliability ratio for private motorized transport	Minimum	0.29	0.24	0.27	0.29	0.24	0.22	0.30	0.24	0.27	0.29	0.25	0.22
	Maximum	0.62	0.57	0.59	0.63	0.56	0.53	0.64	0.56	0.60	0.62	0.56	0.53
	Mode	0.46	0.40	0.43	0.46	0.40	0.37	0.47	0.40	0.43	0.45	0.40	0.37

); and the modal bonus of LRT and BST compared with conventional bus services in mixed traffic (

Table 9. Values employed as modal bonus of LRT and BST compared with conventional bus in mixed traffic.

		Minimum	Maximum	Mode
Modal bonus in comparison with conventional bus [generalized minutes of in-vehicle time]	LRT	1.65	4.95	3.30
	BST	0.00	3.30	1.65

).

4.2. Main Results and Discussion

This subsection presents, in Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14, and briefly discusses a selection of the most relevant results obtained from the artificial case study. In accordance with the uncertainty treatment introduced in the model, most of the figures incorporate the mean value of the output variable as well as two relatively “near-extreme” percentiles. The values of 97.5th and 2.5th percentiles have been selected in this regard, so according to the model there is a 95% probability that the final result falls between these two percentiles. Figure 13 and Figure 14, which refer to the present value of the increase in consumer surplus received by the travelers and therefore do not show an evolution over the assessment period, were configured more appropriately as relative frequency histograms. Figure 3, Figure 4, Figure 5 and Figure 6, since refer to results that would differ between time periods and travel directions, were specifically focused on the conditions of time period P1 and travel direction D1, as these are representative of the weekday peak hour in such direction and thus particularly interesting.

Firstly, Figure 3 depicts the operating or travel speed of the public transport modes existing in each scenario over the entire assessment period for the peak-hour conditions (P1-D1), as operating speed is one of the main elements of the transit service performance offered to travelers [1] (p. 20). The results confirm, as shown in this figure, that the operating speed achieved with the medium-capacity transit systems is widely higher than that of conventional bus with mixed traffic existing in Scenario 0, for which the mean values range between 10.7 and 12.5 km/h. Among the alternative new PT systems, the operating speed provided by LRT in Scenario R (mean values around 26.4 km/h) is somewhat higher than that of BST in Scenario B (mean values ranging between 24.2 and 24.6 km/h). Furthermore, note that the operating speed of both medium-capacity transit systems remains very stable over the years and that the 97.5th and 2.5th percentiles are approximately ±2 km/h above/below the mean value. Nevertheless, in the first years of the assessment period, scenarios R and B (which correspond to the implementation phase of the new PT systems) reveal a moderate decline in operating speed compared with Scenario 0. At this stage of scenarios R and B, the public transit service is still operated by means of buses in mixed traffic, but with decreasing street/highway capacity (see Table 6) due to the construction works and insertion of reserved right-of-way for the new PT modes. This capacity reduction for mixed traffic results in the lessening of the buses’ operating speed.

Figure 4 and Figure 5 quantify the change in the generalized cost of travel from the baseline scenario (0) to the alternative scenarios (R and B) under weekday peak-hour conditions (time period P1 and travel direction D1), both for the modal option of public transport (Figure 4) and private automobiles (Figure 5).

For public transport, Figure 4 shows that these medium-capacity transit systems, once fully implemented and in service, would result in very substantial savings in the generalized cost of travel of this modal alternative compared with the baseline scenario (conventional bus). Savings are slightly higher for the LRT system (mean values range between €4.69 and €5.18 per average trip in Scenario R) than for the BST system (mean savings between €4.20 and €4.54 per trip in Scenario B). In contrast, during the implementation phase of the new public transport modes (first years of the assessment period), Scenarios R and B give rise to a moderate increase in the generalized cost of the public transport option, as the service is provided by means of conventional bus with diminishing street/highway capacity and lower operating speeds.

For private automobiles, Figure 5 exhibits a very clear rise of the generalized cost of travel for users of this modal alternative during the implementation phase of the medium-capacity transit systems, mainly due to the progressive reduction in street/highway capacity for mixed traffic. In accordance with the data adopted for this case study, the increase in generalized cost is slightly higher for Scenario B (mean values up to €1.54 per average trip) than for Scenario R (mean up to €1.10 per trip); on the other hand, the implementation phase is a bit shorter for BST (Scenario B) than for LRT (Scenario R). After the end of the implementation stage, putting the new medium-capacity transit systems into service results in a significant relief of the previous increase of generalized cost for the automobile users. This is because the new PT systems induce some degree of modal shift from private automobile to public transport, moderately alleviating the congestion of the mixed traffic. Indeed, in the course of the maturity phase, the generalized cost of traveling by automobile remains a little higher in Scenarios B and R than in the baseline scenario because of the capacity reduction. During this phase, the mean value of the extra cost varies from €0.70 to €0.52 and from €0.47 to €0.33 per trip in Scenarios B and R, respectively.

Figure 6 presents the modal shares of the public transport alternative in each scenario under the weekday peak-hour conditions (P1-D1), including both the general share (i.e., considering all kinds of travelers, either choice travelers or mode-captive users) and the specific share among only choice travelers. The most prominent conclusion derived from Figure 6 is the appreciable leap in the modal share of public transport that the putting into service of these LRT and BST systems would induce compared with the baseline scenario. In this scenario (0), the PT modal shares would decline slightly over the assessment period from 23.2% to 20.0% (mean values) among all kinds of travelers, and from 12.5% to 8.5% among choice travelers (note the high relative weight of captive PT riders). In the alternative scenarios, after their introduction and growth phases, the new medium-capacity transit systems would reach the highest mean values of their general modal shares: 29.5% for Scenario R and 29.1% for Scenario B. This very slight superiority of LRT over BST in modal shares would remain throughout the service maturity phase, both among all kinds of travelers and among choice travelers specifically.

Figure 7 depicts the annual ridership of the public transport line over the assessment period in each scenario. In agreement with the results obtained for the modal shares, the complete introduction of the new medium-capacity transit systems would result in a quick increase in the annual ridership of the PT line, rising from barely 10 million pax/year in the baseline scenario to 12.35 million pax/year in Scenario R and 12.20 million pax/year in Scenario B (taking the mean values in the 9th year as a reference point). During the remainder of the assessment period, the annual ridership would progressively grow in the three scenarios (note that this trend cannot be taken for absolutely granted, as shown by the decrease in the 97.5th percentiles); at the end of the assessment period, the mean values reach 11.08 million pax/year in Scenario 0, 13.55 million pax/year in Scenario R, and 13.35 million pax/year in Scenario B. The average ridership increase due to the medium-capacity transit systems is therefore around 21% compared to conventional bus, and is only slightly higher for LRT than for BST.

Figure 8 shows the change in the total travelers’ consumer surplus generated in Scenarios R and B by comparison with the baseline scenario (0), while Figure 9, Figure 10 and Figure 11 break down the total change in consumer surplus by group of users of each modal alternative (public transport, private automobile, and motorcycle or moped, respectively). The values shown in these figures add up the results from the six time periods and the two travel directions for each year of the assessment period, without the application of any social discount rate yet.

Thus, Figure 8 indicates that once the medium-capacity transit systems have been fully implemented and put into service, they would generate an important gain in the total consumer surplus of travelers every year, which is moderately higher in Scenario R (LRT) than in Scenario B (BST). From the end of the introduction and growth phase to the termination of the assessment period, the annual gain of total consumer surplus would range, in mean values, from €28.0 million to €39.4 million in Scenario R, and from €22.9 million to €34.8 million in Scenario B. As expected, the group of public transport users (see Figure 9) would be the greatest beneficiary from the implementation of the new medium-capacity transit systems, with aggregate surplus gains during this stage that would be, in mean values, between €33.0 million and €42.0 million per year in Scenario R, and between €30.2 million and €39.0 million per year in Scenario B. In contrast, the groups of automobile users (see Figure 10) and motorbike users (Figure 11) would receive a mild loss in their consumer surplus (note that only Scenario R has a small probability of surplus gain for these groups). This loss would amount to a mean of around €4 ± 2 million per year (slightly higher in Scenario B than in Scenario R) for all automobile users, and around €0.3 ± 0.1 million per year for all motorbike users. The considerable gap in the reduction in the consumer surplus of these two groups is mainly due to the huge difference in the number of affected trips rather than the very different effects on the generalized cost of the two modal alternatives.

However, in the first years of the assessment period, the implementation phase of the new public transport systems shows very different behavior, as the change in total travelers’ consumer surplus has a negative sign during this stage. The reason behind this decrease in consumer surplus is again the reduction in street/highway capacity for mixed traffic, which affects—especially in peak hours—the three groups of travelers during this phase (not only automobile and motorbike users, but also public transport users, as the service is still operated with buses in mixed traffic in the course of the implementation phase). The consumer surplus loss would be somewhat higher in Scenario B than in Scenario R in this case, with the greatest mean values reaching €10.1 million per year for the former and €6.8 million per year for the latter (values in the 4th year in both scenarios). The group of travelers that, as a whole, would be negatively affected by these projects to a greater extent is automobile users (Figure 10), as they might experience a mean loss of consumer surplus up to €12.2 million per year in Scenario B (5th year) and up to €8.7 million per year in Scenario R (6th year). The second highest contribution to this loss of consumer surplus would come from trips made by public transport (Figure 9), while the lowest total impact would be on the group of motorbike users (Figure 11), mainly because of the low number of trips by this modal alternative.

Figure 12 is intended to show the present value of the change in total travelers’ consumer surplus generated in Scenarios R and B, compared with the baseline scenario. This is the key measure for assessing the direct benefits received by the travelers as a result of the hypothetical implementation of the medium-capacity transit systems. The present value, referred in this case to the base year, aggregates the values of the change in consumer surplus produced over the sequence of future years that compose the assessment period. This aggregation would require the application of a discount rate (in this case, a social discount rate (SDR) given the public character of the projects) on account of intertemporal effects. Therefore, Figure 12 plots the present value of those benefits as a function of a variety of possible social discount rates, ranging from 0 to 10% in the graph. This figure reveals a moderate to small advantage of Scenario R in yielding benefits for the travelers. Although this advantage is consistent throughout the range of social discount rates, it diminishes with high SDRs, as the size of the present value also decreases.

It is well known that there is no single generally recommended social discount rate that could be assumed to fit all possible situations, as the SDR usually depends on national recommendations or regulations in practice. However, to develop a more detailed assessment of the gains in consumer surplus produced by the implementation of medium-capacity transit systems in a case study like this, an appropriate SDR value should be set. According to the suggestions of the European Commission’s ‘Guide to Cost-Benefit Analysis of Investment Projects’ [92] (p. 55) for EU countries not eligible for the Cohesion Fund, an SDR of 3% is particularly selected for these purposes. Consequently, Figure 13 and Figure 14 depict the relative frequency histograms of the present value of the change in total travelers’ consumer surplus brough about by the construction of an LRT and BST system, respectively, if an SDR of 3% is employed. In accordance also with the results observed in Figure 12, these figures show a moderately better result with Scenario R (LRT) in terms of the benefits received by travelers. Specifically, the mean present value of the gain of consumer surplus amounts to €574.3 million in Scenario R, versus €506.8 million in Scenario B. As “near-extreme” values, Scenario R entails a 97.5% probability of achieving at least €331.3 million in benefits for travelers, with only a 2.5% probability of exceeding €866.7 million, while Scenario B leads to a 97.5% probability of reaching at least €288.6 million and a 2.5% probability of surpassing €766.5 million.

The question that immediately arises from the results observed in Figure 13 and Figure 14 is how high these travelers’ benefits are compared with the start-up investment cost necessary to construct and put into operation the new medium-capacity transit systems. To answer this question, an estimation of the required investments was performed based on the analysis and update of the detailed information given in [40,41,42]. This estimation led to reference investment costs (including infrastructures and proportional costs of vehicles, depot, and workshops) of €21 million per kilometer for an average LRT system and €13 million per kilometer for a comparable BST system. As the PT line proposed in this case study is 10 km long, those figures would result in total investment costs of €210 million and €130 million for the LRT and BST, respectively. Therefore, with a social discount rate of 3%, the present value of the mean gain of total travelers’ consumer surplus exceeds very widely the required investment costs, both in Scenario R (LRT) and Scenario B (BST), which allows us to anticipate that the net socioeconomic result would be very likely positive (even with 2.5th percentiles of travelers’ consumer surplus) for the medium-capacity transit systems in this case study. Only very high SDR values would tend to reverse this positive result. In the comparative assessment of both transit systems, the mean net positive difference amounts to €364.3 million for Scenario R and €376.8 million for Scenario B, with the recommended SDR of 3%. This means that in this case study, although the gross gain of travelers’ consumer surplus is moderately higher for the LRT, the net difference of mean travelers’ benefits and investment costs turns out to be very slightly favorable to Scenario B (BST). However, the size of this advantage (€12.5 million in favor of BST) seems beforehand too narrow to firmly conclude that Scenario B has a better overall socioeconomic performance in the absence of an exhaustive, full assessment of other evaluation components such as operation, maintenance, and external costs (nevertheless, differences in these factors between scenarios are expected to be substantially lower than those in consumer surplus and investment costs). Therefore, the result found must be more cautiously regarded as a “technical tie”, while still recognizing the slight partial advantage for the BST system.

A final analysis addresses the influence of the adopted SDR on the results, as this value is usually subject to variations between different countries or world regions. In general terms, it can be said that high SDRs tend to favor projects or plans able to yield fast benefits in the short to mid-term through relatively low initial investments, even if the level of those benefits cannot be kept in the long term. On the other hand, low SDRs tend to favor plans or projects that can generate substantial benefits throughout the long term, even if they require large investments in the short term. In other words, high SDRs imply a stronger preference for the near future over the distant future, while low SDRs mean a more balanced preference between the near and distant future. In this case, the net difference of mean travelers’ benefits and investment costs would only be negative with SDRs higher than 8.4% in Scenario R (LRT) and higher than 10.8% in Scenario B (BST). In addition, the comparative analysis of both medium-capacity transit systems reveals that the net result of mean travelers’ benefits and investment costs will be better with the BST system than with the LRT (although by short or moderate margins) for any SDR above 2.3%. On the contrary, the net result would be more favorable with the LRT system only for SDRs below 2.3%. Regarding the generalizability of the results found in this particular case, note that high SDR values (typical of developing economies) would tend to favor BST systems in the evaluation, while low SDRs (usually applied in highly developed countries) advantage LRT systems. This general behavior seems consistent with the predominance of BST in developing economies and LRT in more highly developed countries.

5. Conclusions

The model presented in this article provides a sound basis for the forecasting of future values of a wide set of transport and transport-economic variables that are required for a comprehensive, correct qualitative ex ante evaluation of the two main types of medium-capacity transit systems (light-rail based systems such as LRT or modern tramway, and bus semirapid transit systems) when their possible implementation is proposed for a corridor, axis, or route carrying a medium PT-ridership volume, usually as a replacement for a highly loaded conventional bus line in mixed traffic. The proposed model is based on the general framework of a gravitational, synthetic modeling of trip distribution and modal split with incremental formulations; however, its particular development incorporates the effects, both on demand and supply, brought about by the specific characteristics and differences of these two classes of transit systems. In this regard, the model includes a comprehensive set of modal attributes or cost elements susceptible to change between scenarios and over time, not only for public transport modes but also for private motorized alternatives. Furthermore, while the solid formal, analytical principles on which the model is grounded allow us to set equal external conditions and “game rules” for both types of transit systems, the configuration of the set of possible input variables and subsequent design of the model enable sufficient flexibility for its application to a wide variety of case studies, without the necessity to adhere to specific network schemes, distribution of stops, etc.

This model is distinguished by its consistent integration of all the systematic processes covering the travel demand prognosis, the dynamic forecasting of the full set of supply characteristics and trip attributes, the valuation of the possible modal alternatives as a function of those attributes, and the estimation of the aggregate travelers’ choices in the modal split and trip distribution, including the mutual interdependencies between all those coupled processes. This enables the model to provide a wider, more integral approach to the comparison of both kinds of medium-capacity transit systems, in contrast to the more fragmented or restricted approaches observed in much of the literature, which tend to focus on delimited aspects such as their attraction potential for travelers, investment and operation and maintenance costs, user costs for PT riders only, environmental emissions, or even qualitative judgments. Another advantageous feature is the comprehensive range of input variables that can be entered and modified in the model, which enriches the potential analysis of factors that can influence the results of LRT and BST implementation projects.

Although this study aimed to compare the results of the implementation of public transport systems, the proposed model incorporates, to a degree, a multimodal approach as a crucial requirement to capture the cross effects between different modal alternatives, both in demand and in travel attributes, instead of limiting the analysis to the performance of the PT modes. These cross effects cannot be neglected, as they can lead to significant changes in the consumer surplus for users of other modal alternatives (e.g., automobile users) and would affect subsequent evaluation stages, such as the assessment of environmental external costs (for example, through changes in trip volume made by automobile and resultant emissions). Another complementary characteristic of the developed model is the explicit distinction of different phases over the assessment period in each alternative scenario, on account of the very dissimilar conditions occurring in the course of the implementation and posterior service operation of the public transport systems. This distinction can be especially relevant for capturing additional congestion costs occasioned by the construction works performed during the implementation phase (with reduced street/highway capacity for mixed traffic) of the new systems. Additionally, the model can capture and separately manage the different travel conditions that delimitate a series of time periods such as peak hours, off-peak hours, or any other period considered appropriate (i.e., multiperiod approach), instead of circumscribing the analysis to only one characteristic time period (typically peak hours).

Another contribution of the proposed model is that its practical implementation is designed to meet the requirements of the highest levels of risk analysis in the assessment of projects or plans, as that design incorporates the methodological treatment of uncertainty from the outset of its development to enable the straightforward execution of multiple model simulations, based on repeated random sampling in application of Monte Carlo simulation techniques. The management of randomness in the model covers the uncertainty from data or input variables as well as from certain internal parameters potentially subject to some degree of uncertainty; in addition, the design of the model takes into account the expected existence of correlations between some of the variables subject to randomness. The resulting level of statistical analysis overcomes the weakness and false security of any deterministic approach, and even the shortcomings of some simplified approaches, such as setting a limited number of ‘optimistic’, ‘normal’, and ‘pessimistic’ scenarios.

In practice, the model functioning was successfully tested by applying it to an artificial case study specifically designed to be representative of conditions usually found in corridors with medium PT-ridership volumes, mainly in European cities. Although the numerical results, as well as the conclusions derived, are specific to this particular case—or to other very similar cases—and therefore they should not be overgeneralized or immediately extrapolated to other circumstances, an interesting result is that, for the 10 km long PT line considered in the case study, the LRT system would generate a moderately higher benefit for travelers than the BST (difference of €67.5 million in mean values with an SDR of 3%), which turns into a very slight advantage for the BST (€12.5 million) when the required investment costs are deducted. However, this advantage is so narrow that it might be offset by potential differences in operation, maintenance, and external costs, so the result of this comparative preassessment should be rather deemed a tie. Furthermore, in the mid- and long term, the results of this kind of comparative evaluation may be affected significantly by recent and future technological advances in bus-based systems, as electric-powered vehicles with zero local emissions, autonomous driving, connected vehicles, and platooning alternatives might substantially alter the current conditions underlying the BST versus LRT comparisons.

Regarding the limitations of the developed model, some of the main constraints arise from its lack of full ability to incorporate wider network effects that could affect the analyzed corridors (either one or more), which would need to be introduced in an exogenous manner. With regard to the public transit network, this limitation does not enable the model to handle the potential overlapping of several lines in the same corridor. Meanwhile, for the network of urban roads for private motorized transport, that restriction does not allow the model to consider possible choices of alternative routes at the assignment stage. Another limitation is that the model framework requires to set the same stop locations for the LRT and BST lines as those of the preceding conventional bus line, mainly due to the incremental structure of the demand model. Otherwise, a very detailed, full demand model should be developed by considering all its spatial variability, hugely increasing the complexity of the model and its data requirements. Some additional limitations in the demand model stem from the use of aggregate choice models with weighted mean values, as a more refined model would require its successive, separate application to a wide number of population segments, or even the use of discrete choice models, which also would heavily expand the complexity and data requirements. In addition, the model does not require the utilization of specific stop-level data of boarding and alighting passengers. Although this releases the data requirements and thus extends the applicability of the model, the use of such data could have led to the employment of more refined operation and demand models for public transit systems. Finally, regarding the operation of the PT systems, the model is designed to consider conventional operation only. Therefore, it does not cover the potential impacts of possible unconventional strategies such as skip–stop or express services, which are sometimes used in LRT and BST lines.

Future research that may arise from the work presented in this article can be structured around three main lines of research. The first line would consist of complementing the comparative model presented with the analysis and incorporation of other factors that should be included in a complete socioeconomic evaluation of new LRT or BST projects throughout their life cycle, mainly the operating and maintenance costs involved in the service supply of these PT systems as well as changes in several types of external costs (local air pollution, greenhouse gas emissions, noise, traffic accidents, etc.) generated by the whole set of modal options, either public or private, in the new scenarios. The second line of research concerns the methodical analysis of multiple cases of numerical application of the model—such as the one shown in Section 4—by introducing systematic variations in the values of the main input variables, covering a multidimensional range, in order to analyze the response of the main results to those variations. In this sense, the combined sensitivity of the results to variables such as the line length, annual ridership and modal share of the public transit line in the base year, the average trip length on the line, the value of time, or the street/highway capacity for mixed traffic in the corridor (before and after the intervention) could be systematically analyzed in order to draw more generalizable conclusions, and even develop simplified procedures that depend only on a reduced set of the most influential basic data. Finally, the third line of future research would be intended to surmount some of the limitations and constraints indicated above, aiming to improve the comprehensiveness and accuracy of the current model while keeping the data requirements and computation time within feasible bounds.

In summary, the research work reported here aimed to improve the ex ante evaluation of the main types of medium-capacity transit systems, so that decision making on this topic can be based on prognoses of their future outcomes more reliable, more accurate, and better supported by a consistent theoretical framework. Ultimately, this improvement would contribute, through better-informed decision making, to the selection in each case of the transit system able to yield a higher welfare gain for the society as a whole, resulting in more efficient and sustainable allocation of the funding dedicated to urban and metropolitan public transport policies.