Modelling public transport on‐board congestion: comparing schedule‐based and agent‐based assignment approaches and their implications

Transit systems are subject to congestion that influences system performance and level of service. The evaluation of measures to relieve congestion requires models that can capture their network effects and passengers' adaptation. In particular, on‐board congestion leads to an increase of crowding discomfort and denied boarding and a decrease in service reliability. This study performs a systematic comparison of alternative approaches to modelling on‐board congestion in transit networks. In particular, the congestion‐related functionalities of a schedule‐based model and an agent‐based transit assignment model are investigated, by comparing VISUM and BusMezzo, respectively. The theoretical background, modelling principles and implementation details of the alternative models are examined and demonstrated by testing various operational scenarios for an example network. The results suggest that differences in modelling passenger arrival process, choice‐set generation and route choice model yield systematically different passenger loads. The schedule‐based model is insensitive to a uniform increase in demand or decrease in capacity when caused by either vehicle capacity or service frequency reduction. In contrast, nominal travel times increase in the agent‐based model as demand increases or capacity decreases. The marginal increase in travel time increases as the network becomes more saturated. Whilst none of the existing models capture the full range of congestion effects and related behavioural responses, existing models can support different planning decisions. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of crowding on public transit user travel behavior in a large-scale public transportation system through modeling daily variations

In this paper, the crowding effect in a transit vehicle is modeled in a time-expanded network that considers the daily variation in passenger flows. The study models the daily variation of in-vehicle crowding in a real large-scale transit system. A transit assignment for this real network is modeled and implemented by constructing a crowding cost function that follows the valuation of crowding and by using the reliable shortest path finding method. The direct application of the crowding model to a real network for the Utah Transit Authority indicates that crowd modeling with multi-user classes could influence public transportation system planning and affect the revenues of transit agencies. Moreover, the addition of the disutility factor, crowding, does not always appear to cause an increase in disutility for transit users.     

A bi‐level programming approach — Optimal transit fare under line capacity constraints

The fare of a transit line is one of the important decision variables for transit network design. It has been advocated as an efficient means of coordinating the transit passenger flows and of alleviating congestion in the transit network. This paper shows how transit fare can be optimized so as to balance the passenger flow on the transit network and to reduce the overload delays of passengers at transit stops. A bi‐level programming method is developed to optimize the transit fare under line capacity constraints. The upper‐level problem seeks to minimize the total network travel time, while the lower‐level problem is a stochastic user equilibrium transit assignment model with line capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Transit assignment under crowded conditions

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

Incorporating crowding into the San Francisco activity-based travel model

Information produced by travel demand models plays a large role decision making in many metropolitan areas, and San Francisco is no exception. Being a transit first city, one of the most common uses for San Francisco??s travel model SF-CHAMP is to analyze transit demand under various circumstances. SF-CHAMP v 4.1 (Harold) is able to capture the effects of several aspects of transit provision including headways, stop placement, and travel time. However, unlike how auto level of service in a user equilibrium traffic assignment is responsive to roadway capacity, SF-CHAMP Harold is unable to capture any benefit related to capacity expansion, crowding??s effect on travel time nor or any of the real-life true capacity limitations. The failure to represent these elements of transit travel has led to significant discrepancies between model estimates and actual ridership. Additionally it does not allow decision-makers to test the effects of policies or investments that increase the capacity of a given transit service. This paper presents the framework adopted into a more recent version of SF-CHAMP (Fury) to represent transit capacity and crowding within the constraints of our current modeling software.     

集聚经济视角下轨道交通投资对城市系统均衡的影响

随着城镇化进程加快,城市规模增加所带来的集聚效应和交通拥堵等负外部性之间的矛盾越来越突出,优化城市交通基础设施建设是缓解该矛盾的重要举措。本文同时考虑了集聚经济和交通拥挤两种外部性,构建并求解了一个两区域城市空间结构模型,分三种情况探究了轨道交通的投资引入和道路容量的优化对城市规模和城市空间结构均衡的影响。结果表明,轨道交通的投资引入能够增加城市人口规模和社会福利,使城市结构更加紧凑。但是,随着集聚经济水平的提高,城市规划者应逐步完善公交配套设施,以降低公交拥挤成本,提高公交出行分担率;还应制定相应的福利政策,避免由于个体效用下降而导致人口流出。     

Valuing crowding in public transport: Implications for cost-benefit analysis

This paper investigates the valuation of crowding in public transport trips and its implications in demand estimation and cost-benefit analysis. We use a choice-based stated preference survey where crowding levels are represented by means of specially designed pictures, and use these data to estimate flexible discrete choice models. We assume that the disutility associated with travelling under crowded conditions is proportional to travel time. Our results are consistent with and extend previous findings in the literature: passenger density has a significant effect on the utility of travelling by public transport; in fact, the marginal disutility of travel time in a crowded vehicle (6 standing-passengers/m²) is 2.5 times higher than in a vehicle with available seats. We also compare the effects of different policies for improving bus operations, and the effect of adding crowding valuation in cost-benefit analysis. In doing that, we endogenise the crowding level as the result of the equilibrium between demand and supplied bus capacity. Our results indicate that important benefits may be accrued from policies designed to reduce crowding, and that ignoring crowding effects significantly overestimate the bus travel demand the benefits associated with pure travel time reductions.     

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.     

Special issue: Importance of public transport

The transport demand in most major cities around the world can only be met with a high‐quality public transport system. The requirements on bus, rail, underground and tram systems are manifold with reliability and efficiency as the key factors. The service operating hours and the size of the network are often extended in order to serve the needs better. Further, most metropolitan areas are trying to provide more incentives for citizens to leave the car at home and use the local transit systems instead. The reasons are well known. Not only does a public transport system only make economical sense if it is well used, but most urban areas with a high car‐dependency face at least three major problems; safety, congestion, and pollution (noise and air pollution, land separation, etc.). It is generally recognised that to decrease car usage and to increase public transport usage a stick & carrot approach is needed. The London congestion‐charging scheme is an example since all revenues collected by the scheme are put into the improvement of bus and underground services.     

基于复杂网络的兰州市公交网络分析

城市交通系统是一个动态的、自组织的、开放的复杂巨系统,交通拥挤等问题严重制约着城市有序、快速、高效地发展。文章基于复杂网络理论,以兰州市为例,运用Pajek软件和L空间法,构造了兰州市公交站点网络,并对公交网络的度、累积度和聚类系数进行了分析。结果表明,兰州市公交站点网络具有无标度特性。     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Including passengers’ response to crowding in the Dutch national train passenger assignment model

Transit passengers’ response to crowded conditions has been studied empirically, yet is limitedly included in transport models currently used in the design of policy and infrastructure investments. This has consequences for the practical applicability of these models in studies on, for instance, timetabling, train capacity management strategies, project appraisal, and passenger satisfaction. Here we propose four methods to include the effect of crowding, based on existing studies on passengers’ perception and response as well as often-used crowding indicators. These four alternative methods are implemented in the train passenger assignment procedure of the Dutch national transport model, and evaluated with respect to their impacts on the model results for the Dutch railway network. The four methods relate to four different ways in which an additive trip penalty and/or time-multiplier can be incorporated in the train utility function for different travel purposes, to capture the disutility of crowding as measured by the load factor. The analyses of the test case favor the hybrid method using both a boarding penalty (capturing seat availability upon boarding) and a time-multiplier (capturing physical comfort and safety throughout the trip). This method produces consistent results, while the additional computational effort that it imposes is acceptable. Further empirical underpinning is needed to conclusively show which of these methods best captures passengers’ response behavior quantitatively (for different travel purposes and conditions).     

Integrating congestion pricing,transit subsidies and mode choice

We model and analyze optimal (welfare maximizing) prices and design of transport services in a bimodal context. Car congestion and transit design are simultaneously introduced and consumers choose based on the full price they perceive. The optimization variables are the congestion toll, the transit fare (and hence the level of subsidies) and transit frequency. We obtain six main results: (i) the optimal car-transit split is generally different from the total cost minimizing one; (ii) optimal congestion and transit price are interdependent and have an optimal frequency attached; (iii) the optimal money price difference together with the optimal frequency yield the optimal modal split; (iv) if this modal split is used in traditional stand-alone formulations – where each mode is priced independently–resulting congestion tolls and transit subsidies and fares are consistent with the optimal money price difference; (v) self-financing of the transport sector is feasible; and (vi) investment in car infrastructure induces an increase in generalized cost for all public transport users.     

Calibrating a transit assignment model using smart card data in a large-scale multi-modal transit network

This paper describes a practical automated procedure to calibrate and validate a transit assignment model. An optimization method based on particle swarm algorithm is adopted to minimize a defined error term. This error term which is based on the percentage of root mean square error and the mean absolute percent error encompasses deviation of model outputs from observations considering both segment level as well as the mode level and can be applied to a large scale network. This study is based on the frequency-based assignment model using the concept of optimal strategy while any transit assignment model can be used in the proposed methodological framework. Lastly, the model is validated using another weekday data. The proposed methodology uses automatic fare collection (AFC) data to estimate the origin–destination matrix. This study combines data from three sources: the general transit feed specification, AFC, and a strategic transport model from a large-scale multimodal public transport network. The South-East Queensland (SEQ) network in Australia is used as a case study. The AFC system in SEQ has voluminous and high quality data on passenger boardings and alightings across bus, rail and ferry modes. The results indicate that the proposed procedure can successfully develop a multi-modal transit assignment model at a large scale. Higher dispersions are seen for the bus mode, in contrast to rail and ferry modes. Furthermore, a comparison is made between the strategies used by passengers and the generated strategies by the model between each origin and destination to get more insights about the detailed behaviour of the model. Overall, the analysis indicates that the AFC data is a valuable and rich source in calibrating and validating a transit assignment model.

     

A capacity restraint transit assignment with elastic line frequency

This paper proposes a new formulation for the capacity restraint transit assignment problem with elastic line frequency, in which the line frequency is related to the passenger flows on transit lines. A stochastic user equilibrium transit assignment model with congestion and elastic line frequency is proposed and the equivalent mathematical programming problem is also formulated. Since the passenger waiting time and the line capacity are dependent on the line frequency, a fixed point problem with respect to the line frequency is devised accordingly. The existence of the fixed point problem has been proved. A solution algorithm for the proposed model is presented. Finally, a numerical example is used to illustrate the application of the proposed model and solution algorithm.     

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.     

Should subsidies to urban passenger transport be increased? A spatial CGE analysis for a German metropolitan area

In many countries passenger transport is significantly subsidized in a variety of ways for various reasons. The objective of this paper is to examine efficiency, distributional, environmental (CO₂ emissions) and spatial effects of increasing different kinds of passenger transport subsidies discriminating between household types, travel purposes and travel modes. The effects are calculated by applying a numerical spatial general equilibrium approach calibrated to an average German metropolitan area. In extension to most studies focusing on only one kind of subsidy, we compare the effects of different transport subsidies within the same unified framework that allows to account for two features not yet considered simultaneously in studies on transport subsidies: endogenous labor supply and location decisions. Furthermore, congestion, travel mode choice, travel related CO₂ emissions and institutional details regarding the tax system in Germany are taken into account. The results suggest that optimal subsidy levels are either small or even zero. While subsidizing public transport is welfare enhancing, subsidies to urban road traffic reduce aggregate urban welfare. Concerning the latter it is shown that making investments in urban road infrastructure capacity or reducing gasoline taxes may even be harmful to residents using predominantly automobile. In contrast, pure commuting subsidies hardly affect aggregate urban welfare, but distributional effects are substantial. All policies cause suburbanization of city residents and (except for subsidizing public transport) contribute to urban sprawl by raising the spatial imbalance of residences and jobs but the effect is relatively small. In addition, the policies induce a very differentiated pattern regarding distributional effects, benefits of landowners and environmental effects.     

Traffic and emissions impact of congestion charging in the central Beijing urban area: A simulation analysis

Congestion charging is being considered as a potential measure to address the issue of substantially increased traffic congestion and vehicle emissions in Beijing. This study assessed the impact of congestion charging on traffic and emissions in Beijing using macroscopic traffic simulation and vehicle emissions calculation. Multiple testing scenarios were developed with assumptions in different charging zone sizes, public transit service levels and charging methods. Our analysis results showed that congestion charging in Beijing may increase public transit use by approximately 13%, potentially reduce CO and HC emissions by 60–70%, and reduce NOx emissions by 35–45% within the charging zone. However, congestion charging may also result in increased travel activities and emissions outside of the charging zone and a slight increase in emissions for the entire urban area. The size of charging zone, charging method, and charging rate are key factors that directly influence the impact of congestion charging; improved public transit service needs to be considered as a complementary approach with congestion charging. This study is used by Beijing Transportation Environment and Energy Center (BTEC) as reference to support the development of Beijing’s congestion charging policy and regulation.     

The distribution of crowding costs in public transport: New evidence from Paris

Whilst congestion in automobile traffic increases trip durations, this is often not the case in rail-based public transport where congestion rather leads to in-vehicle crowding, often neglected in empirical studies. Using original survey data from Paris, this article assesses the distribution of comfort costs of congestion in public transport. Estimating willingness to pay for less crowded trips at different levels of in-vehicle passenger density we cannot reject a simple linear relationship between crowding costs and density. We apply our results to the cost-benefit analysis of a recent Parisian public transport project.     

Impact of congestion charging on the transit market: An inter-modal equilibrium model

An inter-modal equilibrium model links an urban road network subject to a congestion charge to a parallel urban transit market, with a view to finding the optimum congestion charge consistent with the commercial decisions of the transit operator(s). A congestion charge is set to maximise social surplus. Travel behaviour is assumed to conform to elastic-demand user equilibrium traffic assignment. The transit market is assumed to be either a profit maximising monopoly or a profit maximising duopoly competing non-cooperatively. The operator(s) set the fares to maximise profits and the supply of transit services are determined by the resulting demand. The problem has been formulated as a bi-level programme with the determination of the congestion charge on the upper level and the setting of transit fares on the lower level. In the case of non-cooperating operators, the Bertrand–Nash equilibrium fares are sought. The results of the model are analysed for a small example based loosely on Edinburgh. This reveals the importance of competition in the transit market for the trade off between the government, the transit provider(s) and the travellers.