Joint modeling of schedule- and frequency-based services in public transport assignment models

Public transport networks today are getting increasingly complex with many lines and possibilities to go from origin to destination. When passengers make their route choice in a public transport network they cannot depart at the minute they want, but must wait until the first departure on the considered line. But how do passengers plan their route if they have a combination of high frequent and low frequent services under the assumption that passengers do not consult the timetable for high frequent services? This paper describes a framework to include both schedule- and frequency-based services in a joint model. Such networks are found in most major cities and especially in the greater Copenhagen area where there is a mix of frequency-based services such as A-busses and the metro and schedule-based services as the S-train and local bus lines. Four different transfer types are identified when transferring between schedule- and frequency-based services. These include a type where the passenger transfers from a frequency-based to a schedule-based line. In this case the passenger has a probability to reach the first departure on the schedule- based line, but can in some cases also miss the first departure and must wait for the next departure. A choice set generation method is developed using the event dominance principle to exclude alternatives which are above a certain threshold. This gives a choice set which is used in a discrete choice model (MNL). On this basis, it is possible to distribute the flow across the different alternatives. Two example cases are used to show the methodology: DTU to Copenhagen Airport and DTU to Brønshøj. The results indicate that there the framework can handle the two types off lines. It is found that the desired departure time, parameters in the utility function and the choice of threshold is crucial to find the correct choice set and distribution of flow across the alternatives. But there is also found improvement points in the choice set generation technique, but especially the discrete choice modelling should be investigated further to include that passengers can take decisions en route

Strategy-based dynamic assignment in transit networks with passenger queues

This thesis develops a mathematical framework to solve the problem of dynamic assignment in densely connected public transport (or transit – the two words are interchangeably used) networks where users do not time their arrival at a stop with the lines’ timetable (if any is published). In the literature there is a fairly broad agreement that, in such transport systems, passengers would not select the single best itinerary available, but would choose a travel strategy, namely a bundle of partially overlapping itineraries diverging at stops along different lines. Then, they would follow a specific path depending on what line arrives first at the stop. From a graph-theory point of view, this route-choice behaviour is modelled as the search for the shortest hyperpath (namely an acyclic sub-graph which includes partially overlapping single paths) to the destination in the hypergraph that describes the transit network. In this thesis, the hyperpath paradigm is extended to model route choice in a dynamic context, where users might be prevented from boarding the lines of their choice because of capacity constraints. More specifically, if the supplied capacity is insufficient to accommodate the travel demand, it is assumed that passenger congestion leads to the formation of passenger First In, First Out (FIFO) queues at stops and that, in the context of commuting trips, passengers have a good estimate of the expected number of vehicle passages of the same line that they must let go before being able to board. By embedding the proposed demand model in a fully dynamic assignment model for transit networks, this thesis also fills in the gap currently existing in the realm of strategy-based transit assignment, where – so far – models that employ the FIFO queuing mechanism have proved to be very complex, and a theoretical framework for reproducing the dynamic build-up and dissipation of queues is still missing.Open Acces

Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0

A heuristic method for a congested capacitated transit assignment model with strategies

This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algo- rithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtain- ing capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested net- works. A set of computational tests on realistic small- and large-scale transit networks un- der various congestion levels are reported, and the characteristics of the proposed method are analyzed.Peer ReviewedPostprint (author's final draft

Analyzing Passenger Incidence Behavior in Heterogeneous Transit Services Using Smartcard Data and Schedule-Based Assignment

Passenger incidence (station arrival) behavior has been studied primarily to understand how changes to a transit service will affect passenger waiting times. The impact of one intervention (e.g., increasing frequency) could be overestimated when compared with another (e.g., improving reliability), depending on the assumption of incidence behavior. Understanding passenger incidence allows management decisions to be based on realistic behavioral assumptions. Earlier studies on passenger incidence chose their data samples from stations with a single service pattern such that the linking of passengers to services was straightforward. This choice of data samples simplifies the analysis but heavily limits the stations that can be studied. In any moderately complex network, many stations may have more than one service pattern. This limitation prevents the method from being systematically applied to the whole network and constrains its use in practice. This paper considers incidence behavior in stations with heterogeneous services and proposes a method for estimating incidence headway and waiting time by integrating disaggregate smartcard data with published timetables using schedule-based assignment. This method is applied to stations in the entire London Overground to demonstrate its practicality; incidence behavior varies across the network and across times of day and reflects headways and reliability. Incidence is much less timetable-dependent on the North London Line than on the other lines because of shorter headways and poorer reliability. Where incidence is timetable-dependent, passengers reduce their mean scheduled waiting time by more than 3 min compared with random incidence

Passengers’ choices in multimodal public transport systems : A study of revealed behaviour and measurement methods

The concept of individual choice is a fundamental aspect when explaining and anticipating behavioural interactions with, and responses to, static and dynamic travel conditions in public transport (PT) systems. However, the empirical rounding of existing models used for forecasting travel demand, which itself is a result of a multitude of individual choices, is often insufficient in terms of detail and accuracy. This thesis explores three aspects, or themes, of PT trips – waiting times, general door-to-door path preferences, with a special emphasis on access and egress trip legs, and service reliability – in order to increase knowledge about how PT passengers interact with PT systems. Using detailed spatiotemporal empirical data from a dedicated survey app and PT fare card transactions, possible cross-sectional relationships between travel conditions and waiting times are analysed, where degrees of mental effort are gauged by an information acquisition proxy. Preferences for complete door-todoorpaths are examined by estimation of full path choice models. Finally, longitudinal effects of changing service reliability are analysed using a biennial panel data approach. The constituent studies conclude that there are otherexplanatory factors than headway that explain waiting times on first boarding stops of PT trips and that possession of knowledge of exact departure times reduces mean waiting times. However, this information factor is not evidentin full path choice, where time and effort-related preferences dominate with a consistent individual preference factor. Finally, a statistically significant on-average adaption to changing service reliability is individual-specific andnon-symmetrical depending on the direction of reliability change, where a relatively large portion of the affected individuals do not appear to respond to small-scale perturbations of reliability while others do, all other thingsbeing equal

Reliable routing in schedule-based transit networks

textA framework is proposed for determining the least expected cost path in a schedule-based time-expanded public transit network where travel times, and thus bus arrival and departure times at stops, are stochastic. Transfer reliability is incorporated in a label-correcting algorithm with a penalty function for the expected waiting time when transferring that reflects the likelihood of making a successful transfer. The algorithm is implemented in transit assignment on an Austin, Texas test network, using actual bus arrival and departure time distributions from vehicle location data. Assignment results are compared with those of a deterministic shortest path based on the schedule and from a calibrated transit assignment model. Simulations of the network and passenger paths are also conducted to evaluate the overall path reliability. The reliable shortest path algorithm is found to penalize transferring and provide paths with improved transfer and overall reliability. The proposed model is realistic, incorporating reliability measures from vehicle location data, and practical, given the efficient shortest path approach and application to transit assignment.Civil, Architectural, and Environmental Engineerin

A model of bus bunching under reliability-based passenger arrival patterns.

If bus service departure times are not completely unknown to the passengers, non-uniform passenger arrival patterns can be expected. We propose that passengers decide their arrival time at stops based on a continuous logit model that considers the risk of missing services. Expected passenger waiting times are derived in a bus system that allows also for overtaking between bus services. We then propose an algorithm to derive the dwell time of subsequent buses serving a stop in order to illustrate when bus bunching might occur. We show that non-uniform arrival patterns can significantly influence the bus bunching process. With case studies we find that, even without exogenous delay, bunching can arise when the boarding rate is insufficient given the level of overall demand. Further, in case of exogenous delay, non-uniform arrivals can either worsen or improve the bunching conditions, depending on the level of delay. We conclude that therefore such effects should be considered when service control measures are discussed

Advanced pricing and rationing policies for large scale multimodal networks

The applying of simplified schemes, such as cordon pricing, as second-best solution to the toll network design problem is investigated here in the context of multiclass traffic assignment on multimodal networks. To this end a suitable equilibrium model has been developed, together with an efficient algorithm capable of simulating large scale networks in quite reasonable computer time. This model implements the theoretical framework proposed in a previous work on the toll optimization problem, where the validity of marginal cost pricing for the context at hand is stated. Application of the model to the real case of Rome shows us, not only that on multimodal networks a relevant share (up to 20%) of the maximum improvements in terms of social welfare achievable with marginal cost pricing can in fact be obtained through cordon pricing, but also that in practical terms rationing is a valid alternative to pricing, thus getting around some of the relevant questions (theoretical, technical, social) the latter raises. As a result we propose a practical method to analyze advanced pricing and rationing policies differentiated for user categories, which enables us to compare alternative operative solutions with an upper bound on social welfare based on a solid theoretical background. (c) 2005 Elsevier Ltd. All rights reserved

Modelling route choice behaviour with incomplete data: an application to the London Underground

This thesis develops a modelling framework for learning route choice behaviour of travellers on an underground railway system, with a major emphasis on the use of smart-card data. The motivation for this topic comes from two respects. On the one hand, in a metropolis, particularly those furnished with massive underground services (e.g. London, Beijing and Paris), severe passenger-traffic congestion may often occur, especially during rush hours. In order to support the public transport managers in taking actions that are more effective in smoothening the passenger flows, there is bound to be a need for better understanding of the passengers’ routing behaviour when they are travelling on such public transport networks. On the other hand, a wealth of travel data is nowadays readily obtainable, largely owing to the widespread implementation of automatic fare collection systems (AFC) as well as popularity of smart cards on the public transport. Nevertheless, a core limitation of such data is that the actual route-choice decisions taken by the passengers might not be available, especially when their journeys involve alternative routes and/or within-station interchanges. Mostly, the AFC systems (e.g. the Oyster system in London) record only data of passengers’ entry and exit, rather than their route choices. We are thus interested in whether it is possible to analytically infer the route-choice information based on the ‘incomplete’ data. Within the scope of this thesis, passengers’ single journeys are investigated on a station basis, where sufficiently large samples of the smart-card users’ travel records can be gained. With their journey time data being modelled by simple finite mixture distributions, Bayesian inference is applied to estimate posterior probabilities for each route that a given passenger might have chosen from all possible alternatives. We learn the route-choice probabilities of every individual passenger in any given sample, conditional on an observation of the passenger’s journey time. Further to this, the estimated posterior probabilities are also updated for each passenger, by taking into account additional information including their entry times as well as the timetables. To understand passengers’ actual route choice behaviour, we then make use of adapted discrete choice model, replacing the conventional dependent variable of actual route choices by the posterior choice probabilities for different possible outcomes. This proposed methodology is illustrated with seven case studies based in the area of central zone of the London Underground network, by using the Oyster smart-card data. Two standard mixture models, i.e. the probability distributions of Gaussian and log-normal mixtures, are tested, respectively. The outcome demonstrates a good performance of the mixture models. Moreover, relying on the updated choice probabilities in the estimation of a multinomial logit latent choice model, we show that we could estimate meaningful relative sensitivities to the travel times of different journey segments. This approach thus allows us to gain an insight into passengers’ route choice preferences even in the absence of observations of their actual chosen routes