Joint optimization of a rail transit line and its feeder bus system

A model is developed for jointly optimizing the characteristics of a rail transit route and its associated feeder bus routes in an urban corridor. The corridor demand characteristics are specified with irregular discrete distributions which can realistically represent geographic variations. The total cost (supplier plus user cost) of the integrated bus and rail network is minimized with an efficient iterative method that successively substitutes variable values obtained through classical analytic optimization. The optimized variables include rail line length, rail station spacings, bus headways, bus stop spacings, and bus route spacing. Computer programs are designed for optimization and sensitivity analysis. The sensitivity of the transit service characteristics to various travel time and cost parameters is discussed. Numerical examples are presented for integrated transit systems in which the rail and bus schedules may be coordinated.     

Long-term planning for ring-radial urban rail transit networks

Extensive work exists on regular rail network planning. However, few studies exist on the planning and design of ring-radial rail transit systems. With more ring transit lines being planned and built in Asia, Europe and the America's, a detailed study on ring transit lines is timely. An analytical model to find the optimal number of radial lines in a city for any demand distribution is first introduced. Secondly, passenger route choice for different rail networks is analyzed, for a many-to-many Origin-Destination (OD) demand distribution, based on a total travel time cost per passenger basis. The routes considered are: (1) radial lines only; (2) ring line only or radial lines and ring line combined; or (3) direct access to a destination without using the rail system. Mathematica and Matlab are used to code the route choice model. A cost-benefit optimization model to identify the feasibility and optimality of a ring line is proposed. Unlike simulations and agent-based models, this model is shown to be easily transferable to many ring-radial transit networks. The City of Calgary is used as an example to illustrate the applicability of each model. The existing urban rail network and trip distribution are major influencing factors in judging the feasibility and optimal location of the ring line. This study shows the potential net benefit of introducing a ring line by assessing changes in passengers’ costs. The changes in passenger cost parameters, such as ride cost and access cost, are shown to greatly influence the feasibility of a ring line.     

Rail line length in a crosstown corridor with many-to-many demand

An analytical model that determines the optimal location and length of rail line along a crosstown transportation corridor with the objective of minimizing the total transportation cost is presented. A general, many-to-many passenger demand pattern is considered. The objective function, which includes the rail and bus riding costs, rail and bus operating costs, rail fleet costs and rail line costs, is minimized by using the classical optimization method with the aid of a computer program developed for the model. The model is applied to the Northwest-South transportation corridor in Calgary, Alberta, and the sensitivity of the optimal rail line location and length to the unit cost and demand parameters at their reasonable ranges is tested. It is found that although the total passenger demand, unit rail line cost, and unit bus operating cost have greater influence than the unit bus and rail riding costs, and unit rail fleet and operating costs, the optimal line length is generally insensitive to all these parameters. It is also found that the length of the existing LRT line in the corridor is comparable to the optimal line length obtained from the model, but the existing line should be extended further south in order to meet the heavier demand in that direction optimally.     

Intermodal Transit System Coordination

In urban areas where transit demand is widely spread, passengers may be served by an intermodal transit system, consisting of a rail transit line (or a bus rapid transit route) and a number of feeder routes connecting at different transfer stations. In such a system, passengers may need one or more transfers to complete their journey. Therefore, scheduling vehicles operating in the system with special attention to reduce transfer time can contribute significantly to service quality improvements. Schedule synchronization may significantly reduce transfer delays at transfer stations where various routes interconnect. Since vehicle arrivals are stochastic, slack time allowances in vehicle schedules may be desirable to reduce the probability of missed connections. An objective total cost function, including supplier and user costs, is formulated for optimizing the coordination of a general intermodal transit network. A four-stage procedure is developed for determining the optimal coordination status among routes at every transfer station. Considering stochastic feeder vehicle arrivals at transfer stations, the slack times of coordinated routes are optimized, by balancing the savings from transfer delays and additional cost from slack delays and operating costs. The model thus developed is used to optimize the coordination of an intermodal transit network, while the impact of a range of factors on coordination (e.g., demand, standard deviation of vehicle arrival times, etc) is examined.     

弹性需求下的轨道交通客流分配模型和算法研究

文章分析了轨道交通客流需求量的影响因素,以拥挤条件下的出行阻抗函数为基础,通过引入弹性需求条件下的轨道交通均衡配流条件,构建了弹性需求的均衡配流模型。根据模型的特点,给出了改进的用于求解弹性需求下的轨道交通均衡配流模型的Frank-wolfe算法。最后通过一个算例说明了算法的有效性和合理性。     

Analysis of light rail rider travel behavior: Impacts of individual,built environment,and crime characteristics on transit access

This paper analyzes factors that influence the mode choice for trips between home and light rail stations, an often neglected part of a person’s trip making behavior. This is important for transit planning, demand modeling, and transit oriented development. Using transit survey data describing St. Louis MetroLink riders in the United States, this study found that some of the factors associated with increased shares of walking relative to other modes were full-time student status, higher income transit riders, and trips made during the evening. It was also found that crime at stations had an impact. In particular, crime made female transit riders more likely to be picked-up/dropped-off at the station. Females are more likely to be picked-up or dropped-off at night. Bus availability and convenience showed that transit riders that have a direct bus connection to a light rail station were more likely to use the bus. Private vehicle availability was strongly associated with increased probability of drive and park, when connecting to light rail.     

Two-phase stochastic program for transit network design under demand uncertainty

This paper develops a reliability-based formulation for rapid transit network design under demand uncertainty. We use the notion of service reliability to confine the stochastic demand into a bounded uncertainty set that the rapid transit network is designed to cover. To evaluate the outcome of the service reliability chosen, flexible services are introduced to carry the demand overflow that exceeds the capacity of the rapid transit network such designed. A two-phase stochastic program is formulated, in which the transit line alignments and frequencies are determined in phase 1 for a specified level of service reliability; whereas in phase 2, flexible services are determined depending on the demand realization to capture the cost of demand overflow. Then the service reliability is optimized to minimize the combined rapid transit network cost obtained in phase 1, and the flexible services cost and passenger cost obtained in phase 2. The transit line alignments and passenger flows are studied under the principles of system optimal (SO) and user equilibrium (UE). We then develop a two-phase solution algorithm that combines the gradient method and neighborhood search and apply it to a series of networks. The results demonstrate the advantages of utilizing the two-phase formulation to determine the service reliability as compared with the traditional robust formulation that pre-specifies a robustness level.     

A simulation model of train travel on a rail transit line

A simplified simulation model for the operational analysis of a rail rapid transit train is presented. The model simulates the movement of a train along a route, and develops the relationships of time—distance, time—speed and distance—speed. The inputs to the model are the profile of speed limits and the dynamic characteristics of the train. Without the information on the track geometry and tractive effort, the model determines the speed of the train at a location based on the previous and future speed limits relative to the location. It was found that the model can fairly accurately simulate the relationship between travel time and distance. A comparison of the train travel times between the actual and simulated runs is presented. Because of the simplicity of input and calculation method, the model can be a useful tool for the “desk-top” analysis of frequently occurring planning problems of a commuter rail or rail rapid transit line, such as the impacts of changes in speed limits, station locations, station stopping policy, addition/elimination of stations, and types of rail cars.     

北京市轨道交通房山线功能定位分析研究

轨道交通线路功能定位对确定线路的技术标准、运营模式、系统制式等具有决定作用.房山线作为北京近期建设的轨道交通,其功能定位存在较多不确定因素,是北京线网规划阶段一个尚未完全解决的问题,也是项目可行性研究的难点之一。通过研究各层面关键因素对房山线功能的影响,对其定位进行分析,从而为该线的设计提供参考.     

A dynamic station strategy to improve the performance of flex-route transit services

As an innovative combination of conventional fixed-route transit and demand responsive service, flex-route transit is currently the most popular type of flexible transit services. This paper proposes a dynamic station strategy to improve the performance of flex-route transit in operating environments with uncertain travel demand. In this strategy, accepted curb-to-curb stops are labeled as temporary stations, which can be utilized by rejected requests for their pick-up and drop-off. The user cost function is defined as the performance measure of transit systems. Analytical models and simulations are constructed to test the feasibility of implementing the dynamic station strategy in flex-route transit services. The study over a real-life flex-route service indicates that the proposed dynamic station strategy could reduce the user cost by up to 30% without any additional operating cost, when an unexpectedly high travel demand surpasses the designed service capacity of deviation services.     

Integrated transit services for minimum cost operation considering heterogeneous demand

Abstract

In large metropolitan areas, public transit is a major mode choice of commuters for their daily travel, which has an important role in relieving congestion on transportation corridors. The purpose of this study is to develop a model which optimizes service patterns (SPs) and frequencies that yield minimum cost transit operation. Considering a general transit route with given stops and origin-destination demand, the proposed model consists of an objective total cost function and a set of constraints to ensure frequency conservation and sufficient capacity subject to operable fleet size. A numerical example is provided to demonstrate the effectiveness of the developed model, in which the demand and facility data of a rail transit route were given. Results show that the proposed model can be applied to optimize integrated SPs and headways that significantly reduce the total cost, while the resulting performance indicators are generated.     

Evolution of public transit modes in a commuter corridor

This paper explores how the selection of public transit modes can be optimized over a planning horizon. This conceptual analysis sacrifices geographic detail in order to better highlight the relations among important factors. First, a set of static models is proposed to identify which type of service, e.g., bus only, rail only, or bus and rail, is the most cost-effective in terms of the average trip cost for given demand. After analyzing essential factors in a long-term planning process, e.g., economies of scale in rail extension and future cost discounting, a dynamic model incorporating such considerations is formulated to optimize the decision over a planning horizon. While analytical solutions can be obtained for some decision variables, the final model is solved with a graphical method by exploring the tradeoffs between the initial and recurring costs. Major findings from this study include: (a) there exists a minimum economic length for a rail line, which can be determined numerically; (b) economies of scale favor large extensions and excess supplied capacity; (c) the rail-only service is largely dominated by the feeder-trunk service, even in the long run.     

Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.     

Modeling transit technology selection in a linear transportation corridor

This paper proposes an analytical model for investigating transit technology selection problem from a perspective of transit authority. Given a transit technology alternative (e.g., metro, light rail transit, or bus rapid transit), the proposed model aims to maximize the social welfare of the transit system by determining the optimal combination of transit line length, number of stations, station location (or spacing), headway, and fare. In the proposed model, the effects of passenger demand elasticity and capacity constraint are explicitly considered. The properties of the model are examined analytically, and a heuristic solution procedure for determining the model solution is presented. By comparing the optimized social welfare for different transit technology alternatives, the optimal transit technology solution can be obtained together with critical population density. On the basis of a simple population growth rate formula, optimal investment timing of a new transit technology can be estimated. The proposed methodology is illustrated in several Chinese cities. Insightful findings are reported on the interrelation among transit technology selection, population density, transit investment cost, and transit line parameter design as well as the comparison between social welfare maximization and profit maximization regimes. Copyright © 2014 John Wiley & Sons, Ltd.     

What determines rail transit passenger volume? Implications for transit oriented development planning

Transit oriented development (TOD) has been an important topic for urban transportation planning research and practice. This paper is aimed at empirically examining the effect of rail transit station-based TOD on daily station passenger volume. Using integrated circuit (IC) card data on metro passenger volumes and cellular signaling data on the spatial distribution of human activities in Shanghai, the research identifies variations in ridership among rail transit stations. Then, regression analysis is performed using passenger volume in each station as the dependent variable. Explanatory variables include station area employment and population, residents’ commuting distances, metro network accessibility, status as interchange station, and coupling with commercial activity centers. The main findings are: (1) Passenger volume is positively associated with employment density and residents’ commuting distance around station; (2) stations with earlier opening dates and serving as transfer nodes tend to have positive association with passenger volumes; (3) metro stations better integrated with nearby commercial development tend to have larger passenger volumes. Several implications are drawn for TOD planning: (1) TOD planning should be integrated with rail transit network planning; (2) location of metro stations should be coupled with commercial development; (3) high employment densities should be especially encouraged as a key TOD feature; and (4) interchange stations should be more strategically positioned in the planning for rail transit network.     

Robust transit network design with stochastic demand considering development density

This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases.     

Optimal stop spacing and headway of congested transit system considering realistic wait times

Abstract

This paper revisits the classical transit scheduling problem and investigates the relationship between stop spacing and headway, considering realistic wait time and operable transit capacity. Headway and stop spacing are important determinants for planning a transit system, which influence the service level as well as the cost of operation. A mathematical model is developed, and the objective function is user travel time which is minimized by the optimized stop spacing and headway, subject to the constraints of operable fleet size and route capacity. Optimal stop spacing and headway solutions are obtained in a numerical example. Sensitivity analysis is conducted, and the effect of model parameters on user travel time is explored.     

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.     

Cost and time damping: evidence from aggregate rail direct demand models

There is a significant body of evidence from both disaggregate choice modelling literature and practical travel demand forecasting that the responsiveness to cost and possibly to time diminishes with journey length. This has, in Britain at least, been termed ‘Cost Damping’, and is recognised in guidance issued by the UK Department for Transport. However, the consistency of the effect across modes and data types has not been established. Cost damping, if it exists, affects both the forecasting of demand and our understanding of behaviour. This paper aims to investigate the evidence for cost and time damping in rail demand using aggregate rail ticket sales data. The rail ticket sales data in Britain has, for many years, formed the basis of analysis of a wide range of impacts of rail demand. It records the number of tickets sold between station pairs, and it is generally felt to provide a reasonably accurate reflection of travel demand. However, the consistency of these direct demand models with choice modelling and highway demand model structures has not been investigated. Rail direct demand models estimated by ticket sales data indicate only slight variation in the fare elasticity with distance, as is evidenced in the largest meta-analysis of price elasticities conducted to date (Wardman in J Transp Econ Policy 48(3):367–384, 2014). This study of UK elasticities shows strong variation between urban and inter-urban trips, presumably a segmentation at least in part by purpose, but less remaining variation by trip length. A lack of variation by length supports the hypothesis of cost damping, because constant cost sensitivity would imply that fare elasticity would increase strongly with distance, because of the increasing impact of higher fares at longer distances. In this paper we indicate that rail direct demand models have some consistency of behavioural paradigm with utility based choice models used in highway planning. We go on to use rail demand data to estimate time and fare elasticities in the context of various cost damping functions. Our empirical contribution is to estimate time elasticities on a basis directly comparable with cost elasticities and to show that the phenomenon of cost damping is strongly present in ticket sales data. This finding implies that cost damping should be included in models intended for multimodal analysis, which may otherwise give incorrect predictions.     

Estimation of urban bus transit marginal cost without cost data

We develop a method to study the industrial structure of urban bus transit without using cost data. To do so, we estimate the marginal cost function under the assumption that firms compete on frequency and adjust frequency to maximize profits. Our methodology is applied to Santiago, Chile. In this case, demand is modeled with a simplified model of transit network assignment. The goal is to consider how frequency, capacity, and on-board passengers affect the bus line’s demand. The marginal cost function is estimated by using the first-order conditions of the firm’s profit maximization problem, using the results of the demand model as data. We conclude that the urban bus transit industry in Santiago exhibits increasing returns to scale for low levels of demand and that these returns are exhausted rapidly at a moderate demand level. Additionally, firms exhibit economies of network expansion, on average.