Schedule-based transit assignment model with vehicle capacity and seat availability

In this paper, we propose a new schedule-based equilibrium transit assignment model that differentiates the discomfort level experienced by sitting and standing passengers. The notion of seat allocation has not been considered explicitly and analytically in previous schedule-based frameworks. The model assumes that passengers use strategies when traveling from their origin to their destination. When loading a vehicle, standing on-board passengers continuing to the next station have priority to get available seats and waiting passengers are loaded on a First-Come-First-Serve (FCFS) principle. The stimulus of a standing passenger to sit increases with his/her remaining journey length and time already spent on-board. When a vehicle is full, passengers unable to board must wait for the next vehicle to arrive. The equilibrium conditions can be stated as a variational inequality involving a vector-valued function of expected strategy costs. To find a solution, we adopt the method of successive averages (MSA) that generates strategies during each iteration by solving a dynamic program. Numerical results are also reported to show the effects of our model on the travel strategies and departure time choices of passengers.     

Stochastic transit equilibrium

We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research.     

A stochastic optimization model for transit network timetable design to mitigate the randomness of traveling time by adding slack time

Transit network timetabling aims at determining the departure time of each trip of all lines in order to facilitate passengers transferring either to or from a bus. In this paper, we consider a bus timetabling problem with stochastic travel times (BTP-STT). Slack time is added into timetable to mitigate the randomness in bus travel times. We then develop a stochastic integer programming model for the BTP-STT to minimize the total waiting time cost for three types of passengers (i.e., transferring passengers, boarding passengers and through passengers). The mathematical properties of the model are characterized. Due to its computational complexity, a genetic algorithm with local search (GALS) is designed to solve our proposed model (OPM). The numerical results based on a small bus network show that the timetable obtained from OPM reduces the total waiting time cost by an average of 9.5%, when it is tested in different scenarios. OPM is relatively effective if the ratio of the number of through passengers to the number of transferring passengers is not larger than a threshold (e.g., 10 in our case). In addition, we test different scale instances randomly generated in a practical setting to further verify the effectiveness of OPM and GALS. We also find that adding slack time into timetable greatly benefits transferring passengers by reducing the rate of transferring failure.     

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.     

Water transit and excess travel: discrete choice modelling of bus and ferry trips in Brisbane,Australia

Recent investment in urban ferry transport has created interest in what value such systems provide in a public transport network. In some cases, ferry services are in direct competition with other land-based transport, and despite often longer travel times passengers still choose water transport. This paper seeks to identify a premium attached to urban water transit through an identification of excess travel patterns. A one-month sample of smart card transaction data for Brisbane, Australia, was used to compare bus and ferry origin–destination pairs between a selected suburban location and the central business district. Logistic regression of the data found that ferry travel tended towards longer travel times (OR?=?2.282), suggesting passengers do derive positive utility from ferry journeys. The research suggests the further need to incorporate non-traditional measures other than travel time for deciding the value of water transit systems.     

A utility-based travel impedance measure for public transit network accessibility

A utility-based travel impedance measure is developed for public transit modes that is capable of capturing the passengers’ behaviour and their subjective perceptions of impedance when travelling in the transit networks. The proposed measure is time-dependent and it estimates the realisation of the travel impedance by the community of passengers for travelling between an origin–destination (OD) pair.The main advantage of the developed measure, as compared to the existing transit impedance measures, relates to its capability in capturing the diversity benefit that the transit systems may offer the society of travellers with different traveling preferences. To clarify the necessity of such capability, we demonstrate the randomness (subjectivity) of travel impedance perceived by transit passengers, through evidence from the observed path choices made in the transit network of the greater Brisbane metropolitan region in Australia.The proposed impedance measure is basically a nested logit “logsum” composition over a generated set of reasonable path options whose systematic utilities are evaluated based on a discrete choice model previously developed and calibrated for the greater Brisbane transit passengers. As a case study, the proposed impedance measure is calculated for all the origin blocks in the Brisbane area, during the morning commutes to the Central Business District (CBD). The results are presented and discussed, and intuitive and important advantages are demonstrated for the proposed measure.     

Mind the map! The impact of transit maps on path choice in public transit

This paper investigates the impact of schematic transit maps on passengers’ travel decisions. It does two things: First, it proposes an analysis framework that defines four types of information delivered from a transit map: distortion, restoration, codification, and cognition. It then considers the potential impact of this information on three types of travel decisions: location, mode, and path choices.¹ Second, it conducts an empirical analysis to explore the impact of the famous London tube map on passengers’ path choice in the London Underground (LUL). Using data collected by LUL from 1998 to 2005, the paper develops a path choice model and compares the influence between the distorted tube map (map distance) and reality (travel time) on passengers’ path choice behavior. Results show that the elasticity of the map distance is twice that of the travel time, which suggests that passengers often trust the tube map more than their own travel experience on deciding the “best” travel path. This is true even for the most experienced passengers using the system. The codification of transfer connections on the tube map, either as a simple dot or as an extended link, could affect passengers’ transfer decisions. The implications to transit operation and planning, such as trip assignments, overcrowding mitigation, and the deployment of Advanced Transit Information System (ATIS), are also discussed.     

Waiting time perceptions at transit stops and stations: Effects of basic amenities,gender, and security

Waiting time in transit travel is often perceived negatively and high-amenity stops and stations are becoming increasingly popular as strategies for mitigating transit riders’ aversion to waiting. However, beyond recent evidence that realtime transit arrival information reduces perceived waiting time, there is limited empirical evidence as to which other specific station and stop amenities can effectively influence user perceptions of waiting time. To address this knowledge gap, the authors conducted a passenger survey and video-recorded waiting passengers at different types of transit stops and stations to investigate differences between survey-reported waiting time and video-recorded actual waiting time. Results from the survey and video observations show that the reported wait time on average is about 1.21 times longer than the observed wait time. Regression analysis was employed to explain the variation in riders’ reported waiting time as a function of their objectively observed waiting time, as well as station and stop amenities, weather, time of the day, personal demographics, and trip characteristics. Based on the regression results, most waits at stops with no amenities are perceived at least 1.3 times as long as they actually are. Basic amenities including benches and shelters significantly reduce perceived waiting times. Women waiting for more than 10 min in perceived insecure surroundings report waits as dramatically longer than they really are, and longer than do men in the same situation. The authors recommend a focus on providing basic amenities at stations and stops as broadly as possible in transit systems, and a particular focus on stops on low-frequency routes and in less safe areas for security measures.     

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.     

An improved headway-based holding strategy for bus transit

Abstract

This paper presents an improved headway-based holding strategy integrating bus transit travel and dwelling time prediction. A support vector machine-based (SVM) model is developed to predict the baseline travel and dwell times of buses based on recent data. In order to reduce prediction errors, an adaptive algorithm is used together with real-time bus operational information and estimated baseline times from SVM models. The objective of the improved holding strategy is to minimize the total waiting times of passengers at the current stop and at successive stops. Considering the time-varying features of bus running, a ‘forgetting factor’ is introduced to weight the most recent data and reduce the disturbance from unexpected incidents. Finally, the improved holding strategy proposed in this study is illustrated using the microscopic simulation model Paramics and some conclusions are drawn.     

A model of stoppings on urban bus routes

The amount of time required to pick up and discharge passengers is an important issue in the planning and modeling of urban bus systems. Several past studies have employed models of this component of bus travel time which are based, in part, on a model of the number of stoppings the bus makes to pick up or discharge passengers. Most past versions of this model have assumed that expected demand does not vary from stop to stop or from trip to trip, but that the number of passengers demanding service at any given stop during any given trip follows a Poisson distribution. An alternative model is derived, based on the assumption that expected demand varies among stops and times of day but is fixed from day to day at any given stop and time of day. Boarding and alighting survey data are used to verify that the “average-demand” Poisson model consistently overestimates the number of stoppings and to calibrate an approximate version of the alternative model. A stop-spacing optimization model previously developed by Kikuchi and Vuchic is reevaluated using the alternative stopping model in place of the average demand model used in the original version. The results are found to be considerably different, thus indicating that transit route optimization models are sensitive to the way in which stopping processes are modeled.     

A practical method to estimate the benefits of improved road network reliability: an application to departing air passengers

This paper develops and applies a practical method to estimate the benefits of improved reliability of road networks. We present a general methodology to estimate the scheduling costs due to travel time variability for car travel. In contrast to existing practical methods, we explicitly consider the effect of travel time variability on departure time choices. We focus on situations when only mean delays are known, which is typically the case when standard transport models are used. We first show how travel time variability can be predicted from mean delays. We then estimate the scheduling costs of travellers, taking into account their optimal departure time choice given the estimated travel time variability. We illustrate the methodology for air passengers traveling by car to Amsterdam Schiphol Airport. We find that on average planned improvements in network reliability only lead to a small reduction in access costs per trip in absolute terms, mainly because most air passengers drive to the airport outside peak hours, when travel time variability tends to be low. However, in relative terms the reduction in access costs due to the improvements in network reliability is substantial. In our case we find that for every 1 Euro reduction in travel time costs, there is an additional cost reduction of 0.7 Euro due to lower travel time variability, and hence lower scheduling costs. Ignoring the benefits from improved reliability may therefore lead to a severe underestimation of the total benefits of infrastructure improvements.     

Optimal coordination of public-transit vehicles using operational tactics examined by simulation

This work focuses on improving transit-service reliability by optimally reducing the transfer time required in the operations of transit networks. Service reliability of public-transit operations is receiving increased attention as agencies are faced with immediate problems of proving credible service while attempting to reduce operating cost. Unreliable service has also been cited as the major deterrent to existing and potential passengers. Due to the fact that most of the public transit attributes are stochastic: travel time, dwell time, demand, etc., the passenger is likely to experience unplanned waiting times and ride times. One of the main components of service reliability is the use of transfers. Transfers have the advantages of reducing operational costs and introducing more flexible and efficient route planning. However its main drawback is the inconvenience of traveling multi-legged trips. This work introduces synchronized (timed) time-tables to diminish the waiting time caused by transfers. Their use, however, suffers from uncertainty about the simultaneous arrival of two (or more) vehicles at an existing stop. In order to alleviate the uncertainty of simultaneous arrivals, operational tactics such as hold, skip stop and short-turn can be deployed considering the positive and negative effects, of each tactic, on the total travel time. A dynamic programming model was developed for minimizing the total travel time resulting with a set of preferred tactics to be deployed. This work describes the optimization model using simulation for validation of the results attained. The results confirm the benefits of the model with 10% reduction of total travel time and more than 200% increase of direct transfers (transfers in which both vehicles arrive simultaneously to the transfer point).     

An activity-based approach for scheduling multimodal transit services

This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.     

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.     

The Share-a-Ride problem with stochastic travel times and stochastic delivery locations

We consider two stochastic variants of the Share-a-Ride problem: one with stochastic travel times and one with stochastic delivery locations. Both variants are formulated as a two-stage stochastic programming model with recourse. The objective is to maximize the expected profit of serving a set of passengers and parcels using a set of homogeneous vehicles. Our solution methodology integrates an adaptive large neighborhood search heuristic and three sampling strategies for the scenario generation (fixed sample size sampling, sample average approximation, and sequential sampling procedure). A computational study is carried out to compare the proposed approaches. The results show that the convergence rate depends on the source of stochasticity in the problem: stochastic delivery locations converge faster than stochastic travel times according to the numerical test. The sample average approximation and the sequential sampling procedure show a similar performance. The performance of the fixed sample size sampling is better compared to the other two approaches. The results suggest that the stochastic information is valuable in real-life and can dramatically improve the performance of a taxi sharing system, compared to deterministic solutions.     

Airline competition and network structure

This paper studies airline networks and their welfare implications in an unregulated environment. Competing airlines may adopt either fully-connected (FC) or hub-and-spoke (HS) network structures; and passengers exhibiting low brand loyalty to their preferred carrier choose an outside option to travel so that markets are partially served by airlines. In this context, carriers adopt hubbing strategies when costs are sufficiently low, and asymmetric equilibria where one carrier chooses a FC strategy and the other chooses a HS strategy may arise. Quite interestingly, flight frequency can become excessive under HS network configurations.     

Large-scale transit market segmentation with spatial-behavioural features

Transit market segmentation enables transit providers to comprehend the commonalities and heterogeneities among different groups of passengers, so that they can cater for individual transit riders’ mobility needs. The problem has recently been attracting a great interest with the proliferation of automated data collection systems such as Smart Card Automated Fare Collection (AFC), which allow researchers to observe individual travel behaviours over a long time period. However, there is a need for an integrated market segmentation method that incorporating both spatial and behavioural features of individual transit passengers. This algorithm also needs to be efficient for large-scale implementation. This paper proposes a new algorithm named Spatial Affinity Propagation (SAP) based on the classical Affinity Propagation algorithm (AP) to enable large-scale spatial transit market segmentation with spatial-behavioural features. SAP segments transit passengers using spatial geodetic coordinates, where passengers from the same segment are located within immediate walking distance; and using behavioural features mined from AFC data. The comparison with AP and popular algorithms in literature shows that SAP provides nearly as good clustering performance as AP while being 52% more efficient in computation time. This efficient framework would enable transit operators to leverage the availability of AFC data to understand the commonalities and heterogeneities among different groups of passengers.     

Transfer demand prediction for timed transfer coordination in public transport operational control

Timed transfer coordination in public transit reduces passenger transfer time by providing seamless interconnected transfers. The problem arises when a Receiving Vehicle (RV) arrives to the transfer stop before a Feeding Vehicle (FV) carrying transferring passengers. Timed transfer coordination in operational control dynamically decides whether a RV is held at the transfer stop to allow transfers, or departs as scheduled. While transfer demand is essential for implementing timed transfer coordination, this variable is generally not available in public transit because of the lack of passenger transfer plans. The problem of acquiring this variable in real‐time has also received limited attention in the related literature. This paper proposes a new method to dynamically predict the transfer demand. We anticipate the transferring probability from each individual passenger by examining historical travel itineraries. Three different types of models (simple analytical, statistical, and computation intelligence model) are developed to forecast the number of transferring passengers. Numerical experiments using observed Automatic Vehicle Location and Automatic Fare Collection data from South East Queensland, Australia show the accuracy and applicability of the proposed models in timed transfer coordination. Copyright © 2017 John Wiley & Sons, Ltd.