A quadratic programming model for designing and evaluating distance-based and zone fares for urban transit

A microcomputer based system for designing and evaluating distance-based and zone fares for transit properties is described. At the heart of the system is an optimization model that finds the fixed charge, mileage charge, and transfer charge that maximize gross revenue subject to constraints on ridership and the form of the fare equation. A linear approximation to the demand curve at the base case values results in a quadratic programming problem. Three alternative modes of using the model system are demonstrated using selected data from the Chicago Transit Authority. Model extensions and proposed future work are outlined.     

Flat versus differentiated transit pricing: What's a fair fare?

Virtually every U.S. bus system today charges its customers flat fares. Recent trends, however, suggest that passengers are traveling farther and proportionally more during peak hours, factors which have contributed toward transit's cost spiral. As deficits continue to soar and available funding tightens, current pricing rationales must be seriously questioned. This paper assesses the efficiency and equity impacts of three California transit agencies' fare structures. Short-distance, off-peak patrons are found to heavily cross-subsidize long-haul commuters. Fares differentiated by distance and time-of-day, in contrast, could improve the transit industry's fiscal posture while eliminating differences in payment rates. Barriers to their implementation remain formidable, however, both in terms of current fare collection capabilities and political acceptability.     

The dynamics of fare and frequency choice in urban transit

This paper investigates the choice of fare and service frequency by urban mass transit agencies. A more frequent service is costly to provide but is valued by riders due to shorter waiting times at stops, and faster operating speeds on less crowding vehicles. Empirical analyses in the 1980s found that service frequencies were too high in most of the cities studied. For a given budget constraint, social welfare could be improved by reducing service frequencies and using the money saved to lower fares. The cross-sectional nature of these analyses meant that researchers were unable to address the question of when the oversupply occurred. This paper seeks to answer that question by conducting a time-series analysis of the bus operations of the Chicago Transit Authority from 1953 to 2005. The paper finds that it has always been the case that too much service frequency was provided at too high a fare. The imbalance between fares and service frequency became larger in the 1970s when the introduction of operating subsidies coincided with an increase in the unit cost of service provision.     

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.     

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.     

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.     

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.     

The impact of fare and gasoline price changes on monthly transit ridership: Empirical evidence from seven U.S. transit authorities

This paper presents eight empirical models of monthly ridership for seven U.S. Transit Authorities. Within the framework of these models, the impacts upon monthly ridership from changes in the real fare and gasoline prices are examined. Important findings are: (1) the elasticities of monthly transit ridership with respect to the real fare are negative and inelastic, ranging from 0.042 to 0.62; and (2) the elasticities of monthly transit ridership with respect to the real gasoline price are positive and inelastic, ranging from 0.08 to 0.80. Such results have important policy implications for decisions based on the relationships of price, revenue, and ridership; and for assessing the impacts of changing gasoline prices upon urban modal choice.     

The cost of equity: Assessing transit accessibility and social disparity using total travel cost

Social equity is increasingly incorporated as a long-term objective into urban transportation plans. Researchers use accessibility measures to assess equity issues, such as determining the amount of jobs reachable by marginalized groups within a defined travel time threshold and compare these measures across socioeconomic categories. However, allocating public transit resources in an equitable manner is not only related to travel time, but also related to the out-of-pocket cost of transit, which can represent a major barrier to accessibility for many disadvantaged groups. Therefore, this research proposes a set of new accessibility measures that incorporates both travel time and transit fares. It then applies those measures to determine whether people residing in socially disadvantaged neighborhoods in Montreal, Canada experience the same levels of transit accessibility as those living in other neighborhoods. Results are presented in terms of regional accessibility and trends by social indicator decile. Travel time accessibility measures estimate a higher number of jobs that can be reached compared to combined travel time and cost measures. However, the degree and impact of these measures varies across the social deciles. Compared to other groups in the region, residents of socially disadvantaged areas have more equitable accessibility to jobs using transit; this is reflected in smaller decreases in accessibility when fare costs are included. Generating new measures of accessibility combining travel time and transit fares provides more accurate measures that can be easily communicated by transportation planners and engineers to policy makers and the public since it translates accessibility measures to a dollar value.     

Does the increase of public transit fares deteriorate air quality in Beijing?

Since 2006, Beijing lowered its public transit fares as a way to improve air quality. However, Beijing increased public transportation fare prices from December 28, 2014, and commuters pay for the distance they traveled rather than a flat fare. This paper explores the effect of Beijing public transit fares increase on air quality. We collect daily data of air pollution and weather variables and use synthetic control method of Abadie and Gardeazabal (2003) to select control units. We then estimate a difference-in-differences model and assess the effect of the policy on air quality index (AQI). We find a 16.28% increase in air pollution in short run. However, we find no longer-run effect on air quality.     

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.     

Passengers’ response to transit fare change: an ex post appraisal using smart card data

Fare change is an effective tool for public transit demand management. An automatic fare collection system not only allows the implementation of complex fare policies, but also provides abundant data for impact analysis of fare change. This study proposes an assessment approach for analyzing the influence when substituting a flat-fare policy with a distance-based fare policy, using smart card data. The method can be used to analyze the impact of fare change on demand, riding distances, as well as price elasticity of demand at different time and distance intervals. Taking the fare change of Beijing Metro implemented in 2014 as a case study, we analyze the change of network demand at various levels, riding distances, and demand elasticity of different distances on weekdays and weekends, using the method established and the smart card data a week before and after the fare change. The policy implication of the fare change was also addressed. The results suggest that the fare change had a significant impact on overall demand, but not so much on riding distances. The greatest sensitivity to fare change is shown by weekend passengers, followed by passengers in the evening weekday peak time, while the morning weekday peak time passengers show little sensitivity. A great variety of passengers’ responses to fare change exists at station level because stations serve different types of land usage or generate trips with distinct purposes at different times. Rising fares can greatly increase revenue, and can shift trips to cycling and walking to a certain extent, but not so much as to mitigate overcrowding at morning peak times. The results are compared with those of the ex ante evaluation that used a stated preference survey, and the comparison illustrates that the price elasticity of demand extracted from the stated preference survey significantly exaggerates passengers’ responses to fare increase.     

The effect of crowding on public transit user travel behavior in a large-scale public transportation system through modeling daily variations

In this paper, the crowding effect in a transit vehicle is modeled in a time-expanded network that considers the daily variation in passenger flows. The study models the daily variation of in-vehicle crowding in a real large-scale transit system. A transit assignment for this real network is modeled and implemented by constructing a crowding cost function that follows the valuation of crowding and by using the reliable shortest path finding method. The direct application of the crowding model to a real network for the Utah Transit Authority indicates that crowd modeling with multi-user classes could influence public transportation system planning and affect the revenues of transit agencies. Moreover, the addition of the disutility factor, crowding, does not always appear to cause an increase in disutility for transit users.     

Management objectives and the causes of mass transit deficits

Based on data for the period from 1948 to 1997, exogenous decreases in demand and increases in costs are estimated to have reduced the annual profitability of the Chicago Transit Authority (CTA) by $1 billion. Half of this decline was recouped by reductions in service, increased fares and increased productivity. Even more would have been recouped had the CTA not given away earlier productivity gains during the 1970s. This was during a period when subsidies were increasing rapidly, and seemingly without constraint. When faced with financial challenges, management has preferred to increase fares rather than reduce service levels to the detriment of social welfare.     

Consequences of service reduction in municipal transit: San Francisco’s muni

Urban transit in the United States is going through a crisis of rising costs, increasing fares, falling patronage, and concomitant service reductions; typical of the pattern is San Francisco’s Municipal Railway, the agency in charge of all the City’s transit. From a basic fare of 15c in 1969, two increases brought the fare to 25c by 1972, and cut sharply into a previously stable patronage. The “Muni”, in an effort to reduce costs and meet its budgeted deficit, attempted to reduce service by ten to fifteen percent. From an analysis of the data which could be obtained, it appears that neither efficiency not equity in the City would have been served by the proposed cutbacks. The analysis draws from a variety of sources and methods in exploring the interactions within the transportation system and within the city budget.     

Transport system management in San Francisco: an assessment

The paper reports the results of a transportation corridor study. The emphasis in the study is in transportation system management (TSM) policies although some capital intensive alternatives are also considered.

The results suggest that currently popular TSM policies in U.S.A., even when augmented with capital intensive changes, have only marginal impacts on modal choices. These currently popular policies, high occupancy vehicle priority lanes, improved bus and express bus service, increased feeder bus service and so forth, appear to confer benefits to well to do suburbanites but do not improve the transportation of urban dwellers.

Another interesting result is that if user costs were increased to cover the full costs of transportation the transit fares for low income people would increase ten percent and the increase for urban dwellers would be about 20 percent. Interestingly, there would be no change in bus fares for either group. However, for high income travellers and suburbanites the increase in transit fares would be in excess of 100 percent. Thus, the current fare structure is inequitable making the low income people and the urban dwellers to pay a much larger share of their transportation cost than the often well to do suburbanites.     

Transit fare differentials: A theoretical analysis

This paper compares the ridership. operator revenue, passenger-km, and consumer surplus in uniform pricing policy versus the differential fare pricing system. The comparisons are assumed that the flat fare is set equal to average differential fares. With mathematical derivation, the paper investigates some of the properties of fare differentiation and discusses characteristics of a general nature. The theoretical results have spelled out the conditions under which pricing policy may yield higher performances. A simple numerical example is used to demonstrate the sensitivity of the model. Some recommendations for setting transit pricing policy are drawn from the results.     

Observed and simulated traffic impacts from the 2013 Bay Area Rapid Transit strike

Despite high costs, many cities build public transit to address regional equity, environmental and economic goals. Although public transit accounts for a minority of trips (～5%), the impact is widely felt when service is suspended during a strike through excess road demand and slower journeys. In 2013, Bay Area Rapid Transit (BART) workers participated in two brief strikes, and the resulting traffic conditions illustrate the value of transit to drivers in the San Francisco Bay Area region. This paper tests the impact of rail transit service interruption on freeway traffic conditions using volumes and travel times. During the strike, regional freeway conditions showed negligible change. However, on facilities that parallel BART service, the impacts are as bad as the worst day of a typical week. Conditions on the San Francisco–Oakland Bay Bridge showed significant impacts with travel times and volumes nearly doubling the baseline median values on the worst day.     

Nonlinear pricing of taxi services

This paper examines the effects of nonlinear fare structures in taxi markets using an extended taxi model with an explicit consideration of perceived profitability. The expected profit, defined as the profit per unit time (inclusive of both occupied and vacant taxi times), that a taxi driver expects to receive from picking up a customer in a particular zone or location, has great impact on the taxi driver’s choice of location in the search for customers. The fare structure directly governs the profitability of taxi rides of different distances originating from different locations. With these explicit considerations, the extended model is intended to look into the market effects of adopting a nonlinear fare structure with declining incremental charges. The proposed nonlinear fare structure could help restore a level-playing field for taxi operators whose businesses have been affected by some taxi drivers who resort to practices such as offering fare discounts or accepting requests for discounted fares from passengers for long-haul trips. Analysis of sensitivity of social welfare and profit gain as well as taxi/customer wait/search times is conducted with respect to the parameters in the nonlinear fare structure for the Hong Kong taxi market, and Pareto-improving nonlinear fare amendments are identified that neither disadvantage any customer nor reduce the taxi operators’ profits.