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.     

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.     

Evaluation of an existing bus network using a transit network optimisation model: a case study of the Hiroshima City Bus network

This study evaluates an existing bus network from the perspectives of passengers, operators, and overall system efficiency using the output of a previously developed transportation network optimisation model. This model is formulated as a bi-level optimisation problem with a transit assignment model as the lower problem. The upper problem is also formulated as bi-level optimisation problem to minimise costs for both passengers and operators, making it possible to evaluate the effects of reducing operator cost against passenger cost. A case study based on demand data for Hiroshima City confirms that the current bus network is close to the Pareto front, if the total costs to both passengers and operators are adopted as objective functions. However, the sensitivity analysis with regard to the OD pattern fluctuation indicates that passenger and operator costs in the current network are not always close to the Pareto front. Finally, the results suggests that, regardless of OD pattern fluctuation, reducing operator costs will increase passenger cost and increase inequity in service levels among passengers.     

An analytic investigation of optimal bus size

The use of smaller buses offers passengers a better service frequency for a given service capacity, but costs more to operate per seat provided. Within this trade-off there is an optimal bus size which maximises social benefit. A mathematical model is described which can be solved analytically to provide an explicit relationship between optimal bus size and factors such as operating cost, level of demand, and demand elasticities. The model includes: passenger demand varying with the generalised cost of travel according to a constant elasticity; the effect of changes in bus occupancy on average waiting times and on operating speed; the financial constraint that farebox revenue must equal operating cost less subsidy; an allowance for external benefits associated with generated demand, and for the effect of the flow of buses on traffic congestion; and an operating cost increasing linearly with bus size. The optimal size varies with the square root of demand, and with the unit cost to the power of 0.1 to 0.2. It also increases slowly with the proportion of cost covered by subsidy. For typical urban operating conditions in the United Kingdom the optimal size for a monopoly service lies between 55 and 65 seats assuming the observed relationship between cost and size; it is possible that changes in working practices could make smaller buses relatively cheaper to operate, so reducing the optimal size, but it seems unlikely to fall below 40 seats.     

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.     

Transit system evaluation: Guideway bus vs. light rail transit

This paper describes a set of specialized spreadsheets that model the cost and performance of transit system options including light rail transit, guideway bus, express bus, and ride sharing. These spreadsheets are demonstrated by comparing a guideway bus (GWB) transit system and a light rail transit (LRT) system proposed for construction in an active rail corridor. The comparisons for assumed levels of transit ridership include guideway geometry, travel time, headways, vehicle requirements, grade crossing protection, and capital and operating costs. The planned GWB system runs on an exclusive dual guideway in the rail right-of-way, and the alternative LRT system operates on the existing rails with new bridges and track as needed for a dual guideway system. The analysis compares the two options for mode splits between 0.5% and 50%. Results show that while both options have approximately the same travel time, the GWB system costs approximately 30% less than the LRT system. The cost difference results primarily from lower GWB vehicle purchase and operating costs. The spreadsheets are available through the McTrans Center at the University of Florida, Gainesville, Florida.     

A cost-competitiveness analysis of charging infrastructure for electric bus operations

This study investigates the cost competitiveness of different types of charging infrastructure, including charging stations, charging lanes (via charging-while-driving technologies) and battery swapping stations, in support of an electric public transit system. To this end, we first establish mathematical models to investigate the optimal deployment of various charging facilities along the transit line and determine the optimal size of the electric bus fleet, as well as their batteries, to minimize total infrastructure and fleet costs while guaranteeing service frequency and satisfying the charging needs of the transit system. We then conduct an empirical analysis utilizing available real-world data. The results suggest that: (1) the service frequency, circulation length, and operating speed of a transit system may have a great impact on the cost competitiveness of different charging infrastructure; (2) charging lanes enabled by currently available inductive wireless charging technology are cost competitive for most of the existing bus rapid transit corridors; (3) swapping stations can yield a lower total cost than charging lanes and charging stations for transit systems with high operating speed and low service frequency; (4) charging stations are cost competitive only for transit systems with very low service frequency and short circulation; and (5) the key to making charging lanes more competitive for transit systems with low service frequency and high operating speed is to reduce their unit-length construction cost or enhance their charging power.     

Inter-city bus routing and timetable setting under stochastic demands

Vehicle fleet routing and timetable setting are essential to the enhancement of an inter-city bus carrier’s operating cost, profit, level of service and competitiveness in the market. In past research the average passenger demand has usually served as input in the production of the final fleet routes and timetables, meaning that stochastic disturbances arising from variations in daily passenger demand in actual operations are neglected. To incorporate the stochastic disturbances of daily passenger demands that occur in actual operations, in this research, we established a stochastic-demand scheduling model. We applied a simulation technique, coupled with link-based and path-based routing strategies, to develop two heuristic algorithms to solve the model. To evaluate the performance of the proposed model and the two solution algorithms, we developed an evaluation method. The test results, regarding a major Taiwan inter-city bus operation, were good, showing that the model and the solution algorithms could be useful in practice.     

Optimal slack time for timed transfers at a transit terminal

At transit terminals where two routes interchange passengers, total system costs may be reduced by allowing some “slack” time in the vehicle schedules to decrease the probability of missed connections. Transfer cost functions are formulated and used to determine optimal slack time for simple systems with transfers between one bus route and one rail line. Some analytic results are derived for empirical discrete and Gumbel distributions of bus arrival times. Relations between the optimal slack times and headways, transfer volumes, passenger time values, bus operating costs, and standard deviations of bus and train arrivals are also developed numerically using normally distributed arrivals. However, the proposed numerical approach can optimize slack times for any observed arrival distributions. The results provide some guidelines on desirable slack times and show that schedule coordination between the two routes is not worth attempting when standard deviations of arrivals exceed certain levels. Possible extensions of this work are suggested in the last section.     

Optimization of headways with stop‐skipping control: a case study of bus rapid transit system

Bus rapid transit system is designed to provide high‐quality and cost‐efficient passenger transportation services. In order to achieve this design objective, effective scheduling strategies are required. This research aims at improving the operation efficiency and service quality of a BRT system through integrated optimization of its service headways and stop‐skipping strategy. Based on cost analysis for both passengers and operation agencies, an optimization model is established. A genetic algorithms based algorithm and an application‐oriented solution method are developed. Beijing BRT Line 2 has been chosen as a case study, and the effectiveness of the optimal headways with stop‐skipping services under different demand levels has been analyzed. The results has shown that, at a certain demand level, the proposed operating strategy can be most advantageous for passengers with an accepted increase of operating costs, under which the optimum headway is between 3.5 and 5.5 min for stop‐skipping services during the morning peak hour depending on the demand with the provision of stop‐skipping services. The effectiveness of the optimal headways with stop‐skipping services is compared with those of existing headways and optimal headways without stop‐skipping services. The results show that operating strategies under the optimal headways with stop‐skipping services outperforms the other two operating strategies with respect to total costs and in‐vehicle time for passengers. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Optimal starting location of an HOV lane for a linear monocentric urban area

This paper analyzes the optimal starting location of a high-occupancy-vehicle (HOV) lane for a linear monocentric urban area. Both travel time and carpooling costs are taken into account. The research proposes an analytical framework for the case with a continuum demand distribution along a highway corridor. The objective is assumed to maximize social welfare of the transportation system, which is the difference between the total user benefit and travel cost. Numerical analysis via simulation experiments was conducted to seek the existence of an optimal solution. Based on the results of a sensitivity analysis, we find a specific relationship between the carpooling cost and the optimal design of the starting point of an HOV lane.     

Feeder-trunk or direct lines? Economies of density,transfer costs and transit structure in an urban context

A feeder-trunk scheme has been labeled as superior in urban areas due to the presence of economies of density (decreasing average operating cost) along the avenues served by trunk lines. We compare this structure against three types of direct lines structures (no transfers) to serve a stylized public transport network where several flows converge into a main avenue, simultaneously optimizing fleet and vehicle sizes considering both users’ and operators’ costs. The best structure is shown to depend not only on the total passenger volume but also on demand imbalance, demand dispersion in the origins and the length of the trunk line. The region where the feeder-trunk structure dominates depends largely on the value assigned to the pure transfer penalty.     

Integrated modeling of high performance passenger and freight train planning on shared-use corridors in the US

This paper studies strategic level train planning for high performance passenger and freight train operations on shared-use corridors in the US. We develop a hypergraph-based, two-level approach to sequentially minimize passenger and freight costs while scheduling train services. Passenger schedule delay and freight lost demand are explicitly modeled. We explore different solution strategies and conclude that a problem-tailored linearized reformulation yields superior computational performance. Using realistic parameter values, our numerical experiments show that passenger cost due to schedule delay is comparable to in-vehicle travel time cost and rail fare. In most cases, marginal freight cost increase from scheduling more passenger trains is higher than marginal reduction in passenger schedule delay cost. The heterogeneity of train speed reduces the number of freight trains that can run on a corridor. Greater tolerance for delays could reduce lost demand and overall cost on the freight side. The approach developed in the paper could be applied to other scenarios with different parameter values.     

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.     

基于客户满意度的货运动车组开行方案研究

高铁货运逐渐兴起,本文对货运动车组开行方案优化进行了研究。针对高铁运输安全、快捷、运输成本较低等特性,提出以货运动车组及客货混编动车组为主,客运动车组捎带运输为补充的开行模式,结合运输需求、线路通过能力等限条件,以运输成本最小和货主满意度最大为目标,建立多目标综合优化模型,运用线性加权组合法,以lingo软件为依托进行求解。通过算例给出具体开行方案,并对同一运输区间各种运输方式的单位成本及用时进行对比分析。结果表明,相对于传统运输方式,高铁货运综合运输成本较低,用时更短,能够兼顾运输企业与货主的双重要求;所建模型优化效果明显,可为未来货运动车组的开行提供参考。     

Planning of integrated transit network for bus and LRT

An integrated approach is suggested for the planning and evaluation of mass transport systems which includes a bus network and LRT/RTS in urban areas. This approach involves a simplified procedure for determining mass transit demand, bus route network generation and evaluation, light or rapid transit corridor identification and its patronage determination in the presence of bus networks. Scheduling of a mass transportation system based on marginal ridership concept is also suggested for a given fleet size. All the three major components (demand estimation, route network generation and scheduling) iterate and interact each other with a feedback mechanism for the desired optimal solution in terms of performance indicators. Necessary interactive software packages for all the above subsystems have been developed.     

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.     

Assessing the social costs of urban transport infrastructure options in low and middle income countries

ABSTRACT

This paper develops cost models for urban transport infrastructure options in situations where motorcycles and various forms of taxis are important modes of transport. The total social costs (TSCs) of conventional bus, Bus Rapid Transit (BRT), Monorail, Metro (Elevated Rail), car, motorcycle, Taxi and Uber are calculated for an urban corridor covering operator, user and external costs. Based on the parameters for a 7?km corridor in Hanoi, Vietnam, the results show the lowest average social cost (ASC) transport modes for different ranges of demand. Motorcycle might be the best option at low demand levels while conventional bus has advantages with low-medium demand. At medium demand levels, bus-based technologies and Monorail are competitive options while Metro, with a higher person capacity, is the best alternative at the highest demand levels. Compared to other modes, the ASCs of car and Taxi/Uber are greater because of high capital cost (related to vehicles) per passenger and low occupancy. Transport planners and decision makers in low and middle income countries (LMICs) can draw on the findings of this study. However, various limitations are identified and additional research is suggested.     

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.