A time series analysis of monthly ridership for an urban rail rapid transit line

This paper presents two time series regression models, one in linear form and the other in logarithmic form, to estimate the monthly ridership of a single urban rail rapid transit line. The model was calibrated for a time period of about six and a half years (from 1978–1984) based on ridership data provided by a transit authority, gasoline prices provided by a state energy department, and other data.The major findings from these models are: (1) seasonal variations of ridership are –6.26%, or –6.20% for the summer period, and 4.77%, or 4.62% for the October period; (2) ridership loss due to a station closure is 2.46% or 2.41%; and (3) elasticities of monthly ridership are –0.233 or –0.245 with respect to real fare, 0.113 or 0.112 with respect to real gasoline price, and 0.167 or 0.185 with respect to real bridge tolls for the competing automobile trips. Such route specific application results of this inexpensive approach provide significant implications for policymaking of individual programs in pricing, train operation, budgeting, system changes, etc., as they are in the case reported herein and would be in many other cities.     

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.     

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.     

Forecasting ridership for a metropolitan transit authority

The recent volatility in gasoline prices and the economic downturn have made the management of public transportation systems particularly challenging. Accurate forecasts of ridership are necessary for the planning and operation of transit services. In this paper, monthly ridership of the Metropolitan Tulsa Transit Authority is analyzed to identify the relevant factors that influence transit use. Alternative forecasting models are also developed and evaluated based on these factors—using regression analysis (with autoregressive error correction), neural networks, and ARIMA models—to predict transit ridership. It is found that a simple combination of these forecasting methodologies yields greater forecast accuracy than the individual models separately. Finally, a scenario analysis is conducted to assess the impact of transit policies on long-term ridership.     

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.     

The asymmetric effects of gasoline prices on public transportation use in Taiwan

This study investigates the asymmetric effects of gasoline prices on public transportation use in Taiwan. The empirical results obtained are as follows. First, we verify that gasoline price is an important determinant of transit demand. Gasoline prices have significantly positive effects on bus and mass rapid transit (MRT) use. Second, MRT ridership is more sensitive than bus and railway ridership to gasoline price and income. In the face of oil prices escalation and economic growth, the MRT system should have higher priority in public transportation planning. Third, the effects of gasoline prices on bus and MRT use are asymmetric. Bus and MRT use increases faster when gasoline prices rise than it decreases when gasoline prices fall. The transit agencies should adjust operating strategies faster in the rising of oil prices than in the falling of oil prices. It is important for transit planning to use oil prices as signals and increase the flexibility of operation in dealing with the changes in ridership. Some strategies, such as enhancing the availability of transfer information and updating transit information timely, are helpful to move passengers efficiently.     

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.     

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.     

A model for forecasting public transit

This study develops a model that explains public transit ridership in Orange Country, California over quarterly periods during the 1974–1988 period. The model uses a Cobb-Douglas functional form and a Cochrane-Orcutt iterative procedure to measure the association between public transit ridership and the potential number of users, relative level of public transit service, relative price of public transit, seasonality, and external shocks. Relative measures of the explanatory variables are used to reduce the potential for multicollinearity and give greater confidence in the reliability of the estimated elasticities. The model is then used to prepare conditional quarterly forecasts for ridership in 1988 and unconditional quarterly forecasts during the 1989–1993 period.     

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.     

Impact of weather on urban transit ridership

Utilizing daily ridership data, literature has shown that adverse weather conditions have a negative impact on transit ridership and in turn, result in revenue loss for the transit agencies. This paper extends this discussion by using more detailed hourly ridership data to model the weather effects. For this purpose, the daily and hourly subway ridership from New York City Transit for the years 2010–2011 is utilized. The paper compares the weather impacts on ridership based on day of week and time of day combinations and further demonstrates that the weather’s impact on transit ridership varies based on the time period and location. The separation of ridership models based on time of day provides a deeper understanding of the relationship between trip purpose and weather for transit riders. The paper investigates the role of station characteristics such as weather protection, accessibility, proximity and the connecting bus services by developing models based on station types. The findings indicate substantial differences in the extent to which the daily and hourly models and the individual weather elements are able to explain the ridership variability and travel behavior of transit riders. By utilizing the time of day and station based models, the paper demonstrates the potential sources of weather impact on transit infrastructure, transit service and trip characteristics. The results suggest the development of specific policy measures which can help the transit agencies to mitigate the ridership differences due to adverse weather conditions.     

A time-series analysis of public transit ridership in Portland,Oregon, 1971–1982

This paper examines the factors affecting changes in transit ridership in Portland, Oregon, during the period 1971 through 1982. A time-series methodology is used to investigate the effects of service level, travel costs, and market size at the system, sector, and route levels. Transfer function and multiple time-series models are compared. Intervention analysis is used to determine the impact of 81 service-level changes and 5 fare changes. A comparison is made of the elasticities estimated for these changes with elasticities developed from other studies.     

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.     

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.     

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.     

Ridership estimation for short-range transit planning

The objective of this research was to develop a simple transit ridership estimation model system for short-range planning. The main feature of the model system is that it exploits knowledge of transit link volumes which are obtained readily from on-off counts. Extensive use is made of default values for model parameters, taken directly from the transportation literature. The remaining parameters can be derived easily from generally available land-use and socioeconomic data. Expensive household surveys and time-consuming model calibrations are not required. A sequence of simple trip generation, trip distribution and modal split models generate trip-purpose specific transit trip tables, denoted as “trial” trip tables. These trip tables and observed transit link volumes are used in a linear programming model which serves as a correction mechanism. The gain in accuracy is achieved by using the ridership information contained in the transit link volumes. The corrected trip tables may be used in a pivot-point analysis to estimate changes in ridership and revenue. The results of a test application of the model system indicate that it can generate accurate ridership estimates when reliable transit link volumes are available from on-off counts, and when the trial transit trip tables as derived from the first three component models are reasonably accurate.     

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.     

Revenue allocation methods for integrated transit systems

Revenue allocation in the context of an integrated transit system involves the splitting of joint revenues derived from passengers taking system trips, that is, trips that involve a transfer between properties of two or more of the participants in an integrated system. The general nature of the revenue allocation problem is first reviewed. Next, a framework for constructing and assessing revenue allocation models is developed. A macroprocess model is described; categories of variables that merit consideration for inclusion in revenue/cost allocation formulas are discussed; and criteria for evaluation of models are examined. After doing this, five general approaches to the problem of allocating joint revenues are discussed and evaluated. Finally, a general revenue-sharing model based on ridership is developed. The model is then used to examine several relevant issues in pricing system trips and fare collection.     

Policy analysis of third party electronic coupons for public transit fares

Mobile technologies are generating new business models for urban transport systems, as is evident from recent startups cropping up from the private sector. Public transport systems can make more use of mobile technologies than just for measuring system performance, improving boarding times, or for analyzing travel patterns. A new transaction model is proposed for public transport systems where travelers are allowed to pre-book their fares and trade that demand information to private firms. In this public-private partnership model, fare revenue management is outsourced to third party private firms such as big box retail or large planned events (such as sports stadiums and theme parks), who can issue electronic coupons to travelers to subsidize their fares. This e-coupon pricing model is analyzed using marginal cost theory for the transit service and shown to be quite effective for monopolistic coupon rights, particularly for demand responsive transit systems that feature high cost fares, non-commute travel purposes, and a closed access system with existing pre-booking requirements. However, oligopolistic scenarios analyzed using game theory and network economics suggest that public transport agencies need to take extreme care in planning and implementing such a policy. Otherwise, they risk pushing an equivalent tax on private firms or disrupting the urban economy and real estate values while increasing ridership.     

Nature and/or nurture? Analyzing the determinants of transit ridership across US urbanized areas

Public subsidy of transit services has increased dramatically in recent years, with little effect on overall ridership. Quite obviously, a clear understanding of the factors influencing transit ridership is central to decisions on investments in and the pricing and deployment of transit services. Yet the literature about the causes of transit use is quite spotty; most previous aggregate analyses of transit ridership have examined just one or a few systems, have not included many of the external, control variables thought to influence transit use, and have not addressed the simultaneous relationship between transit service supply and consumption. This study addresses each of these shortcomings by (1) conducting a cross-sectional analysis of transit use in 265 US urbanized areas, (2) testing dozens of variables measuring regional geography, metropolitan economy, population characteristics, auto/highway system characteristics, and transit system characteristics, and (3) constructing two-stage simultaneous equation regression models to account for simultaneity between transit service supply and consumption. We find that most of the variation in transit ridership among urbanized areas – in both absolute and relative terms – can be explained by factors outside of the control of public transit systems: (1) regional geography (specifically, area of urbanization, population, population density, and regional location in the US), (2) metropolitan economy (specifically, personal/household income), (3) population characteristics (specifically, the percent college students, recent immigrants, and Democratic voters in the population), and (4) auto/highway system characteristics (specifically, the percent carless households and non-transit/non-SOV trips, including commuting via carpools, walking, biking, etc.). While these external factors clearly go a long way toward determining the overall level of transit use in an urbanized area, we find that transit policies do make a significant difference. The observed range in both fares and service frequency in our sample could account for at least a doubling (or halving) of transit use in a given urbanized area. Controlling for the fact that public transit use is strongly correlated with urbanized area size, about 26% of the observed variance in per capita transit patronage across US urbanized areas is explained in the models presented here by service frequency and fare levels. The observed influence of these two factors is consistent with both the literature and intuition: frequent service draws passengers, and high fares drive them away.