Optimal transit fare in a bimodal network under demand uncertainty and bounded rationality

This paper investigates the optimal transit fare in a simple bimodal transportation system that comprises public transport and private car. We consider two new factors: demand uncertainty and bounded rationality. With demand uncertainty, travelers are assumed to consider both the mean travel cost and travel cost variability in their mode choice decision. Under bounded rationality, travelers do not necessarily choose the travel mode of which perceived travel cost is absolutely lower than the one of the other mode. To determine the optimal transit fare, a bi‐level programming is proposed. The upper‐level objective function is to minimize the mean of total travel cost, whereas the lower‐level programming adopts the logit‐based model to describe users' mode choice behaviors. Then a heuristic algorithm based on a sensitivity analysis approach is designed to solve the bi‐level programming. Numerical examples are presented to illustrate the effect of demand uncertainty and bounded rationality on the modal share, optimal transit fare and system performance. Copyright © 2013 John Wiley & Sons, Ltd.     

A reliability‐based traffic assignment model for multi‐modal transport network under demand uncertainty

In densely populated and congested urban areas, the travel times in congested multi‐modal transport networks are generally varied and stochastic in practice. These stochastic travel times may be raised from day‐to‐day demand fluctuations and would affect travelers' route and mode choice behaviors according to their different expectations of on‐time arrival. In view of these, this paper presents a reliability‐based user equilibrium traffic assignment model for congested multi‐modal transport networks under demand uncertainty. The stochastic bus frequency due to the unstable travel time of bus route is explicitly considered. By the proposed model, travelers' route and mode choice behaviors are intensively explored. In addition, a stochastic state‐augmented multi‐modal transport network is adopted in this paper to effectively model probable transfers and non‐linear fare structures. A numerical example is given to illustrate the merits of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

A bi‐level programming approach — Optimal transit fare under line capacity constraints

The fare of a transit line is one of the important decision variables for transit network design. It has been advocated as an efficient means of coordinating the transit passenger flows and of alleviating congestion in the transit network. This paper shows how transit fare can be optimized so as to balance the passenger flow on the transit network and to reduce the overload delays of passengers at transit stops. A bi‐level programming method is developed to optimize the transit fare under line capacity constraints. The upper‐level problem seeks to minimize the total network travel time, while the lower‐level problem is a stochastic user equilibrium transit assignment model with line capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Passenger route guidance system for multi‐modal transit networks

In many public transport oriented cities in the world, especially Asian cities, the public transport system has been developed extensively, to the extent that it has become increasingly difficult to navigate. Although inter‐modal transfers are common and often necessary, a complete set of the routes across transport modes is generally not presented in a form that is accessible to travelers, as each operator would only publish its own routes. Moreover, the common nonlinear fare tables together with inter‐modal fare discounts pose challenges to travelers in deciding their best routes. This study develops a multi‐modal passenger route guidance system, called eFinder, to aid travelers with their combined mode‐route choices. We discuss the architecture and features of this system in this study. This system forms a platform for disseminating public transit information and should complement further development and use of the public transport network by enabling travelers to make informed choices.     

Estimation of origin‐destination matrices for a multimodal public transit network

This paper presents a procedure for the estimation of origin‐destination (O‐D) matrices for a multimodal public transit network. The system consists of a number of favored public transit modes that are obtained from a modal split process in a traditional four‐step transportation model. The demand of each favored mode is assigned to the multimodal network, which is comprised of a set of connected links of different public transit modes. An entropy maximization procedure is proposed to simultaneously estimate the O‐D demand matrices of all favored modes, which are consistent with target data sets such as the boarding counts and line segment flows that are observed directly in the network. A case study of the Hong Kong multimodal transit network is used to demonstrate the effectiveness of the proposed methodology.     

Integrating congestion pricing,transit subsidies and mode choice

We model and analyze optimal (welfare maximizing) prices and design of transport services in a bimodal context. Car congestion and transit design are simultaneously introduced and consumers choose based on the full price they perceive. The optimization variables are the congestion toll, the transit fare (and hence the level of subsidies) and transit frequency. We obtain six main results: (i) the optimal car-transit split is generally different from the total cost minimizing one; (ii) optimal congestion and transit price are interdependent and have an optimal frequency attached; (iii) the optimal money price difference together with the optimal frequency yield the optimal modal split; (iv) if this modal split is used in traditional stand-alone formulations – where each mode is priced independently–resulting congestion tolls and transit subsidies and fares are consistent with the optimal money price difference; (v) self-financing of the transport sector is feasible; and (vi) investment in car infrastructure induces an increase in generalized cost for all public transport users.     

Tradable credits scheme and transit investment optimization for a two‐mode traffic network

This paper proposes an optimization model to minimize the “system costs” and guide travelers' behavior by exploring the optimal bus investment and tradable credits scheme design in a bimodal transportation system. Travelers' transport mode choice behavior (car or bus) and the modal equilibrium conditions between these two forms of transport are studied in the tradable credits scheme. Public transport priority is highlighted by charging car travelers credits only. The economies of scale presented by the transit system under the tradable credit scheme are analyzed by comparing the marginal cost and average cost. Numerical examples are presented to demonstrate the model. Furthermore, the effects of tradable credits schemes on bus investment and travelers' modal choice behavior are explored based on scenario discussions. Copyright © 2016 John Wiley & Sons, Ltd.     

Traffic dynamics in a bi-modal transportation network with information provision and adaptive transit services

This paper has two major components. The first one is the day-to-day evolution of travelers’ mode and route choices in a bi-modal transportation system where traffic information (predicted travel cost) is available to travelers. The second one is a public transit operator adjusting or adapting its service over time (from period to period) based on observed system conditions. Particularly, we consider that on each day both travelers’ past travel experiences and the predicted travel cost (based on information provision) can affect travelers’ perceptions of different modes and routes, and thus affect their mode choice and/or route choice accordingly. This evolution process from day to day is formulated by a discrete dynamical model. The properties of such a dynamical model are then analyzed, including the existence, uniqueness and stability of the fixed point. Most importantly, we show that the predicted travel cost based on information provision may help stabilize the dynamical system even if it is not fully accurate. Given the day-to-day traffic evolution, we then model an adaptive transit operator who can adjust frequency and fare for public transit from period to period (each period contains a certain number of days). The adaptive frequency and fare in one period are determined from the realized transit demands and transit profits of the previous periods, which is to achieve a (locally) maximum transit profit. The day-to-day and period-to-period models and their properties are also illustrated by numerical experiments.     

The Downs–Thomson Paradox with responsive transit service

Downs (1962) and Thomson (1977) suggested that highway capacity expansion may produce counterproductive effects on the two-mode (auto and transit) transport system (Downs–Thomson Paradox). This paper investigates the occurrence of this paradox when transit authority can have different economic objectives (profit-maximizing or breakeven) and operating schemes (frequency, fare, or both frequency and fare). For various combinations of economic objectives and operating schemes, the interaction between highway expansion and transit service is explored, as well as its impact on travelers’ mode choices and travel utilities. Further, for each combination, the conditions for occurrence of the Downs–Thomson Paradox are established. We show that the paradox never occurs when transit authority is profit-maximizing, but it is inevitable when the transit authority is running to maximize travelers’ utility while maintaining breakeven. This is because the former transit authority tends to enhance transit service (e.g., raise frequency or reduce fare) when facing an expanded highway; and on the contrary, the latter tends to compromise transit service (e.g., reduce frequency or raise fare). Both analytical and numerical examples are provided to verify the theoretical results.     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Modelling public transport on‐board congestion: comparing schedule‐based and agent‐based assignment approaches and their implications

Transit systems are subject to congestion that influences system performance and level of service. The evaluation of measures to relieve congestion requires models that can capture their network effects and passengers' adaptation. In particular, on‐board congestion leads to an increase of crowding discomfort and denied boarding and a decrease in service reliability. This study performs a systematic comparison of alternative approaches to modelling on‐board congestion in transit networks. In particular, the congestion‐related functionalities of a schedule‐based model and an agent‐based transit assignment model are investigated, by comparing VISUM and BusMezzo, respectively. The theoretical background, modelling principles and implementation details of the alternative models are examined and demonstrated by testing various operational scenarios for an example network. The results suggest that differences in modelling passenger arrival process, choice‐set generation and route choice model yield systematically different passenger loads. The schedule‐based model is insensitive to a uniform increase in demand or decrease in capacity when caused by either vehicle capacity or service frequency reduction. In contrast, nominal travel times increase in the agent‐based model as demand increases or capacity decreases. The marginal increase in travel time increases as the network becomes more saturated. Whilst none of the existing models capture the full range of congestion effects and related behavioural responses, existing models can support different planning decisions. Copyright © 2016 John Wiley & Sons, Ltd.     

Validation of a schedule‐based capacity restraint transit assignment model for a large‐scale network

This paper describes the application of a capacity restraint trip assignment algorithm to a real, large‐scale transit network and the validation of the results. Unlike the conventional frequency‐based approach, the network formulation of the proposed model is dynamic and schedule‐based. Transit vehicles are assumed to operate to a set of pre‐determined schedules. Passengers are assumed to select paths based on a generalized cost function including in‐vehicle and out‐of‐vehicle time and line change penalty. The time‐varying passenger demand is loaded onto the network by a time increment simulation method, which ensures that the capacity restraint of each vehicle during passenger boarding is strictly observed. The optimal‐path and path‐loading algorithms are applied iteratively by the method of successive averages until the network converges to the predictive dynamic user equilibrium. The Hong Kong Mass Transit Railway network is used to validate the model results. The potential applications of the model are also discussed.     

Why do people fare evade? A global shift in fare evasion research

ABSTRACT

Fare evasion is a significant concern for most transit authorities. The traditional approach to fare compliance has focussed on modifying the physical control of ticketing or ticket inspection rates. Yet recently the perspective on fare evasion has begun to shift toward profiling the fare evader or understanding the customer motivations to fare evade. This paper uses a literature review method to document the characteristics of these three perspectives on fare evasion: the conventional transit system perspective, the customer profiling perspective and the customer motivations perspective. We find that the conventional transit system perspective, although straightforward to measure and control, has its limits particularly in “open” transit systems. The customer profiling perspective attempts to identify, based on demographics, which customers are more likely to fare evade. However this perspective has little use beyond profiling and is ethically questionable. The customer motivations perspective provides a richer understanding of how customers define fare evasion and what attitudes, social norms and circumstances motivates them to fare evade. Considering that between 20% and 40% of a city’s residents admit to fare evading at some point, understanding these complex motivations can help improve revenue compliance at a time when most governments heavily subsidise their transit systems.     

A methodology for choosing between fixed‐route and flex‐route policies for transit services

Flex‐route transit brings together the low cost operability of fixed‐route transit with the flexibility of demand responsive transit, and in recent years, it has become the most popular type of flexible transit service. In this paper, a methodology is proposed to help planners make better decisions regarding the choice between a conventional fixed‐route and a flex‐route policy for a specific transit system with a varying passenger demand. A service quality function is developed to measure the performance of transit systems, and analytical modeling and simulations are used to reproduce transit operation under the two policies. To be closer to reality, two criteria are proposed depending on the processing of rejected requests in the assessment of the service quality function for flex‐route services. In various scenarios, critical demand densities, which represent the switching points between the two competing policies, are derived in a real‐world transit service according to the two criteria. Copyright © 2014 John Wiley & Sons, Ltd.     

Impact of ITS measures on public transport: A Case study

Intelligent Transport Systems (ITS) have a wide range of applications. They range from the more traditional signal coordination system to concepts such as smart cars and smart roads. This paper describes transit‐based ITS measures in Singapore. The island‐state has plans to double the current 90 km rail network over the next ten years and has also implemented or committed to implement many ITS initiatives that impact upon the public transport systems. The aim of these investments is to achieve a high transit modal share using a comprehensive transit network. ITS measures that can promote this aim include: automatic vehicle location systems for buses and taxis, integrated transit fare systems using contactless smart cards, rail information systems, multi‐modal travel guides on Internet and electronic road pricing. The potential impacts of these measures are delay reduction, more comfort, productivity gain and better network accessibility. ITS measures do not necessarily add physical capacity to a public transport system but are excellent supporting measures to encourage the modal shift to transit, particularly if a quality transit system is already in place.     

A GIS‐based method to identify cost‐effective routes for rural deviated fixed route transit

Deviated fixed route transit (DFRT) service connecting rural and urban areas is a growing transportation mode in the USA. Little research has been done to develop frameworks for route design. A methodology to explore the most cost‐effective DFRT route is presented in this paper. The inputs include potential DFRT demand distribution and a road network. A heuristic is used to build possible routes by starting at urban cores and extending in all network directions in certain length increments. All the DFRT routes falling in the length range desired by the users are selected. The cost effectiveness of those routes, defined by operating cost per passenger trip, is compared. The most cost‐effective route is selected and presented in a GIS map. A case study illustrates the methodology in several Tennessee metropolitan regions. The most cost‐effective route length is case specific; some routes (e.g. those out of our Nashville case) are most cost effective when short, while others (e.g. those out of Memphis) are most cost effective when long. Government agencies could use the method to identify routes with the lowest operating cost per passenger given a route length or an operating cost budget. Copyright © 2016 John Wiley & Sons, Ltd.     

Analogy of fixed route shared taxi (taxi khattee) and bus services under various demand density and economical conditions

Taxi khattee is a fixed route unregulated shared taxi. It is a very common mode of transportation in Iran. Fixed route, unscheduled operation, open, unlimited pick‐up and drop‐off locations, and share ride are common features of taxi khattees. Low passenger capacity and working in high demand corridors provides for the possibility of high service frequencies any time of the day. Taxi khattees are similar to jitneys, which are obsolete or illegal in many countries. The aim of this research is to design transit network of an area using taxi khattees in addition to buses. The methodology employed in this paper simultaneously considers the costs to the users and operators on the one hand, and those of the public non‐users on the other hand. Taxi khattees are used in the design of a multimodal network along with buses to characterize the appropriate economic domain for their use. Moreover, their operation indices are compared against those of buses. A sensitivity analysis is carried out on various performance measures. Results show taxi khattees should be used in areas where population density is low, work force is inexpensive, social costs are not considered in fare calculation, and users' value of time is high. The study contradicts the common belief that since taxi khattees provide a high frequency compared to buses, they are economically plausible to use in a transit fleet. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimizing sustainable feeder bus operation considering realistic networks and heterogeneous demand

A mathematical model is developed to optimize social and fiscal sustainable operation of a feeder bus system considering realistic network and heterogeneous demand. The objective total profit is a nonlinear, mixed integer function, which is maximized by optimizing the number of stops, headway, and fare. The stops are located which maximize the ridership. The demand elasticity for the bus service is dependent on passengers' access distance, wait time, in‐vehicle time, and fare. An optimization algorithm is developed to search for the optimal solution that maximizes the profit. The modeling approach is applied to planning a bus transit system within Woodbridge, New Jersey. Copyright © 2011 John Wiley & Sons, Ltd.     

Nature of influence of out‐of‐vehicle time‐related attributes on transit attractiveness: a random parameters logit model analysis

This paper describes the nature of the impacts of walking distances and waiting time on transit use. The relative trade‐offs of walking and transfer components with other transit service attributes are also discussed. A total of 449 completed stated‐preference interviews were collected; with six observations from each respondent, the total number of observations was 2694. This data set was used to estimate the coefficients in different utility functions using a random parameters logit model. The results demonstrated that walking distances to and from transit stops have important and significant nonlinear negative influences on the attractiveness of transit. Transfer waiting time was also shown to have a significant nonlinear negative impact on transit attractiveness. The random parameters logit model had a better model fit than the standard logit model. Some of the findings obtained here are novel, while others are consistent with previous works. These findings have implications for both theory and practice. Copyright © 2014 John Wiley & Sons, Ltd.     

A procedure for estimating transit subsidization requirements for developing countries

The paper presents a procedure that has been developed for estimating subsidization requirements for urban transit services in developing countries. The procedure is based on a subsidization policy of reducing transport expenditure burden on the average commuter, by maintaining his transport expenditure-income ratio at a reasonable level. It is designed for both regulated and deregulated transport markets. It requires, as input, historical data (previous year) on fare, productivity, and load factor for the transport service or mode concerned, the transport expenditure-income ratio distribution of the commuters, and the current level of commuter personal transport allowance. It is based on the premise that transport expenditure-income ratio is inversely related to income. The subsidization formula developed in the paper yields a level of subsidy that is commensurate with the level of control a government is able to exercise over transit operations.