An integrated Bayesian approach for passenger flow assignment in metro networks

This paper proposes an integrated Bayesian statistical inference framework to characterize passenger flow assignment model in a complex metro network. In doing so, we combine network cost attribute estimation and passenger route choice modeling using Bayesian inference. We build the posterior density by taking the likelihood of observing passenger travel times provided by smart card data and our prior knowledge about the studied metro network. Given the high-dimensional nature of parameters in this framework, we apply the variable-at-a-time Metropolis sampling algorithm to estimate the mean and Bayesian confidence interval for each parameter in turn. As a numerical example, this integrated approach is applied on the metro network in Singapore. Our result shows that link travel time exhibits a considerable coefficient of variation about 0.17, suggesting that travel time reliability is of high importance to metro operation. The estimation of route choice parameters conforms with previous survey-based studies, showing that the disutility of transfer time is about twice of that of in-vehicle travel time in Singapore metro system.     

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

This paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimating metro passengers’ path choices by combining self-reported revealed preference and smart card data

With the help of automated fare collection systems in the metro network, more and more smart card (SC) data has been widely accumulated, which includes abundant information (i.e., Big Data). However, its inability to record passengers’ transfer information and factors affecting passengers’ travel behaviors (e.g., socio-demographics) limits further potential applications. In contrast, self-reported Revealed Preference (RP) data can be collected via questionnaire surveys to include those factors; however, its sample size is usually very small in comparison to SC data. The purpose of this study is to propose a new set of approaches of estimating metro passengers’ path choices by combining self-reported RP and SC data. These approaches have the following attractive features. The most important feature is to jointly estimate these two data sets based on a nested model structure with a balance parameter by accommodating different scales of the two data sets. The second feature is that a path choice model is built to incorporate stochastic travel time budget and latent individual risk-averse attitude toward travel time variations, where the former is derived from the latter and the latter is further represented based on a latent variable model with observed individual socio-demographics. The third feature is that an algorithm of combining the two types of data is developed by integrating an Expectation-Maximization algorithm and a nested logit model estimation method. The above-proposed approaches are examined based on data from Guangzhou Metro, China. The results show the superiority of combined data over single data source in terms of both estimation and forecasting performance.     

A practical model for transfer optimization in a transit network: Model formulations and solutions

This paper studies the transit network scheduling problem and aims to minimize the waiting time at transfer stations. First, the problem is formulated as a mixed integer programming model that gives the departure times of vehicles in lines so that passengers can transfer between lines at transfer stations with minimum waiting times. Then, the model is expanded to a second model by considering the extra stopping time of vehicles at transfer stations as a new variable set. By calculating the optimal values for these variables, transfers can be better performed. The sizes of the models, compared with the existing models, are small enough that the models can be solved for small- and medium-sized networks using regular MIP solvers, such as CPLEX. Moreover, a genetic algorithm approach is represented to more easily solve larger networks. A simple network is used to describe the models, and a medium-sized, real-life network is used to compare the proposed models with another existing model in the literature. The results demonstrate significant improvement. Finally, a large-scale, real-life network is used as a case study to evaluate the proposed models and the genetic algorithm approach.     

Multi-objective optimization of a road diet network design

The present study focuses on the development of a model for the optimal design of a road diet plan within a transportation network, and is based on rigorous mathematical models. In most metropolitan areas, there is insufficient road space to dedicate a portion exclusively for cyclists without negatively affecting existing motorists. Thus, it is crucial to find an efficient way to implement a road diet plan that both maximizes the utility for cyclists and minimizes the negative effect on motorists. A network design problem (NDP), which is usually used to find the best option for providing extra road capacity, is adapted here to derive the best solution for limiting road capacity. The resultant NDP for a road diet (NDPRD) takes a bi-level form. The upper-level problem of the NDPRD is established as one of multi-objective optimization. The lower-level problem accommodates user equilibrium (UE) trip assignment with fixed and variable mode-shares. For the fixed mode-share model, the upper-level problem minimizes the total travel time of both cyclists and motorists. For the variable mode-share model, the upper-level problem includes minimization of both the automobile travel share and the average travel time per unit distance for motorists who keep using automobiles after the implementation of a road diet. A multi-objective genetic algorithm (MOGA) is mobilized to solve the proposed problem. The results of a case study, based on a test network, guarantee a robust approximate Pareto optimal front. The possibility that the proposed methodology could be adopted in the design of a road diet plan in a real transportation network is confirmed.     

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.     

Optimization of a feeder-bus route design by using a multiobjective programming approach

This paper presents a feeder-bus route design model, capable of minimizing route length, minimizing maximum route travel time of planned routes, and maximizing service coverage for trip generation. The proposed model considers constraints of route connectivity, subtour prevention, travel time upper bound of a route, relationships between route layout and service coverage, and value ranges of decision variables. Parameter uncertainties are dealt with using fuzzy numbers, and the model is developed as a multiobjective programming problem. A case study of a metro station in Taichung City, Taiwan is then conducted. Next, the programming problem in the case study is solved, based on the technique for order preference by similarity to ideal solution approach to obtain the compromise route design. Results of the case study confirm that the routes of the proposed model perform better than existing routes in terms of network length and service coverage. Additionally, increasing the number of feeder-bus routes decreases maximum route travel time, increases service coverage, and increases network length. To our knowledge, the proposed model is the first bus route design model in the literature to consider simultaneously various stakeholder needs and support for bus route planners in developing alternatives for further evaluation efficiently and systematically.     

Exploring the role of social capital influence variables on travel behaviour

This paper explores the potential role of individual trip characteristics and social capital network variables in the choice of transport mode. A sample of around 100 individuals living or working in one suburb of Madrid (i.e. Las Rosas district of Madrid) participated in a smartphone short panel survey, entering travel data for an entire working week. A Mixed Logit model was estimated with this data to analyze shifts to metro as a consequence of the opening of two new stations in the area. Apart from classical explanatory variables, such as travel time and cost, gender, license and car ownership, the model incorporated two “social capital network” variables: participation in voluntary activities and receiving help for various tasks (i.e. child care, housekeeping, etc.). Both variables improved the capacity of the model to explain transport mode shifts. Further, our results confirm that the shift towards metro was higher in the case of people “helped” and lower for those participating in some voluntary activities.     

Identifying the spatial distribution of public transportation trips by node and community characteristics

ABSTRACT

Identifying the spatial distribution of travel activities can help public transportation managers optimize the allocation of resources. In this paper, transit networks are constructed based on traffic flow data rather than network topologies. The PageRank algorithm and community detection method are combined to identify the spatial distribution of public transportation trips. The structural centrality and PageRank values are compared to identify hub stations; the community detection method is applied to reveal the community structures. A case study in Guangzhou, China is presented. It is found that the bus network has a community structure, significant weekday commuting and small-world characteristics. The metro network is tightly connected, highly loaded, and has no obvious community structure. Hub stations show distinct differences in terms of volume and weekend/weekday usage. The results imply that the proposed method can be used to identify the spatial distribution of urban public transportation and provide a new study perspective.     

A model and solution algorithm for dynamic deterministic user equilibrium assignment

Abstract

In this paper a route-based dynamic deterministic user equilibrium assignment model is presented. Some features of the linear travel time model are first investigated and then a divided linear travel time model is proposed for the estimation of link travel time: it addresses the limitations of the linear travel time model. For the application of the proposed model to general transportation networks, this paper provides thorough investigations on the computational issues in dynamic traffic assignment with many-to-many OD pairs and presents an efficient solution procedure. The numerical calculations demonstrate that the proposed model and solution algorithm produce satisfactory solutions for a network of substantial size with many-to-many OD pairs. Comparisons of assignment results are also made to show the impacts of incorporation of different link travel time models on the assignment results.     

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.

     

Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach

With a particular emphasis on the end-to-end travel time prediction problem, this paper proposes an information-theoretic sensor location model that aims to minimize total travel time uncertainties from a set of point, point-to-point and probe sensors in a traffic network. Based on a Kalman filtering structure, the proposed measurement and uncertainty quantification models explicitly take into account several important sources of errors in the travel time estimation/prediction process, such as the uncertainty associated with prior travel time estimates, measurement errors and sampling errors. By considering only critical paths and limited time intervals, this paper selects a path travel time uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework with a unified modeling of both recurring and non-recurring traffic conditions. An analytical determinant maximization model and heuristic beam-search algorithm are used to find an effective lower bound and solve the combinatorial sensor selection problem. A number of illustrative examples and one case study are used to demonstrate the effectiveness of the proposed methodology.     

Mapping spatial accessibility of public transportation network in an urban area – A case study of Shanghai Hongqiao Transportation Hub

Accessibility is a key metric when assessing the efficiency of an urban public transportation network. This research develops a methodology for evaluating spatial accessibility of a system with multiple transportation modes in an urban area, Shanghai Hongqiao Transportation Hub (SHTH) and its surrounding area. The method measured total traveling time as an accessibility indicator, which summed the time people spent on walking, waiting, transfer and transportation in a journey from the SHTH to destinations. Spatial accessibility was classified into five levels from very high to very low. The evaluation was conducted at a cell-by-cell basis under an overall scenario and three specific scenarios. Evaluation results were presented in a series of maps. The overall accessibility scenario shows a concentric-ring trend decreasing from the SHTH to the fringe of the study area. Areas along the metro lines generally have a much higher accessibility than those along the bus lines with some exceptions where bus routes play a more important role. Metro stations identified as either time-saving or time-consuming points are mainly distributed around the urban center. Some suggestions are proposed for improving accessibility of public transportation network in the study area. The results from this study provide a scientific basis and useful information for supporting decision-making on urban planning, and assisting dwellers to travel in a time-efficient manner. The methodology offers a simple, flexible way to the spatial evaluation, metro station identification and network modification of accessibility of public transportation systems with multiple transportation modes.     

Optimal speed detector density for the network with travel time information

In the expressway network, detectors are installed on the links for detecting the travel time information while the predicted travel time can be provided by the route guidance system (RGS). The speed detector density can be determined to influence flow distributions in such a way that the precision of the travel time information and the social cost of the speed detectors are optimized, provided that each driver chooses the minimum perceived travel time path in response to the predicted travel time information. In this paper, a bilevel programming model is proposed for the network with travel time information provided by the RGS. The lower-level problem is a probit-based traffic assignment model, while the upper-level problem is to determine the speed detector density that minimizes the measured travel time error variance as well as the social cost of the speed detectors. The sensitivity analysis based algorithm is proposed for the bilevel programming problem. Numerical examples are provided to illustrate the applications of the proposed model and of the solution algorithm.     

Eco-routing problem considering fuel consumption and probabilistic travel time budget

Road transportation is one of the major sources of greenhouse gas emissions. To reduce energy consumption and alleviate this environmental problem, this study aims to develop an eco-routing algorithm for navigation systems. Considering that both fuel consumption and travel time are important factors when planning a trip, the proposed routing algorithm finds a path that consumes the minimum amount of gasoline while ensuring that the travel time satisfies a specified travel time budget and an on-time arrival probability. We first develop link-based fuel consumption models based on vehicle dynamics, and then the Lagrangian-relaxation-based heuristic approach is proposed to efficiently solve this NP-hard problem. The performance of the proposed eco-routing strategy is verified in a large-scale network with real travel time and fuel consumption data. Specifically, a sensitivity analysis of fuel consumption reduction for travel demand and travel time buffer is discussed in our simulation study.     

Recognizing metro-bus transfers from smart card data

Transfer points between metro and bus services remain an elusive, yet critical junction for transportation practitioners. Based on massive Smart Card (SC) data, previous studies apply a one-size-fits-all criterion to discriminate between transfers. However, this is not sufficiently convincing for different transfer pairs. To counter this problem, this study applies an association rules algorithm and cluster analysis to recognize metro-to-bus transfers using SC data, and demonstrates transfer recognition in a case study based on SC data collected during a week in Nanjing, China. It is shown that 85% of the transfer-recognition results are quite stable through the whole week, and the median transfer time between metro and bus is below 20?min. The method proposed in this study can be used to identify the busiest transfer points and to obtain average transfer times, which facilitates a smarter and more efficient public transit network.     

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.     

Transit network design based on travel time reliability

This paper presents a transit network optimization method, in which travel time reliability on road is considered. A robust optimization model, taking into account the stochastic travel time, is formulated to satisfy the demand of passengers and provide reliable transit service. The optimization model aims to maximize the efficiency of passenger trips in the optimized transit network. Tabu search algorithm is defined and implemented to solve the problem. Then, transit network optimization method proposed in this paper is tested with two numerical examples: a simple route and a medium-size network. The results show the proposed method can effectively improve the reliability of a transit network and reduce the travel time of passengers in general.     

Solving the station-based one-way carsharing network planning problem with relocations and non-linear demand

One-way station-based carsharing systems allow users to return a rented car to any designated station, which could be different from the origin station. Existing research has been mainly focused on the vehicle relocation problem to deal with the travel demand fluctuation over time and demand imbalance in space. However, the strategic planning of the stations’ location and their capacity for one-way carsharing systems has not been well studied yet, especially when considering vehicle relocations simultaneously. This paper presents a Mixed-integer Non-linear Programming (MINLP) model to solve the carsharing station location and capacity problem with vehicle relocations. This entails considering several important components which are for the first time integrated in the same model. Firstly, relocation operations and corresponding relocation costs are taken into consideration to address the imbalance between trip requests and vehicle availability. Secondly, the flexible travel demand at various time steps is taken as the input to the model avoiding deterministic requests. Thirdly, a logit model is constructed to represent the non-linear demand rate by using the ratio of carsharing utility and private car utility. To solve the MINLP model, a customized gradient algorithm is proposed. The application to the SIP network in Suzhou, China, demonstrates that the algorithm can solve a real world large scale problem in reasonable time. The results identify the pricing and parking space rental costs as the key factors influencing the profitability of carsharing operators. Also, the carsharing station location and fleet size impact the vehicle relocation and carsharing patronage.     

A reliability-based assignment method for railway networks with heterogeneous passengers

Travel reliability can play an important role in shaping travelers’ route choice behavior. This paper develops a railway passenger assignment method to capture the reliability-based route choices, where the trains can have stochastic delays. The overall travel reliability has two components: the travel time reliability (of trains) and the associated transfer reliability (of connections). In this context, mean-and-variance-based effective travel cost is adopted to model passengers’ evaluation of different travel options in the railway network. Moreover, passengers are heterogeneous as they may evaluate the effective travel cost differently, and they may have different requirements for the successful transfer probability (if transfers are involved in the trip). The determination of travel time reliability (of trains) is based on the travel delay distribution, and the successful transfer probability is calculated based on the delay probabilities of two trains in the transfer process. An algorithm has been designed for solving the model, and numerical examples are presented to test and illustrate the model.