Modeling a rail transit alignment considering different objectives

An optimization model for station locations for an on-ground rail transit line is developed using different objective functions of demand and cost as both influence the planning of a rail transit alignment. A microscopic analysis is performed to develop a rail transit alignment in a given corridor considering a many-to-one travel demand pattern. A variable demand case is considered as it replicates a realistic scenario for planning a rail transit line. A Genetic Algorithm (GA) based on a Geographical Information System (GIS) database is developed to optimize the station locations for a rail transit alignment. The first objective is to minimize the total system cost per person, which is a function of user cost, operator cost, and location cost. The second objective is to maximize the ridership or the service coverage of the rail transit alignment. The user cost per person is minimized separately as the third objective because the user cost is one of the most important decision-making factors for planning a transit system from the users’ perspective. A transit planner can make an informed decision between various alternatives based on the results obtained using different objective functions. The model is applied in a case study in the Washington, DC area. The optimal locations and sequence of stations obtained using the three objective functions are presented and a comparative study between the results obtained is shown in the paper. In future works we will develop a combinatorial optimization problem using the aforementioned objectives for the rail transit alignment planning and design problem.     

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.     

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 computer model for finding the time-dependent minimum path in a transit system with fixed schedules

This paper describes the development of a computer model and algorithms for finding the time-dependent minimum path between two stations in a multi-route, multi-mode transit system running to fixed schedules. Selection of the minimum path can be based either on journey time or on weighted time. A worked example using a simple transit network is given to illustrate how the model works. The model has several applications in transport planning: it can be used for generating route schedule information to guide transit users, for assisting in route schedule coordination, and for analyzing transit system accessibility.     

An activity-based approach for scheduling multimodal transit services

This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.     

A subway planning bi-objective multi-period optimization model integrating timetabling and vehicle scheduling: a case study of Tehran

Due to the interaction among different planning levels and various travel demands during a day, the transit network planning is of great importance. In this paper, a bi-objective multi-period planning model is proposed for the synchronization of timetabling and vehicle scheduling. The main aim of the problem is to minimize the weighted transfer waiting time in the interchange stations along with the operational costs of vehicles. In order to demonstrate the effectiveness of the proposed integrated model, a real case study of Tehran subway is considered. The proposed model is solved by the ε-constraint method and some outstanding results are achieved.

     

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.     

Transit trip distribution model considering land use differences between catchment areas

Sustainable land use planning and advanced public transport system are believed to be effective solutions to traffic congestion. To this end, it is important to reveal the relationship between transit ridership and land use. However, current Direct Ridership Models only focus on the relationship between single station's boarding volume and the corresponding catchment area land use. This paper analyzed the ridership distribution between transit stations by considering the land use difference between catchment areas. Land use difference was calculated from point of interest (POI) data extracted from an electronic map of Beijing; transit trip distribution volume was obtained from ‘automatic fare collection’ facility. After data specification, a transit ridership distribution model was proposed and calibrated. The calibration results suggest that land use difference has a directly proportional correlation with transit ridership distribution. The research findings build a bridge between detailed urban form and public transport, which is of significance for the further research of sustainable urban planning. Copyright © 2016 John Wiley & Sons, Ltd.     

A network equilibrium approach for modelling activity-travel pattern scheduling problems in multi-modal transit networks with uncertainty

An understanding of the interaction between individuals’ activities and travel choice behaviour plays an important role in long-term transit service planning. In this paper, an activity-based network equilibrium model for scheduling daily activity-travel patterns (DATPs) in multi-modal transit networks under uncertainty is presented. In the proposed model, the DATP choice problem is transformed into a static traffic assignment problem by constructing a new super-network platform. With the use of the new super-network platform, individuals’ activity and travel choices such as time and space coordination, activity location, activity sequence and duration, and route/mode choices, can be simultaneously considered. In order to capture the stochastic characteristics of different activities, activity utilities are assumed in this study to be time-dependent and stochastic in relation to the activity types. A concept of DATP budget utility is proposed for modelling the uncertainty of activity utility. An efficient solution algorithm without prior enumeration of DATPs is developed for solving the DATP scheduling problem in multi-modal transit networks. Numerical examples are used to illustrate the application of the proposed model and the solution algorithm.     

Investigating the impact of stochastic vehicle arrivals to optimal stop spacing and headway for a feeder bus route

Stop spacing and service frequency (i.e., the inverse of headway) are key elements in transit service planning. The trade‐offs between increasing accessibility and reducing travel time, which affect transit system performance, need to be carefully evaluated. The objective of this study is to optimize stop spacing and headway for a feeder bus route, considering the relationship between the variance of inter‐arrival time (VIAT), which yields the minimum total cost (including user and operator costs). A solution algorithm, called successive substitution, is adapted to efficiently search for the optimal solutions. In a numerical example, the developed model is applied to planning a feeder bus route in Newark, New Jersey. The results indicate that the optimal stop spacing should be longer that those suggested by previous studies where the impact of VIAT was ignored. Reducing VIAT via certain operational control strategies (i.e., holding/stop‐skipping, transit signal priority) may shorten stop spacing and improve accessibility. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

山地旅游轨道交通线路规划的适应性评价

山地景区地势复杂,其发展普遍受交通所限,为了提高山地景区的运营效益、带动经济发展,国内部分景区规划和修建了山地旅游轨道交通。本文列举了山地旅游轨道交通特征及线路规划模式,从地理环境、自然环境、供需环境及与常规公交的关系四个角度分析,对应建立四个子系统,并选取具有山地旅游轨道交通特性的评价指标体系,利用层次分析法和变异系数法组合赋权重,运用灰色关联分析法的评价模型,据此判断线路规划方案适应性的优劣。     

Transit assignment under crowded conditions

This paper presents a transit assignment algorithm for crowded networks. Both congestion in vehicles and queuing at stations are explicitly taken into account in predicting passenger flows for a fixed pattern of origin-destination trip demands. The overflow effects due to insufficient capacity of transit lines are considered to be concentrated at transit stations, while the in-vehicle congestion effects (or discomforts) are considered to be dependent on in-vehicle passenger volume. Overflow delay at a transit station is dependent on the number of excess passengers required to wait for the next transit car. We use a logit model to determine the split between passengers that chose to wait for the next transit car and passengers that chose to board on the alternative transit lines. The proposed algorithm predicts how passenger will choose their optimal routes under both queuing and crowded conditions.     

Mobility evaluation for urban public transportation

Summary

This paper has reported on a study of relative opportunity—not absolute opportunity. Minimum absolute standards for mobility or accessibility are difficult to justify. Some additional study into the development and application of absolute mobility standards may be warranted.

The application of the mobility evaluation model has primarily focused upon a corridor line‐haul system. Conclusions suggest that such a system will not markedly improve existing transit mobility levels in either the peak hour or the off‐peak. The experimental work has verified this conclusion, and more importantly, it has detailed quantitatively the exact levels and spatial distribution of mobility improvements. However, this study does not include a comprehensive analysis of all methods of mobility enhancement, nor does it undertake a comparison of alternative means of mobility improvement. Certainly other methods to improve access to opportunities should be explored before policy considerations are finalized. These methods include other transit solutions, land use alternatives, socio‐economic policies, and other‐mode transportation alternatives. The accessibility technique and mobility indices approach appears to have general applicability in the analysis of optimal strategies for system evaluation.

Of interest is an examination of alternative feeder transit systems to the corridor line. Additional research with the model might point out the maximum mobility effects expected through improved collector service in the suburbs, with corridor line‐haul to the CBD.

The indices are also readily available for a comparison of mobility patterns for different urban areas. Application of the program to transit and socio‐economic data for a set of cities would yield an indication of the relative mobility levels provided. Such data might be considered as an evaluation criterion for future transit funding by federal officials.

In addition, the model is currently being considered by UMTA as a tool to aid in the evaluation of the equitable distribution of transit system benefits as defined in Title VI of the Civil Rights Act of 1964.²⁵ The mobility output would serve as an indicator of the levels‐of‐service provided to certain disadvantaged urban groups. For this application the computer model is being altered to achieve compatability with the Transportation Planning System (UTPS) computer model package developed by UMTA.     

Short range transit planning in Cairo

This paper describes an approach to short‐range planning that was developed to analyze and suggest improvements to the existing transit system serving metropolitan Cairo. The methodology is based on a corridor‐by‐corridor analysis which not only brings the scale of analysis down to a level which is necessary to address operational issues, but also results in a technology transfer strategy which allows the local planners to apply and test planning techniques in one corridor while more advanced techniques are developed for another. Procedures using the results of a system‐wide on‐board transit survey are developed to allocate the bus fleet to the existing bus network, identify new express services, and identify new direct services. Because the effectiveness of procedures used in short‐range transit planning depends on the existence of accurate data, and given the resources required for a large‐scale survey, the development of planning procedures based on a continuing monitoring program is also recommended. This paper concludes that although techniques using on‐board surveys are limited in their applicability, the corridor‐based approach to planning is sound.

     

Optimal resource allocation among transit agencies for fleet management

Most transit agencies require government support for the replacement of their aging fleet. A procedure for equitable resource allocation among competing transit agencies for the purpose of transit fleet management is presented in this study. The proposed procedure is a 3-dimensional model that includes the choice of a fleet improvement program, agencies that may receive them, and the timing of investments. Earlier efforts to solve this problem involved the application of 1- or 2-dimensional models for each year of the planning period. These may have resulted in suboptimal solution as the models are blind to the impact of the fleet management program of the subsequent years. Therefore, a new model to address a long-term planning horizon is proposed. The model is formulated as a non-linear optimization problem of maximizing the total weighted average remaining life of the fleet subjected to improvement program and budgetary constraints. Two variants of the problem, one with an annual budget constraint and the other with a single budget constraint for the entire planning period, are formulated. Two independent approaches, namely, branch and bound algorithm and genetic algorithm are used to obtain the solution. An example problem is solved and results are discussed in details. Finally, the model is applied to a large scale real-world problem and a detailed analysis of the results is presented.     

An algorithm for finding reasonable paths in transit networks

In this paper, reasonable paths in transit networks are defined as possible paths that satisfy the acceptable time criterion and transfer‐walk criterion. A recursive algorithm for finding all of the reasonable paths in a transit network that does not involve a rapid increase in program run‐time with network size is presented. Realistic transit networks in Hong Kong and Guangzhou were selected as case studies of the different phases of the development of a trip planning system. Transport planning practitioners and potential users were invited to test the system to evaluate its performance. The results of the prototype evaluation were satisfactory, and the viability of the system as a useful tool for supporting decision‐making has been confirmed by the positive feedback that was obtained from survey questionnaires.     

Non-commitment bias in public opinion on transit usage

Estimation of ridership on a new transit system in an area where no comparable service existed before is a difficult task of transit planning. Traditional modal split models cannot be used in these cases, because no data or basis for developing a new model or adjusting a “borrowed” model are available. One of the techniques which can be used in this type of situation, is to perform a “concept test” based on public opinion. This approach, however, is plagued with the phenomenon of non-commitment bias of interviewees, and tends to overestimate the ridership. A new fixed route and fixed schedule transit service in Johnson City in Tennessee provided a rare opportunity to perform an investigation on the non-commitment bias through “before” and “after” surveys. The analysis of the non-commitment and actual responses of a sample of residents revealed substantial bias. Overall, the non-commitment ridership estimate was about twice (100% greater than) the actual ridership.:It was also observed that the bias was higher for persons owning automobiles, and for work and shopping trips.     

An optimization model for integrated transit-parking policy planning

The optimization model proposed in this paper is aimed to assist city councils (or other transport authorities) in the planning of integrated transit-parking policies. The objective is to minimize the joint operating deficit of the transit and parking operators while ensuring given minimum levels of (motorized) mobility in a city. The key decision variables are transit fares and parking fees. The impact of price changes on transit and car modal shares are described by logit functions of the generalized travel costs. The practical utility of the model is illustrated with a case study involving a midsize city in Portugal.