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.     

Assessing social equity in distance based transit fares using a model of travel behavior

The goal of this study is to develop and apply a new method for assessing social equity impacts of distance-based public transit fares. Shifting to a distance-based fare structure can disproportionately favor or penalize different subgroups of a population based on variations in settlement patterns, travel needs, and most importantly, transit use. According to federal law, such disparities must be evaluated by the transit agency, but the area-based techniques identified by the Federal Transit Authority for assessing discrimination fail to account for disparities in distances travelled by transit users. This means that transit agencies currently lack guidelines for assessing the social equity impacts of replacing flat fare with distance-based fare structures. Our solution is to incorporate a joint ordinal/continuous model of trip generation and distance travelled into a GIS Decision Support System. The system enables a transit planner to visualize and compare distance travelled and transit-cost maps for different population profiles and fare structures. We apply the method to a case study in the Wasatch Front, Utah, where the Utah Transit Authority is exploring a switch to a distance-based fare structure. The analysis reveals that overall distance-based fares benefit low-income, elderly, and non-white populations. However, the effect is geographically uneven, and may be negative for members of these groups living on the urban fringe.     

Normative framework for transit fare policy-making

This paper presents a normative model for transit fare policy-making. Key elements of the model are: establishing service policy and ridership objectives, developing an overall financial philosophy, making fare level decisions, making structural pricing decisions, and designing implementation strategies. In general, the overall objectives of a transit agency regarding service quality and ridership levels should be the main impetus behind any fare program. Identifying where transit lies on the continuum of being a public versus a private service should frame the overall financial philosophy of a transit agency. From this the specification of farebox recovery targets should follow. Deciding upon structural aspects of a fare program perhaps represents one of the most important and most frequently overlooked steps of the process. Specific cost-based and value-based fare strategies should be considered. Implementation involves making the adopted fare strategy work. Key implementation issues are: fare payment and collection techniques, necessary service changes, marketing and promotional programs, and consensus-building. The model presented calls for feedback among these steps to allow an iterative, yet comprehensive, approach to fare policy-setting.     

Transit pricing research

Several decades of research on transit pricing have provided clear insights into how riders respond to price changes in both the transit and automobile sectors. For the most part, riders are insensitive to changes in either fare levels, structures, or forms of payments, though this varies considerably among user groups and operating environments. Since riders are approximately twice as sensitive to changes in travel time as they are to changes in fares, a compelling argument can be made for operating more premium quality transit services at higher prices. Such programs could be supplemented by vouchers and concessionary programs to reduce the burden of higher fares on low-income users. Also, cross-elasticity research suggests that higher automobile prices would have a significantly greater affect on ridership than lower fares. Most research on transit fare structures shows that the common practice of flat fares is highly inequitable, penalizing short-distance and off-peak users. Free fare programs have proven quite costly for each new transit user attracted and have rarely lured motorists to transit. Free fares limited to downtowns have been more successful than systemwide free fare programs. While prepayment schemes have met with success in the U.S. and Europe, honor fares have suffered from excessive revenue losses in at least one case in the U.S. Some of the more noteworthy fare policy successes in North America have been Bridgeport's combined pass-fare program, Allentown's deep discounts, Ottawa's major fare reduction and differentiation, and Columbus's substantial midday discount. As paratransit and other new transit alternatives to conventional bus continue to emerge, new, more differentiated fare practices can be expected in the future.     

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.     

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.     

Impact evaluation of a mass transit fare change on demand and revenue utilizing smart card data

Transit fares are an effective tool for demand management. Transit agencies can raise revenue or relieve overcrowding via fare increases, but they are always confronted with the possibility of heavy ridership losses. Therefore, the outcome of fare changes should be evaluated before implementation. In this work, a methodology was formulated based on elasticity and exhaustive transit card data, and a network approach was proposed to assess the influence of distance-based fare increases on ridership and revenue. The approach was applied to a fare change plan for Beijing Metro. The price elasticities of demand for Beijing Metro at various fare levels and trip distances were tabulated from a stated preference survey. Trip data recorded by an automatic fare collection system was used alongside the topology of the Beijing Metro system to calculate the shortest path lengths between all station pairs, the origin–destination matrix, and trip lengths. Finally, three fare increase alternatives (high, medium, and low) were evaluated in terms of their impact on ridership and revenue. The results demonstrated that smart card data have great potential with regard to fare change evaluation. According to smart card data for a large transit network, the statistical frequency of trip lengths is more highly concentrated than that of the shortest path length. Moreover, the majority of the total trips have a length of around 15 km, and these are the most sensitive to fare increases. Specific attention should be paid to this characteristic when developing fare change plans to manage demand or raise revenue.     

上海轨道交通清分系统架构中应用云计算技术的探讨

通过对上海轨道交通清分系统构架的现状分析,明确清分、线路中央计算机、车站计算机等系统之间业务功能的调整方向。根据云计算技术的特点,阐述在城市轨道交通自动售检票系统中如何建立私有云计算系统、不同服务层次服务的对象以及实施的技术路线,并提出城市轨道交通自动售检票系统云计算构架的设想与模型。     

Estimating multimodal transit ridership with a varying fare structure

This paper studies public transport demand by estimating a system of equations for multimodal transit systems where different modes may act competitively or cooperatively. Using data from Athens, Greece, we explicitly correct for higher-order serial correlation in the error terms and investigate two, largely overlooked, questions in the transit literature; first, whether a varying fare structure in a multimodal transit system affects demand and, second, what the determinants of ticket versus travelcard sales may be. Model estimation results suggest that the effect of fare type on ridership levels in a multimodal system varies by mode and by relative ticket to travelcard prices. Further, regardless of competition or cooperation between modes, fare increases will have limited effects on ridership, but the magnitude of these effects does depend on the relative ticket to travelcard prices. Finally, incorrectly assuming serial independence for the error terms during model estimation could yield upward or downward biased parameters and hence result in incorrect inferences and policy recommendations.     

Optimal transit subsidy policy

The basic justification for transit subsidy is that such a subsidy is necessary, given substantial economies of scale, in order to permit fares to be set at a level which will result in reasonably efficient use of the service. Efficiency is not, however, merely a matter of the level of the fares but even more of the fare structure and pattern. Major changes in fare patterns are needed to permit reasonable efficiency of utilization to be attained, and full advantage derived from subsidy. Differentiation according to time and direction, as well as the distance of travel, is required. Ideally, competing modes such as the private automobile should be priced at marginal cost, differentially by time and place, and the subsidy should be derived from taxes on land values in the areas where such values are enhanced by the presence of transit service at low fares. In the absence of such conditions, fares should differ from marginal cost in ways that take into account the impacts of transit fare variations on auto traffic and congestion, and on the subsidy requirements and the adverse impacts of the taxes imposed to finance the subsidy.In addition to these economic efficiency considerations there may be added considerations of distributional impact and political acceptability, which may modify the optimal solution somewhat but should not greatly change the main outlines of the patterns to be recommended.     

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.     

Optimizing fare and headway to facilitate timed transfer considering demand elasticity

Fare and service frequency significantly affect transit users’ willingness to ride, as well as the supplier's revenue and operating costs. To stimulate demand and increase productivity, it is desirable to reduce the transfer time from one route to another via efficient service coordination, such as timed transfer. Since demand varies both temporally and spatially, it may not be cost-effective to synchronize vehicle arrivals on all connecting routes at a terminal. In this paper, we develop a schedule coordination model to optimize fare and headway considering demand elasticity. The headway of each route is treated as an integer-multiple of a base common headway. A discounted (reduced) fare is applied as an incentive to encourage ridership and, thus, stimulate public transit usage. The objective of the proposed coordination model is used to maximize the total profit subject to the service constraint. A numerical example is given to demonstrate the applicability of the proposed model. The results show that the optimized fare and headway may be carefully applied to yield the maximum profit. The relationship between the decision variables and model parameters is explored in the sensitivity analysis.     

Secrets of success: assessing the large increases in transit ridership achieved by Houston and San Diego transit providers

This paper summarizes and updates the findings from an earlier study by the same authors of transit systems in Houston (all bus) and San Diego (bus and light rail). Both systems achieved unusually large increases in transit ridership during a period in which most transit systems in other metropolitan areas were experiencing large losses. Based on ridership models estimated using cross section and time series data, the paper quantifies the relative contributions of policy variables and factors beyond the control of transit operators on ridership growth. It is found that large ridership increases in both areas are caused principally by large service increases and fare reductions, as well as metropolitan employment and population growth. In addition, the paper provides careful estimates of total and operating costs per passenger boarding and per passenger mile for Houston's bus operator and San Diego's bus and light rail operators. These estimates suggest that the bus systems are more cost-effective than the light rail system on the basis of total costs. Finally, the paper carries out a series of policy simulations to analyze the effects of transit funding levels and metropolitan development patterns on transit ridership and farebox recovery ratio.     

Some evidence of transit demand elasticities

This paper draws together empirical evidence from a variety of sources about the magnitudes of transit price elasticities and cross-elasticities. A number of different practical measures of demand elasticity are first defined and some expectations about magnitude are discussed. Evidence is then collated from the analysis of transit operating statistics, from experience in demonstration projects and from attempts to develop cross-sectional models of demand and modal choice.In general, all of the limited evidence available suggests that transit demand is inelastic with respect to money price. Typically, ridership is significantly more sensitive to changes in the level of service (particularly door-to-door journey time) than to changes in fare, although service elasticities also are usually numerically less than unity.In broad terms, short-run direct fare elasticities are characteristically observed to lie within the range of -0.1 to –0.7. A more precise value in a particular instance will depend on a variety of factors in ways which largely support a priori notions. Thus in very large cities, central city areas, at peak hours, and in other circumstances where the prices of alternative modes are high, transit fare elasticities are usually numerically at the lower end of the range.Estimates of cross-elasticities (representing the volumes of transit traffic diverted to other modes by transit price increases) are much harder to come by, and in fact only a few very uncertain estimates are presented here.This paper is a condensation of an Urban Institute Working Paper of the same title (WP 708-52, November 1971). Opinions expressed are those of the author and do not necessarily represent the views of The Urban Institute or its sponsors.     

The impact of transport pricing policy on individual energy consumption: a modeling case study in Kumamoto

To investigate the impact of traffic pricing policies on energy consumption, this study shows a microeconomic quantitative analysis scheme to simulate individual consumption behaviors from a microeconomic viewpoint. Energy consumption is estimated based on individual demand of non‐mobility goods and mobility goods under nine policy scenarios based on strategies of gasoline tax adding and mass transit fare reduction independently or combined. Results show that gasoline tax adding has strong effects on consumption behaviors. Energy consumption reduces mostly because of less consumption of non‐mobility goods and car trips. However, policy of mass transit fare reduction has limited impact on energy saving because consumption of non‐mobility goods and mass transit trips increases, but the number of car trips decline by only a small percentage. Comparing with single‐type policy, policies that combined gasoline tax adding and mass transit fare reduction show less energy consumption. Findings suggest that policies that increase cost of car trips, such as gasoline tax adding, are very helpful to reduce the consumption of non‐mobility goods and car trips, which contribute to less energy consumption. However, reducing cost of mass transit trips suggests limited effect on energy saving. Copyright © 2015 John Wiley & Sons, Ltd.     

Public transit service operation strategy under indifference thresholds‐based bi‐modal equilibrium

This paper investigates public transit service (fare and frequency) operation strategies in a bi‐modal network with assumption of indifference thresholds‐based travelers' mode choice behavior. Under such behavior, users would switch to a new mode only if its utility is larger than the utility of current mode plus a threshold. The concept of indifference thresholds‐based bi‐modal equilibrium (ITBE) and the properties of the ITBE solution are explicitly proposed. Considering transit operator's different economic objectives (profit‐maximizing, no‐deficit and total system cost‐minimizing), the effect of indifference thresholds on transit fare and frequency schemes is studied. Some numerical experiments are accompanied to verify the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Time‐of‐day transit pricing: comparative US and international experiences

Experiences with time‐of‐day transit pricing in the U.S. are reviewed in this article and compared to those in other countries. Emphasis is placed on examining ridership, financial and efficiency impacts associated with time‐of‐day pricing, along with highlighting innovative approaches to implementing fare differentials. American time‐of‐day fare structures have been about evenly split between off‐peak discounts, peak‐period surcharges, and programmes involving differential rates of fare increases between peak and off‐peak hours. Although most American operators introduced time‐of‐day differentials to encourage ridership shifts to the off‐peak period, available evidence suggests that they have been only marginally successful in doing so. Off‐peak users were generally found to be far more fare‐sensitive to discounts than peak passengers were to surcharges. Only in a handful of American cities were significant efficiency and financial benefits from time‐of‐day pricing recorded, though in those few places, they tended to be substantial. The most successful American programmes have been those which collect fares on the basis of bus runs and direction of trips (rather than the exact time) and which aggressively market their programmes under the aegis of ‘bargain fares’. It is concluded that useful lessons can be gained by sharing policy insights from experiments with differential transit pricing in both the US and elsewhere.     

Optimization of Fare Structure and Service Frequency for Maximum Profitability of Transit Systems

Abstract

Providing efficient public transportation has been recognized as a potential way of alleviating congestion, improving mobility, mitigating air pollution, and reducing energy consumption. Many people use public transportation systems for their daily commute, while others use different transportation modes (e.g. cars, taxis, carpools, etc.). Inexpensive fares with good transit service encourages ridership, and the resulting revenue may be used to provide better service. Optimization of transit service frequency and its associated fare structure is desirable in order to increase revenue at reasonable transit operating expenditure. The objective of the study reported here is to maximize profit subject to service capacity constraint, while elastic demand is considered. The solution methodology is developed and applied to solve the profit maximization problem in a case study based on Newark, NJ, USA. Numerical results, including optimal solutions and sensitivity analyses, are presented. It is found that an optimal temporal headway and differential fare structure that maximizes total profit for the studied subway system can be efficiently solved.     

A simulation of transit bus emissions along an urban corridor: Evaluating changes under various service improvement strategies

This study investigates the impacts of transit improvement strategies on bus emissions along a busy corridor in Montreal, Canada. The local transit provider, Société de Transport de Montréal, has implemented a number of strategies which include the use of smart cards, limited-stop (express bus) service, and reserved bus lanes along this corridor. Using data collected on-board for instantaneous speeds and stop-level ridership, we estimated bus emissions of greenhouse gases and other pollutants at three levels: road segment, bus-stop, and per passenger. A regression of segment-level emissions against a number of explanatory variables reveals that reserved bus lanes and express bus service reduce emissions significantly. On the other hand, smart card use reduces idling emissions compared to other fare payment methods. Our findings are of most relevance for transit planners who are seeking to implement different strategies to reduce emissions and improve transit performance.     

Transit passenger response: Short and long term elasticities using time series analysis

This paper investigates the effects of price and service changes on transit ridership. The concept of elasticity is introduced and the traditional methods for estimating elasticities are discussed. In this paper an extra dimension is added by investigating short and long term elasticities. Time series analysis, developed by Box and Jenkins is chosen for the analysis. The Box and Jenkins methodology is applied to a monthly time series of average weekday ridership on the Chicago Transit Authority (CTA) rail system. Four categories of explanatory variables are investigated: fare on the CTA rail system, service provided on the CTA rail system, cost of car trips and weather effects. The effects of gas prices and rail service were found to be significant; however the results indicate a twelve month delay before service changes influence ridership. The effect of transit fares was found to be insignificant, indicating that both the short and long term fare elasticities are zero.