A bi-level programming for bus lane network design

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.     

Fixed‐route taxi system: route network design and fleet size minimization problems

This paper introduces the taxi route network design problem (TXRNDP) for a fixed‐route taxi service operating in Iran and, in similar form, in various other developing countries. The service operates fairly similar to regular transit services in that vehicles are only permitted to follow a certain predetermined route on the network. The service is provided with small size vehicles and main features are that vehicles only depart if full and that there are no intermediate boarding stops. In Iran the service attracts a high modal share but requires better coordination which is the main motivation for the present study. We develop a mathematical programming model to minimize the total travel time experienced by passengers while constraining the number of taxi lines, the trip transfer ratio and the length of taxi lines. A number of assumptions are introduced in order to allow finding an exact rather than heuristic solution. We further develop a linear programming solution to minimize the number of taxis required to serve the previously found fixed‐route taxi network. Results of a case study with the city of Zanjan, Iran, illustrate the resulting taxi flows and suggest the capability of the proposed model to reduce the total travel time, the total waiting time and the number of taxi lines compared to the current taxi operation. Copyright © 2016 John Wiley & Sons, Ltd.     

A stochastic multimodal reliable network design problem under adverse weather conditions

This paper formulates a network design problem (NDP) for finding the optimal public transport service frequencies and link capacity expansions in a multimodal network with consideration of impacts from adverse weather conditions. The proposed NDP aims to minimize the sum of expected total travel time, operational cost of transit services, and construction cost of link capacity expansions under an acceptable level of variance of total travel time. Auto, transit, bus, and walking modes are considered in the multimodal network model for finding the equilibrium flows and travel times. In the proposed network model, demands are assumed to follow Poisson distribution, and weather‐dependent link travel time functions are adopted. A probit‐based stochastic user equilibrium, which is based on the perceived expected travel disutility, is used to determine the multimodal route of the travelers. This model also considers the strategic behavior of the public transport travelers in choosing their routes, that is, common‐line network. Based on the stochastic multimodal model, the mean and variance of total travel time are analytical estimated for setting up the NDP. A sensitivity‐based solution algorithm is proposed for solving the NDP, and two numerical examples are adopted to demonstrate the characteristics of the proposed model. Copyright © 2014 John Wiley & Sons, Ltd.     

Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.     

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.     

A hybrid scheme for real‐time prediction of bus trajectories

The uncertainty associated with public transport services can be partially counteracted by developing real‐time models to predict downstream service conditions. In this study, a hybrid approach for predicting bus trajectories by integrating multiple predictors is proposed. The prediction model combines schedule, instantaneous and historical data. The contribution of each predictor as well as values of respective parameters is estimated by minimizing the prediction error using a linear regression heuristic. The hybrid method was applied to five bus routes in Stockholm, Sweden, and Brisbane, Australia. The results indicate that the hybrid method consistently outperforms the timetable and delay conservation prediction method for different route layouts, passenger demands and operation practices. Model validation confirms model transferability and real‐time applicability. Generating more accurate predictions can help service users adjust their travel plans and service providers to deploy proactive management and control strategies to mitigate the negative effects of service disturbances. Copyright © 2017 John Wiley & Sons, Ltd.     

Optimal design of a short‐turning strategy considering seat availability

We develop a methodology to optimize the schedule coordination of a full‐stop service pattern and a short‐turning service pattern on a bus route. To capture the influence of bus crowding and seat availability on passengers' riding experience, we develop a Markov model to describe the seat‐searching process of a passenger and an approach to estimate the transition probabilities of the Markov model. An optimization model that incorporates the Markov model is proposed to design the short‐turning strategy. The proposed model minimizes the total cost, which includes operational cost, passengers' waiting time cost and passengers' in‐vehicle travel time cost. Algorithm is developed to produce optimal values of the decision variables. The proposed methodology is evaluated in a case study. Compared with methodologies that ignore the effect of bus crowding, the proposed methodology could better balance bus load along the route and between two service patterns, provide passengers with better riding experience and reduce the total cost. In addition, it is shown that the optimal design of the short‐turning strategy is sensitive to seat capacity. Copyright © 2016 John Wiley & Sons, Ltd.     

The allocation of buses in heavily utilized networks with overlapping routes

Many transit systems outside North America are characterized by networks with extensively overlapping routes and buses frequently operating at, or close to, capacity. This paper addresses the problem of allocating a fleet of buses between routes in this type of system; a problem that must be solved recurrently by transit planners. A formulation of the problem is developed which recognizes passenger route choice behavior, and seeks to minimize a function of passenger wait time and bus crowding subject to constraints on the number of buses available and the provision of enough capacity on each route to carry all passengers who would select it. An algorithm is developed based on the decomposition of the problem into base allocation and surplus allocation components. The base allocation identifies a feasible solution using an (approx.) minimum number of buses. The surplus allocation is illustrated for the simple objective of minimizing the maximum crowding level on any route. The bus allocation procedure developed in this paper has been applied to part of the Cairo bus system in a completely manual procedure, and is proposed to be the central element of a short-range bus service planning process for that city.     

A comparison of accuracy and cost of attribute data in analysis of transit service areas using GIS

User oriented transit service is designed to meet the particular needs of a selected group of travelers. Transit Routes are located to provide convenient linkages between user's origin and destination in such a way that out-of-vehicle time, such as access and transfer time, is minimized. Planning transit routes requires understanding demographics, land use and travel patterns in an area. The dynamic nature of these systems necessitates regular review and analysis to insure that the transit system continues to meet the needs of the area it serves. Geographic Information Systems (GIS) provide a flexible framework for planning and analyzing transit routes and stops. Socioeconomic, demographic, housing, land use, and traffic data may be modeled in a GIS to identify efficient and effective corridors to locate routes. Part of the route location and analysis problem requires estimating population within the service area of a route. A route's service area is defined using walking distance or travel time. The problem of identifying service areas for park and ride or auto/bus users is not considered here, but assumed analogous to walk/bus trips. This paper investigates the accuracy and costs associated with the use of different attribute data bases to perform service area analysis for transit routes using GIS. A case study is performed for Logan, Utah, where a new fixed route service is operated. The case study illustrates the use of census data, postal data, data collected from aerial photographs, and data collected during a field survey using the network area analysis technique for transit service area analysis. This comparison allows us to describe the amount of error introduced by various spatial modeling techniques of data bases representing a variety of aggregation levels.     

Plan-based flexible bus bridging operation strategy

Bus bridging has been widely used to connect stations affected by metro disruptions such that stranded passengers could resume their journeys. Previous studies generally assumed that a bus operates exclusively on one bridging route with given frequency, which limits the service flexibility and reduce the operational efficiency. We propose a strategy to instruct buses to operate on predefined bridging routes once they are dispatched from depots. Buses are allowed to flexibly serve different bridging routes. Each bus operates based on a bridging plan that lists the stations to serve in sequence instead of route frequencies. A two-stage model is developed to optimize the bridging plans and their assignments to buses with the objectives that balance the operational priorities between minimizing bus bridging time and reducing passenger delay. A Weight Shortest Processing Time first (WSPT) rule based heuristic algorithm is developed to solve the proposed model. The developed model is further incorporated in a rolling horizon framework to handle dynamic passenger arrivals during the disruption period. The effectiveness of the proposed strategy is demonstrated in comparison with alternative strategies in real-world case studies.     

A simulation‐based reliability assessment approach for congested transit network

This paper is an attempt to develop a generic simulation‐based approach to assess transit service reliability, taking into account interaction between network performance and passengers' route choice behaviour. Three types of reliability, say, system wide travel time reliability, schedule reliability and direct boarding waiting‐time reliability are defined from perspectives of the community or transit administration, the operator and passengers. A Monte Carlo simulation approach with a stochastic user equilibrium transit assignment model embedded is proposed to quantify these three reliability measures of transit service. A simple transit network with a bus rapid transit (BRT) corridor is analysed as a case study where the impacts of BRT components on transit service reliability are evaluated preliminarily.     

Flexible feeder transit route design to enhance service accessibility in urban area

To improve the accessibility of transit system in urban areas, this paper presents a flexible feeder transit routing model that can serve irregular‐shaped networks. By integrating the cost efficiency of fixed‐route transit system and the flexibility of demand responsive transit system, the proposed model is capable of letting operating feeder busses temporarily deviate from their current route so as to serve the reported demand locations. With an objective of minimizing total bus travel time, a new operational mode is then proposed to allow busses to serve passengers on both street sides. In addition, when multiple feeder busses are operating in the target service area, the proposed model can provide an optimal plan to locate the nearest one to response to the demands. A three‐stage solution algorithm is also developed to yield meta‐optimal solutions to the problem in a reasonable amount of time by transforming the problem into a traveling salesman problem. Numerical studies have demonstrated the effectiveness of the proposed model as well as the heuristic solution approach. Copyright © 2015 John Wiley & Sons, Ltd.     

A portfolio theory of route choice

Although many individual route choice models have been proposed to incorporate travel time variability as a decision factor, they are typically still deterministic in the sense that the optimal strategy requires choosing one particular route that maximizes utility. In contrast, this study introduces an individual route choice model where choosing a portfolio of routes instead of a single route is the best strategy for a rational traveler who cares about both journey time and lateness when facing stochastic network conditions. The proposed model is compared with UE and SUE models and the difference in both behavioral foundation and model characteristics is highlighted. A numerical example is introduced to demonstrate how such model can be used in traffic assignment problem. The model is then tested with GPS data collected in metropolitan Minneapolis–St. Paul, Minnesota. Our data suggest there is no single dominant route (defined here as a route with the shortest travel time for a 15 day period) in 18% of cases when links travel times are correlated. This paper demonstrates that choosing a portfolio of routes could be the rational choice of a traveler who wants to optimize route decisions under variability.     

Proactive route guidance to avoid congestion

We propose a proactive route guidance approach that integrates a system perspective: minimizing congestion, and a user perspective: minimizing travel inconvenience. The approach assigns paths to users so as to minimize congestion while not increasing their travel inconvenience too much. A maximum level of travel inconvenience is ensured and a certain level of fairness is maintained by limiting the set of considered paths for each Origin-Destination pair to those whose relative difference with respect to the shortest (least-duration) path, called travel inconvenience, is below a given threshold. The approach hierarchically minimizes the maximum arc utilization and the weighted average experienced travel inconvenience. Minimizing the maximum arc utilization in the network, i.e., the ratio of the number of vehicles entering an arc per time unit and the maximum number of vehicles per time unit at which vehicles can enter the arc and experience no slowdown due to congestion effects, is a system-oriented objective, while minimizing the weighted average experienced travel inconvenience, i.e., the average travel inconvenience over all eligible paths weighted by the number of vehicles per time unit that traverse the path, is a user-oriented objective. By design, to ensure computational efficiency, the approach only solves linear programming models. In a computational study using benchmark instances reflecting a road infrastructure encountered in many cities, we analyze, for different levels of maximum travel inconvenience and, the minimum maximum arc utilization and the weighted average experienced travel inconvenience. We find that accepting relatively small levels of maximum travel inconvenience can result in a significant reduction, or avoiding, of congestion.     

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.     

Evaluation of a public transportation level of service concept

The level of service of a bus line is evaluated by its operational characteristics, particularly by the ratio between average bus travel time on a given route and the average passenger car travel time on the shortest distance between the origin and the destination of the bus in question. It is shown that the level-of-service measure may be predicted by such independent variables as route length, average distance between bus stations, number of signalized and unsignalized intersections, and the ratio between such intersections. It is hypothesized that use of other independent variables such as boarding and alighting passengers, or volume to capacity ratio on the route concerned, could improve the predictive power of the suggested models. Further research is recommended on the effect of these latter variables and other operational variables which might influence bus level of service, and also on the comparison between direct bus lines and lines which use transfer points.     

Ridership estimation procedure for a transit corridor with new bus rapid transit service

Ridership estimation is a critical step in the planning of a new transit route or change in service. Very often, when a new transit route is introduced, the existing routes will be modified, vehicle capacities changed, or service headways adjusted. This has made ridership forecasts for the new, existing, and modified routes challenging. This paper proposes and demonstrates a procedure that forecasts the ridership of all transit routes along a corridor when a new bus rapid transit (BRT) service is introduced and existing regular bus services are adjusted. The procedure uses demographic data along the corridor, a recent origin–destination survey data, and new and existing transit service features as inputs. It consists of two stages of transit assignment. In the first stage, a transit assignment is performed with the existing transit demand on the proposed BRT and existing bus routes, so that adjustments to the existing bus services can be identified. This transit assignment is performed iteratively until there is no adjustment in transit services. In the second stage, the transit assignment is carried out with the new BRT and adjusted regular bus services, but incorporates a potential growth in ridership because of the new BRT service. The final outputs of the procedure are ridership for all routes and route segments, boarding and alighting volumes at all stops, and a stop‐by‐stop trip matrix. The proposed ridership estimation procedure is applicable to a new BRT route with and without competing regular bus routes and with BRT vehicles traveling in dedicated lanes or in mixed traffic. The application of the proposed procedure is demonstrated via a case study along the Alameda Corridor in El Paso, Texas. Copyright © 2015 John Wiley & Sons, Ltd.     

A genetic algorithm-based method for improving quality of travel time prediction intervals

The transportation literature is rich in the application of neural networks for travel time prediction. The uncertainty prevailing in operation of transportation systems, however, highly degrades prediction performance of neural networks. Prediction intervals for neural network outcomes can properly represent the uncertainty associated with the predictions. This paper studies an application of the delta technique for the construction of prediction intervals for bus and freeway travel times. The quality of these intervals strongly depends on the neural network structure and a training hyperparameter. A genetic algorithm–based method is developed that automates the neural network model selection and adjustment of the hyperparameter. Model selection and parameter adjustment is carried out through minimization of a prediction interval-based cost function, which depends on the width and coverage probability of constructed prediction intervals. Experiments conducted using the bus and freeway travel time datasets demonstrate the suitability of the proposed method for improving the quality of constructed prediction intervals in terms of their length and coverage probability.     

Analyzing urban bus service reliability at the stop, route, and network levels

Improving the reliability of bus service has the potential to increase the attractiveness of public transit to current and prospective riders. An understanding of service reliability is necessary to develop strategies that help transit agencies provide better services. However, few studies have been conducted analyzing bus reliability in the metropolis of China. This paper presents an in-depth analysis of service reliability based on bus operational characteristics in Beijing. Three performance parameters, punctuality index based on routes (PIR), deviation index based on stops (DIS), and evenness index based on stops (EIS), are proposed for the evaluation of bus service reliability. Reliability involves routes, stops, punctuality, deviation, and evenness. The relationship among the three parameters is discussed using a numerical example. Subsequently, through a sampling survey of bus lines in Beijing, service reliability at the stop, route, and network levels are estimated. The effects of route length, headway, the distance from the stop to the origin terminal, and the use of exclusive bus lanes are also analyzed. The results indicate low service reliability for buses in Beijing and a high correlation between service reliability and route length, headway, distance from the stop to the origin terminal, and the provision of exclusive bus lanes.     

A bikeway network design model for urban areas

This work develops a bikeway network design model for cycling in urban areas. The objectives of the proposed model are to minimize cyclist risk, maximize cyclist comfort, maximize service coverage for residents, and minimize the impact of the bikeway on existing traffic. The proposed model considers the following constraints: bikeway type, monetary budgets, path continuities, and value ranges of decision variables. Grey numbers are employed to deal with parameter uncertainties, and the proposed model is developed as a multi-objective grey 0–1 programming problem. A case study of the Xinyi District, Taipei City, is conducted. The grey one-stage algorithm is applied to solve this problem. In total, six non-dominated alternatives are generated for the case study. In comparing model alternatives with the existing network, this work confirms that the existing biking network prioritizes cyclist comfort. Scenario analyses indicate that maintaining the lower bound of the length percentage of wooded areas at 20–40 % generates better performance than that of the other scenarios, while decreasing the number of traffic accidents only decreases cyclist risk and does not alter the other objectives. The proposed model is the first network design model for bikeways in literature and will assist bikeway planners in developing alternatives for further evaluation and in developing detailed designs efficiently and systematically.