Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors

Microeconomic optimisation of scheduled public transport operations has traditionally focused on finding optimal values for the frequency of service, capacity of vehicles, number of lines and distance between stops. In addition, however, there exist other elements in the system that present a trade-off between the interests of users and operators that have not received attention in the literature, such as the optimal selection of a fare payment system and a designed running speed (i.e., the cruising speed that buses maintain in between two consecutive stops). Alternative fare payment methods (e.g., on-board and off-board, payment by cash, magnetic strip or smart card) have different boarding times and capital costs, with the more efficient systems such as a contactless smart card imposing higher amounts of capital investment. Based on empirical data from several Bus Rapid Transit systems around the world, we also find that there is a positive relationship between infrastructure cost per kilometre and commercial speed (including stops), achieved by the buses, which we further postulate as a linear relationship between infrastructure investment and running speed. Given this context, we develop a microeconomic model for the operation of a bus corridor that minimises total cost (users and operator) and has five decision variables: frequency, capacity of vehicles, station spacing, fare payment system and running speed, thus extending the traditional framework. Congestion, induced by bus frequency, plays an important role in the design of the system, as queues develop behind high demand bus stops when the frequency is high. We show that (i) an off-board fare payment system is the most cost effective in the majority of circumstances; (ii) bus congestion results in decreased frequency while fare and bus capacity increase, and (iii) the optimal running speed grows with the logarithm of demand.     

Optimization of grid bus transit systems with elastic demand

Current analytic models for optimizing urban bus transit systems tend to sacrifice geographic realism and detail in order to obtain their solutions. The models presented here shows how an optimization approach can be successful without oversimplifying spatial characteristics and demand patterns of urban areas and how a grid bus transit system in a heterogeneous urban environment with elastic demand is optimized. The demand distribution over the service region is discrete, which can realistically represent geographic variation. Optimal network characteristics (route and station spacings), operating headways and fare are found, which maximize the total operator profit and social welfare. Irregular service regions, many‐to‐many demand patterns, and vehicle capacity constraints are considered in a sequential optimization process. The numerical results show that at the optima the operator profit and social welfare functions are rather flat with respect to route spacing and headway, thus facilitating the tailoring of design variables to the actual street network and particular operating schedule without a substantial decrease in profit. The sensitivities of the design variables to some important exogenous factors are also presented.     

Time of day intervals partition for bus schedule using GPS data

Time of day partition of bus operating hours is a prerequisite of bus schedule design. Reasonable partition plan is essential to improve the punctuality and level of service. In most mega cities, bus vehicles have been equipped with global positioning system (GPS) devices, which is convenient for transit agency to monitor bus operations. In this paper, a new algorithm is developed based on GPS data to partition bus operating hours into time of day intervals. Firstly, the impacts of passenger demand and network traffic state on bus operational performance are analyzed. Then bus dwell time at stops and inter-stop travel time, which can be attained based on GPS data, are selected as partition indexes. For buses clustered in the same time-of-day interval, threshold values of differences in dwell time at stops and inter-stop travel time are determined. The buses in the same time-of-day interval should have adjacent dispatching numbers, which is set as a constraint. Consequently, a partition algorithm with three steps is developed. Finally, a bus route in Suzhou China is taken as an example to validate the algorithm. Three partition schemes are given by setting different threshold values for the two partition indexes. The present scheme in practice is compared with the three proposed schemes. To balance the number of ToD intervals and partition precision, a Benefit Evaluation Index is proposed, for a better time-of-day interval plan.     

Optimization of bus stop locations for improving transit accessibility

A mathematical model is developed in this paper to improve the accessibility of a bus service. To formulate the optimization model, a segment of a bus route is given, on which a number of demand entry points are distributed realistically. The objective total cost function (i.e. the sum of supplier and user costs) is minimized by optimizing the number and locations of stops, subject to non‐additive users' value of time. A numerical example is designed to demonstrate the effectiveness of the method thus developed to optimize the bus stop location problem. The sensitivity of the total cost to various parameters (e.g. value of users' time, access speed, and demand density) and the effect of the parameters on the optimal stop locations are analyzed and discussed.     

Crowding in public transport systems: Effects on users,operation and implications for the estimation of demand

The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers’ wellbeing, valuation of waiting and in-vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) models, we show that alternative assumptions concerning the threshold load factor that triggers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy levels, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of disutility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.     

Analytical model for calibrating delay at congested bus stops

Abstract

A model is proposed to calculate the overall operating and delay times spent at bus stops due to passenger boarding and alighting and the time lost to queuing caused by bus stop saturation. A formula for line demand at each stop and the interaction between the buses themselves is proposed and applied to different bus stops depending on the number of available berths. The application of this model has quantified significant operational delays suffered by users and operator due to consecutive bus arrival at stops, even with flows below bus stop capacity.     

Modeling the interaction between buses,passengers and cars on a bus route using a multi-agent system

This paper models part of a public transport network (PTN), specifically, a bus route, as a small-size multi-agent system (MAS). The proposed approach is applied to a case study considering a ‘real world’ bus line within the PTN in Auckland, New Zealand. The MAS-based analysis uses modeling and simulation to examine the characteristics of the observed system – autonomous agents interacting with one another – under different scenarios, considering bus capacity and frequency of service for existing and projected public transport (PT) demand. A simulation model of a bus route is developed, calibrated and validated. Several results are attained, such as when the PT passenger load is not close to bus capacity, this load has no effect on average passenger waiting time at bus stops. The model proposed can be useful to practitioners as a tool to model the interaction between buses and other agents.     

Extension of Newell's dispatching policy to the case of sensitive demand

This paper has extended Newell's dispatching policy to the case of sensitive demand which is characterized by a linear mode split model with two major factors, wait time and transit fare. Three objective functions both with and without vehicle capacity constraint are analyzed, including profit maximization, maximization of a combination of net user benefit and operator profit, and maximization of net user benefit subject to a deficit constraint. Closed-form solutions associated with various system parameters are obtained. It is shown that under sensitive demand conditions the optimal dispatching rate is approximately proportional to the square root of the total demand rate, if vehicle size is not binding and it is strictly proportional to the total demand rate, if vehicle size is binding.     

Enhanced bus operations: The Curitiba model and its applicability to China

Buses will remain the backbone of public transport systems for some time to come because of their lower cost and higher flexibility in relation to rail transport. However, buses are perceived as being an inferior mode of public transport and do not offer as much carrying capacity as rail transport. Following the Curitiba model, this paper looks at the potential for transferring some of the key advantages of rail transport to bus operations. This involves transforming bus stops into enclosed stations, with ticket purchase and/or checking in the station and at‐grade access to vehicles. It also involves the extensive use of bus lanes. The potential contribution of transport telematics is looked at, in particular the use of smartcards for payment in a closed fare system. The potential role of the Curitiba model for China is assessed in the context of toll road construction.     

Towards modal choice decision-making models: A case study of Lagos state transport corporation bus riders

Identification of the socioeconomic factors which affect the demand for buses, and the analysis of the use of the other transport modes by bus users are the two main objectives of this article. Work and school trips are highlighted as being very important trip purposes in Lagos metropolis by the multiple discriminant analysis model. It identifies mode of transport, distance, travel time, reliability, and the number of stops as significant mode choice variables. Multiple linear regression models for work and school trips identify mode of transport, transfort fare, travel time, annual income, and crew behaviour as significant variables in the choice of transport mode. These findings support the two alternative hypotheses of the study that the choice of bus is related to the individual perception of the quality of service of the different modes and that socioeconomic characteristics of the riders influence the patronage of buses. The attention of policy makers for the 22 transport corporations that operate inter-and intra-urban services in all the 21 states and the federal capital of Abuja in Nigeria is drawn to the importance of these variables for decisions.     

What is behind fare evasion in urban bus systems? An econometric approach

Fare evasion is a problem in many public transport systems around the world and policies to reduce it are generally aimed at improving control and increasing fines. We use an econometric approach to attempt explaining the high levels of evasion in Santiago, Chile, and guide public policy formulation to reduce this problem. In particular, a negative binomial count regression model allowed us to find that fare evasion rates on buses increase as: (i) more people board (or alight) at a given bus door, (ii) more passengers board by a rear door, (iii) buses have higher occupancy levels (and more doors) and (iv) passengers experience longer headways. By controlling these variables (ceteris paribus), results indicate that evasion is greater during the afternoon and evening, but it is not clear that it is higher during peak hours. Regarding socioeconomic variables, we found that fare evasion at bus stops located in higher income areas (municipalities) is significantly lower than in more deprived areas. Finally, based on our results we identified five main methods to address evasion as alternatives to more dedicated fine enforcement or increased inspection; (i) increasing the bus fleet, (ii) improving the bus headway regularity, (iii) implementing off-board payment stations, (iv) changing the payment system on board and (v) changing the bus design (number of doors or capacity). Our model provides a powerful tool to predict the reduction of fare evasion due to the implementation of some of these five operational strategies, and can be applied to other bus public transport systems.     

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.     

Multiple period optimization of bus transit systems

Analytic models are developed for optimizing bus services with time dependence and elasticity in their demand characteristics. Some supply parameters, i.e. vehicle operating costs and speeds are also allowed to vary over time. The multiple period models presented here allow some of the optimized system characteristics (e.g. route structure) to be fized at values representing the best compromise over different time periods, while other characteristics (e.g. service headways) may be optimized within each period. In a numerical example the demand is assumed to fluctuate over a daily cycle (e.g. peak, offpeak and night), although the same models can also be used for other cyclical or noncyclical demand variations over any number of periods. Models are formulated and compared for four types of conditions, which include steady fixed demand, cyclical fixed demand, steady equilibrium demand and cyclical equilibrium demand. When fixed demand is assumed, the optimization objective is minimum total system cost, including operator cost and user cost, while operator profit and social welfare are the objective functions maximized for equilibrium demand. The major results consist of closed form solutions for the route spacings, headways, fares and costs for optimized feeder bus services under various demand conditions. A comparison of the optimization results for the four cases is also presented. When demand and bus operating characteristics are allowed to vary over time, the optimal functions are quite similar to those for steady demand and supply conditions. The optimality of a constant ratio between the headway and route spacing, which is found at all demand densities if demand is steady, is also maintained with a multi-period adjustment factor in cyclical demand cases, either exactly or with a relatively negligible approximation. These models may be used to analyze and optimize fairly complex feeder or radial bus systems whose demand and supply characteristics may vary arbitrarily over time.     

Development and validation of energy demand uncertainty model for electric city buses

The prediction of electric city bus energy demand is crucial in order to estimate operating costs and to size components such as the battery and charging systems. Unfortunately, there are unpredictable dynamic factors that can cause variation in the energy demand, particularly concerning driver choices and traffic levels. The impact of these factors on energy demand has been difficult to study since fast computing sufficiently accurate dynamic simulation models have been missing, properly quantified in terms of relevant inputs which contribute to energy demand. The objective is to develop and validate a novel electric city bus model for computing the energy demand, to study the nature and impact of various input factors. The developed equation-based model predicted real-world electric city bus energy consumption within 0.1% error. The most crucial unmeasurable input factors were the driven bus route, the number of stops, the elevation profile, the traffic level and the driving style. This understanding can be used to specify routes and stops for a given electric bus battery capacity. Worst-case scenarios are also necessary for electric bus sizing analysis. The best- and worst-case levels of the crucial factors were identified and with them synthetic best- and worst-case speed profiles were generated to demonstrate their effect to the energy demand. While the measured nominal consumption was 0.70 kWh/km, the computed range of variation was between 0.19 kWh/km and 1.34 kWh/km. For design sizing purposes, an electric city bus can have a broad range of possible energy consumption rates due to mission condition variations.     

Integrated optimization of bus priority operations in connected vehicle environment

Most previous works associated with transit signal priority merely focus on the optimization of signal timings, ignoring both bus speed and dwell time at bus stops. This paper presents a novel approach to optimize the holding time at bus stops, signal timings, and bus speed to provide priority to buses at isolated intersections. The objective of the proposed model is to minimize the weighted average vehicle delays of the intersection, which includes both bus delay and impact on nearby intersection traffic, ensuring that buses clear these intersections without being stopped by a red light. A set of formulations are developed to explicitly capture the interaction between bus speed, bus holding time, and transit priority signal timings. Experimental analysis is used to show that the proposed model has minimal negative impacts on general traffic and outperforms the no priority, signal priority only, and signal priority with holding control strategies (no bus speed adjustment) in terms of reducing average bus delays and stops. A sensitivity analysis further demonstrates the potential of the proposed approach to be applied to bus priority control systems in real‐time under different traffic demands, bus stop locations, and maximum speed limits. Copyright © 2016 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.     

Optimal bus service patterns and frequencies considering transfer demand elasticity with genetic algorithm

This paper attempts to optimize bus service patterns (i.e., all-stop, short-turn, and express) and frequencies which minimize total cost, considering transfer demand elasticity. A mathematical model is developed based on the objective total cost for a generalized bus route, which is optimized subject to a set of constraints ensuring sufficient capacity, an operable bus fleet, and service frequency conservation. To optimize the integrated service of a bus route with many stops, which is a combinatorial optimization problem, a genetic algorithm is developed and applied to search for the solution. A case study, based on a real-world bus route in New Jersey, is conducted to demonstrate the applicability and effectiveness of the developed model and the solution algorithm. Results show that the proposed methodology is fairly efficient, and the optimized bus service significantly reduces total cost.     

Estimating the demand for urban bus travel

The disadvantages of conventional transportation study models, in particular their large data requirements and their weaknesses in dealing with changes in trip generation rates have led to a need for a simple model that can quickly and at low cost examine alternative public transport strategies.This paper investigates simple economic models of bus demand, examines alternative variables that can be used and discusses some alternative model forms. It demonstrates the results of a model using data from twelve urban bus operators in Britain and compares the results with those from other types of study. The model utilises fare and service quality elasticities to explain the decline in passengers on urban bus services, and derives an average elasticity with respect to fare changes of –0.31 and with respect to service quality changes of +0.62. It is estimated that fare rises accounted for 13% of the 43% decline in passengers over the last fifteen years, vehicle mileage reductions for 14.3% and that only 15.7% was due to such factors as rising car ownership which are often given as the cause of declining bus patronage.The results, by showing that passengers are far more sensitive to changes in service than they are to fare rises, are a useful guide to the broader public transport policy issues, and the paper concludes that the model does provide a useful method of forecasting public transport demand at a strategic level. Further work is needed, however, to establish more accurate forecasts for different types of passenger and studies are now being undertaken to establish these and to construct an operational forecasting model that can be applied with only limited data requirements     

Modeling and optimizing urban bus transit considering headway variation for cost and service reliability analysis

Due to the stochastic nature of traffic conditions and demand fluctuations, it is a challenging task for operators to maintain reliable services, and passengers often suffer from longer travel times. A failure to consider this issue while planning bus services may lead to undesirable results, such as higher costs and a deterioration in level of service. Considering headway variation at route stops, this paper develops a mathematical model to optimize bus stops and dispatching headways that minimize total cost, consisting of both user and operator costs. A Genetic Algorithm is applied to search for a cost-effective solution in a real-world case study of a bus transit system, which improves service reliability in terms of a reduced coefficient of variation of headway.     

Estimation of bus dwell time using univariate time series models

A significant proportion of bus travel time is contributed by dwell time for passenger boarding and alighting. More accurate estimation of bus dwell time (BDT) can enhance efficiency and reliability of public transportation system. Regression and probabilistic models are commonly used in literatures where a set of independent variables are used to define the statistical relationship between BDT and its contributing factors. However, due to technical and monetary constraints, it is not always feasible to collect all the data required for the models to work. More importantly, the contributing factors may vary from one bus route to another. Time series based methods can be of great interest as they require only historical time series data, which can be collected using a facility known as automatic vehicle location (AVL) system. This paper assesses four different time series based methods namely random walk, exponential smoothing, moving average (MA), and autoregressive integrated moving average to model and estimate BDT based on AVL data collected from Auckland. The performances of the proposed methods are ranked based on three important factors namely prediction accuracy, simplicity, and robustness. The models showed promising results and performed differently for central business district (CBD) and non‐CBD bus stops. For CBD bus stops, MA model performed the best, whereas for non‐CBD bus stops, ARIMA model performed the best compared with other time series based models. Copyright © 2014 John Wiley & Sons, Ltd.