Urban Transit Network Research Articles

Determining capacity flexibility of the urban transit network under different transit operation conditions

This paper proposes the capacity flexibility models of transit networks to describe the ability of urban transit networks to accommodate the changes in passenger demands. In order to keep the variations of the average passenger travel time in a reasonable way, the concept of coefficient of variation (CoV) is introduced to measure and limit the deviation from a baseline time of the average passenger travel time. The CoV could transform the capacity flexibility values to non-dimensional form in order to compare the capacity flexibility characteristics of different scale transit networks on an equal basis. The genetic algorithm with deep search (GA-DS) for this problem is proposed to find the approximating optimal solution of the capacity flexibility models more effectively. The algorithm has been tested with benchmark problems reported in the existing literature. The optimal solution of the flexibility models shows that the flexibility values are further improved by reducing the number of stops for transit routes under different transit operation conditions. At last, the influence factors of the capacity flexibility of transit systems are discussed to address reliable transit services.

Stochastic fast charging scheduling of battery electric buses with energy storage systems design

Under the background of urban green and low-carbon economic development, battery electric buses (BEBs) together with fast charging technologies are considered as an effective way in promoting carbon emissions reduction and improving energy efficiency. However, challenges arise during daily peak periods, at which BEB charging activities cause increased operation costs and substantial stress on the power grid. To fill the gaps, this work introduces energy storage systems (ESSs) into the BEB fast-charging scheduling problem. A stochastic programming model considering uncertain discharge efficiencies of ESSs is established, aiming to minimize total operation costs of fast charging stations. It is then transformed into a deterministic one with a manageable scenario sample size, using an integrated sample average approximation (SAA) and K-means approach, as well as an integrated SAA and K-means++ approach. We also present a heuristic algorithm and an improved genetic algorithm to solve the transformed model. Numerical studies based on a real-life urban transit network in Shanghai, China, are conducted to demonstrate the effectiveness of the proposed methods. Sensitivity analysis further reveals the impact of charging power on total operation cost.

A Multilayer Network Approach for the Bimodal Bus–Pedestrian Line Planning Problem

In this paper, we formulate and solve the urban line planning problem considering a multilayer representation of a bimodal transportation network. Classical formulations are usually constructed over a planar network, which implies the need to introduce several strong non-linearities in terms of frequencies when modeling transfer times. In the proposed network representation, each candidate line is stored in a specific layer and the passengers’ movements for each origin–destination pair are modelled considering a strategy subgraph, contributing to a sparse model formulation that guarantees feasibility and simplifies the assignment process. The methodology is first tested using the Mandl network, obtaining results that are comparable in terms of quality with the best metaheuristic approaches proposed in the scientific literature. With the aim of testing its applicability to large scenarios, the proposed approach is then used to design the main urban transit network of Seville, a large scenario with 141 nodes and 454 links, considering artificial unfavorable demand data. The reasonable computation time required to exactly solve the problem to optimality confirms the possibility of using the multilayer approach to deal with multimodal network design strategic problems.

Multi-objective multi-agent deep reinforcement learning to reduce bus bunching for multiline services with a shared corridor

Bus bunching is a long-standing problem in transit operation and ruining the regularity of transit service. In a typical urban transit network setting of multiple lines with a shared corridor, bus bunching becomes more frequent as there is more uncertainty inside the shared corridor. While multi-agent reinforcement learning (MARL) has been a promising scheme for learning efficient control policy in a multi-agent system, few studies have explored its applicability in multi-line transit control scenarios. In this study, we focus on a basic transit network where there are two bus lines with a shared corridor. An efficient MARL framework is proposed to learn multi-line bus holding control to avoid bus bunching. Specifically, we design observation and reward functions that incorporate multi-line information. In addition, a preference weights producer is introduced to update the objective weights towards a good trajectory evaluation during daily transit operation. In this way, we handle the multi-objective issue in multi-line control. In experimental studies, we validate the superiority of the method in real-world bus lines. Results show that the state and reward augmented with multi-line information benefit MARL in multi-line bus control. Besides, by updating preference weights towards less passenger waiting time, the regularity of transit service is further improved.

Forecasting passenger flows and headway at train level for a public transport line: Focus on atypical situations

This paper proposes a computer vision framework based on deep learning approaches for the real-time prediction of passenger loads and train headways in a metro line in an urban transit network. The short-term prediction problem is formulated as an image completion task. The train journeys on the metro line are represented as images, with the pixels denoting the train data, including the departure location, time, and load. Metro line applicative constraints, e.g., irregular time sampling of trains and univariate space, are considered in the images. Several deep learning-based architectures are investigated, including two new architectures based on transformers. Finally, an in-depth analysis and comparison of the models is performed based on a real test case of Paris metro line 9, for which a large database was collected over three years. This allowed us to include numerous instances with atypical transport system performance indicators (e.g., strikes, lockdowns, and disruptions) and to design a methodology (based on a latent space representation of the dataset) to identify and label interesting test cases. We evaluate and demonstrate the robustness of the proposed approaches numerically and study their limits for passenger loads and headways in atypical scenarios.

Framework for the Analysis and Enhancement of the Accessibility of Large-Scale Urban Transit Networks: A Data-Driven Study for the City of Lyon, France

Accessibility to a fixed point of interest is a powerful indicator for quantifying the strengths and weaknesses of a multimodal pedestrian and transit network. However, it is difficult to predict the impact on accessibility deriving from the insertion of a new infrastructure and its contribution to the urban landscape. This paper uses graph science and multisource open data to implement a tool for studying accessibility in combination with several network performance indicators. The tool allows determination of whether a transit infrastructure project can be beneficial for its potential users. In this paper, we propose to compute gravity-based accessibility, temporally bounded by an isochrone [Formula: see text]. We assume that the user always favors the shortest route, her rationality conditioned by real-time applications provided by network operators. By the proposed approach, the impacts on accessibility deriving from the construction of a new infrastructure, such as a new transit line, can be effectively quantified and the actors of urban planning can visually evaluate the consequences of their projects to make more informed decisions.

Validation of a multi-modal transit route choice model using smartcard data

Validation of travel demand models, although recognised as important, is seldom undertaken. This study adds to the scarce literature in this field by undertaking an external validation of a multi-modal transit route choice model. The model was estimated using smart card data for the urban transit network of Amsterdam before the introduction of a new metro line and is used to predict changes in travel behaviour after the network change. To validate, the model was checked for changes in estimated parameters between the two time periods, and predictive ability was evaluated at different aggregation levels. Although most model parameters were found to be unstable between the two contexts, the predictive performance at all levels was similar to the locally estimated model. Moreover, individual choices and transit mode-share predictions were found to be close to the observed ones. The errors were relatively larger for the link and route-level predictions, some of which could be attributed to the assumptions made regarding consideration choice set given as input to the model. On comparing alternative model specifications, using generic instead of mode-specific travel attributes lead to a strong degradation in predictive performance. Conversely, a model incorporating overlap between routes, with a better model fit in the base period, did not offer a clear improvement in prediction performance. The study highlights the need to validate transit route choice models before using them for deriving policy recommendations, especially in this data-rich age in which it can often be undertaken at a relatively low additional cost.

An interactive analytics approach for sustainable and resilient case studies: a machine learning perspective

ABSTRACT Sustainable development is a problem-solving method that simultaneously accounts for the economic, environmental, and social impacts of actions. Decision-makers have recently recognised the need for sustainable development. Multiobjective optimisation is the most reliable technique to solve multiple sustainable development goals. However, there needs to be more research examining the role of interactive methods in multiobjective optimisation problems. To integrate machine learning and human interactions, this paper develops a new three-stage interactive algorithm in business analytics, called the interactive Nautilus-based algorithm, to address complex problems. To show the method’s applicability, this paper uses the proposed algorithm in three sustainable and resilient case studies. The selected cases are the river pollution problem, the urban transit network design problem, and the resilience problem. Moreover, the proposed algorithm is compared with two other algorithms for validation purposes. The results reveal that the proposed algorithm outperforms non-interactive algorithms by providing superior solutions.

An evaluation framework for operational interventions on urban mass public transport during a pandemic

Decision making in a rapidly changing context, such as the development and progression of a pandemic, requires a dynamic assessment of multiple variable and competing factors. Seemingly beneficial courses of action can rapidly fail to deliver a positive outcome as the context changes. In this paper, we present a flexible data-driven agent-based simulation framework that considers multiple outcome criteria to increase opportunities for safe mobility and economic interactions on urban transit networks while reducing the potential for Covid-19 contagion in a dynamic setting. Using a case study of the Victoria line on the London Underground, we model a number of operational interventions with varied demand levels and social distancing constraints including: alterations to train headways, dwell times, signalling schemes, and train paths. Our model demonstrates that substantial performance gains ranging from 12.3–195.7% can be achieved in metro service provision when comparing the best performing operational scheme and headway with those realised on the Victoria line during the pandemic.

Planning of integrated mobility-on-demand and urban transit networks

We envision a multimodal transportation system where Mobility-on-Demand (MoD) service is used to serve the first mile and last mile of transit trips. For this purpose, the current research formulates an optimization model for designing an integrated MoD and urban transit system. The proposed model is a mixed-integer non-linear programming model that captures the strategic behavior of passengers in a multimodal network through a passenger assignment model. It determines which transit routes to operate, the frequency of the operating routes, the fleet size of vehicles required in each transportation analysis zone to serve the demand, and the passenger flow on both road and transit networks. A Benders decomposition approach with several enhancements is proposed to solve the given optimization program. Computational experiments are presented for the Sioux Falls multimodal network. The results show a significant improvement in the congestion in the city center with the introduction and optimization of an integrated transportation system. The proposed design allocates more vehicles to the outskirt zones in the network (to serve the first mile and last mile of transit trips) and more frequency to the transit routes in the city center. The integrated system significantly improves the share of transit passengers and their level of service in comparison to the base optimized transit system. The sensitivity analysis of the bus and vehicle fleet shows that increasing the number of buses has more impact on improving the level of service of passengers compared to increasing the number of MoD vehicles. Finally, we provide managerial insights for deploying such multimodal service.

Mapping the transit network of greater Cartagena with mobile phones: Coverage, accessibility, and informality

Emerging methods enable researchers and citizens to map transit networks through participatory processes to understand travel patterns, the location of formal and informal transit networks, and the geography of origin and destination points within urban areas. In this paper, we provide a detailed description of the method applied to map the formal and informal urban transit network of the metropolitan area of Cartagena, Colombia. A basic mapping of the entire network at the metropolitan level examines relationships between urban growth and transit supply. We converted the transit data into a static GTFS feed to calculate the coverage and accessibility of the mapped systems. To assess coverage, we compared the percentage of the urban areas served by formal, semi-formal and informal transit. To measure accessibility, we calculated the percentage of population and jobs that can be reached by each transit system from every location in the metropolitan area within four timeframes. Our analysis indicated transit deserts, mostly urban peripheries, which exclude disadvantaged groups from social and professional opportunities. We share the innovations developed and lessons we learned to facilitate transit mapping in other cities with high levels of informal transit. Our static GTFS data adds to a growing repository of open transit data sources that engage citizens, empower researchers, and inform public policy.

Short-Term Online Forecasting for Passenger Origin–Destination (OD) Flows of Urban Rail Transit: A Graph–Temporal Fused Deep Learning Method

Predicting short-term passenger flow accurately is of great significance for daily management and for a timely emergency response of rail transit networks. In this paper, we propose an attention-based Graph–Temporal Fused Neural Network (GTFNN) that can make online predictions of origin–destination (OD) flows in a large-scale urban transit network. In order to solve the key issue of the passenger hysteresis in online flow forecasting, the proposed GTFNN takes finished OD flow and a series of features, which are known or observable, as the input and performs multi-step prediction. The model is constructed from capturing both spatial and temporal characteristics. For learning spatial characteristics, a multi-layer graph neural network is proposed based on hidden relationships in the rail transit network. Then, we embedded the graph convolution into a Gated Recurrent Unit to learn spatial–temporal features. For learning temporal characteristics, a sequence-to-sequence structure embedded with the attention mechanism is proposed to enhance its ability to capture both local and global dependencies. Experiments based on real-world data collected from Chongqing’s rail transit system show that the metrics of GTFNN are better than other methods, e.g., the SMAPE (Symmetric Mean Absolute Percentage Error) score is about 14.16%, with a range from 5% to 20% higher compared to other methods.

An incentive subsidy mechanism for bus lines based on service level

Reasonable financial subsidies can promote public transport enterprises to raise service level, attract public transport passengers and improve the efficiency of fiscal funds. There are various bus lines that make up the urban public transit network. In this study, the single bus line is taken as the research object to establish the close relationship between the service level and the subsidy. An incentive bus subsidy method including measurement and effect evaluation is proposed. The measurement method is a dual-objective model that considers public welfare and market characteristics, and aims at maximizing the expected welfare of passengers and enterprises. The effect evaluation method of the incentive subsidy is designed to manage bus enterprises by the calculation and comparison of service level indicators. A practical example is presented to verify the effectiveness of the bus subsidy method, and shows how to regulate the bus enterprises when the bus service level declines. This study provides a method for the scientific design of incentive bus subsidies, which can encourage bus enterprises to improve their level of service, and help the government to optimize the decision-making on public transport subsidy policy.

Strategy-based transit stochastic user equilibrium model with capacity and number-of-transfers constraints

Vehicle capacity and number-of-transfers constraints are critical in transit network equilibrium because (1) transit vehicles cannot carry passengers over their capacity and (2) transit passengers typically avoid paths with numerous transfers. In this paper, we propose a strategy-based transit stochastic user equilibrium (SUE) model that considers capacity and number-of-transfers constraints for an urban congested transit network. A route-section-based method is used for the transit network representation. The transit passengers’ route choice behavior is assumed to obey the logit model, and a route-section-based path size correction factor is developed to handle the route overlapping issue. The transit line capacity and maximum number-of-transfers constraints are considered in the model. We then formulate the strategy-based transit SUE problem as a variational inequality (VI) problem. A transit path-set generation procedure is proposed to identify a transit path with a limited number of transfers using the route-section-based network representation. The diagonalization method is chosen to solve the VI problem due to the asymmetric cost function, and the diagonalized problem can be solved using a path-based partial linearization algorithm embedded with an iterative balancing scheme, which is used here to handle the numerous capacity constraints. Numerical examples are conducted to demonstrate the features of the proposed model and performance of the developed algorithm. The results show that the vehicle capacity and number of transfers would strongly impact the passenger flow patterns.

Frequency-based path flow estimator for transit origin-destination trip matrices incorporating automatic passenger count and automatic fare collection data

A frequency-based path flow estimator is proposed to estimate the transit passenger origin–destination (OD) matrix in an urban congested transit network. The proposed model not only considers the effect of congestion under an equilibrium framework, but also benefits from being formulated as a single-level model with the route-section-based network representation. Multiple transit data sources are incorporated, including automatic passenger count, automatic fare collection and automatic vehicle location data. A path-based diagonalization approach embedded with an iterative balancing scheme is developed to solve the model. Case studies are conducted to demonstrate the features and applicability of the proposed model and algorithm.

Applying Ollivier-Ricci curvature to indicate the mismatch of travel demand and supply in urban transit network

Urban transit networks need to be upgraded in accordance with urban development. While methods have been studied to design an optimal transit network given the locations of stations, these methods focus on the whole network as the optimization object. However, the strategy to improve parts of an existing transit network based on the gap between travel demand and infrastructure supply is rarely investigated. Different parts of the same network should not have the same priority to be upgraded. An evaluation method is required for this purpose to decide which parts of a transit network should be upgraded first. We argue that Ollivier-Ricci curvature, a concept from differential geometry, can serve as the evaluation method. The basic hypothesis is that Ollivier-Ricci curvature indicates the theoretical attractiveness of the fastest path between any two nodes, thereby capturing the internal structure of the transit network. Meanwhile, travel demand and behavior can be approximated by urban mobility big data. By comparing the theoretical attractiveness and the flow volume between a path between two stations, the traits of lines with mismatched supply and demand are identified, and macro strategies are suggested. A case study in Beijing demonstrates how the proposed method works out followed by a comparison with traditional betweenness centrality analysis.

Research on Optimization of Urban Public Transport Network Based on Complex Network Theory

The urban public transportation system is an important part of urban transportation, and the rationality of public transportation routes layout plays a vital role in the transportation of the city. Improving the efficiency of public transportation can have a positive impact on the operation of the public transportation system. This paper uses complex network theory and the symmetry of the up and down bus routes and stations to establish an urban public transit network model and calculates the probability of passengers choosing different routes in the public transit network according to passenger travel impedance. Based on passenger travel impedance, travel path probability and passenger travel demand, the links are weighed, and the network efficiency calculation method is improved. Finally, the public transit network optimization model was established with network efficiency as the objective function and solved by the ant colony algorithm. In order to verify the effectiveness of the model and the solution method, this paper selects areas in Nanguan District of Changchun City for example analysis. The result shows that the efficiency of the optimized network is 8.5% higher than that of the original network, which proves the feasibility of the optimized model and solution method.

Perception of overlap in multi-modal urban transit route choice

Capturing unobserved correlation between overlapping routes is a non-trivial problem in route choice modelling. For urban transit networks, research so far has been inconclusive on how this overlap is perceived by travellers. We estimate a series of path size correction logit (PSCL) models to account for alternative specifications of route overlap, including a new definition of overlap in terms of transfer nodes is proposed for multi-leg journeys. Our estimation is performed on smart card data from Amsterdam. The results indicate that the overlap between transit routes is valued positively when incorporated using either link-based, leg-based or transfer node-based PSC individually, with the transfer node-based PSC resulting in the best model fit. When considered simultaneously, the overlap of transfer nodes is valued positively by the travellers, but the subsequent overlap of journey legs is valued negatively, implying that travellers prefer having multiple (distinct) travel options at common transfer locations.

Pareto routing and scheduling of dynamic urban rail transit services with multi-objective cross entropy method

This paper presents a Pareto optimization framework for routing and scheduling dynamic rail transit network services. We first develop an event-based dynamic transit network model that can capture the evolution of passenger demand and service operations with incorporation of passengers’ transfers and recirculation of limited number of train vehicles over different service lines. A multi-objective optimizer is then built upon the transit model which seeks jointly the settings of service lines and schedules that could minimize passengers’ journey times, transfer rates, and operator’s cost. The problem is solved by a cross-entropy method (CEM) which samples potential solutions from statistically tractable distribution models with iterative updates via maximum likelihood. The operational constraints are explicitly incorporated in the solution process which enhances the feasibility of the sampled solutions and hence effectiveness of the computational process compared with other metaheuristics used in the literature. A CEM-based ranking algorithm is further developed for deriving the Pareto-frontiers for the multi-objective transit network routing and scheduling. The proposed framework is applied and tested on the Hong Kong Light Rail Transit (LRT) network using real world scenario data. The results reveal new insights on how the existing operational settings could be improved. The present study contributes to urban transit network service planning with advanced computational techniques.

Exploring the resilience assessment framework of urban road network for sustainable cities

Urban space for new transportation facilities cannot meet the increasing traffic demand. Afterward, scholars gradually increased attention to the resilience evaluation of urban road networks. Therefore, we proposed a resilience assessment framework of the urban road networks, including the resilience performance index, the robustness index, and the recovery index. Then we simulated the cascading failure based on a nonlinear load-capacity model with two capacity control parameters: α and β. Results show that the intersection-based attack has the most significant impact on resilience, and resilience is positively correlated with the node degree of the attacked intersection. The increase of α and β could enhance the resilience, and the urban road network achieves the best resilience performance when α=0.3,β=0.5. Compared with the deliberate attack strategy, the resilience performance under the random attack strategy is more robust. This research can provide the foundation for optimizing urban road networks and multi-mode urban public transit networks.