Assessing the financial and social costs of public transport in differing operating environments and with endogenous demand

This paper uses a previously developed spreadsheet cost model which simulates public transport modes operated on a 12-km route to analyse the total costs of different passenger demand levels. The previous cost model was a very powerful tool to estimate the social and operator costs for different public transport technologies. However, as the model is strategic, some basic assumptions were made which are relaxed in this paper. First, the speed-flow equation in the original spreadsheet model assumes that speed decreases according to the ratio of the current frequency and the lane capacity which is based on the safety headway without taking into account passenger boardings. However, this may vary in different operating environments. Therefore, the speed-flow equation is improved by moving from a linear equation to a piecewise equation that considers the features of different operating environments. Second, the model assumes that supply is sufficient to meet demand. However, when the level of demand is high for the lower-capacity public transport technologies, passengers may find the incoming vehicle full and therefore, they have to wait more than one service interval. This paper applies queuing theory to investigate the probability of having to wait longer than the expected service headways which will affect the average passenger waiting time. The extra waiting time for each passenger is calculated and applied in the spreadsheet cost model. Third, the original model assumed that demand was externally fixed (exogenous). To evaluate the differences after applying these equations, endogenous demand rather than exogenous demand will be investigated by using the elasticities for passenger waiting time and journey time.     

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.     

Total cost minimizing transit route structures considering trips towards CBD and periphery

The total cost minimizing approach to design transit systems is extended here beyond the usual dimensions of fleet (frequency) and vehicle size in order to examine the most appropriate spatial setting of transit lines as well. Motivated by the case of large cities in Latin America, characterized by high volumes of relatively long urban trips, we analyze the best ways to provide public transport services in a simplified urban setting represented by an extended cross-shaped network, where short trips (periphery–center) and long trips (periphery–periphery) coexist, generating economies of density. Three families of strategic lines structures are compared: mostly direct, feeder–trunk and hub and spoke. For each structure fleet and vehicle sizes are optimized, considering total (users’ and operators’) costs. The best structure is found parametrically in total passenger volume, the proportion of long trips and the value of the transfer penalty. The advantages of each dominating structure are explained in terms of factors like idle capacity, waiting or in-vehicle times and number of transfers.     

Evaluation of an existing bus network using a transit network optimisation model: a case study of the Hiroshima City Bus network

This study evaluates an existing bus network from the perspectives of passengers, operators, and overall system efficiency using the output of a previously developed transportation network optimisation model. This model is formulated as a bi-level optimisation problem with a transit assignment model as the lower problem. The upper problem is also formulated as bi-level optimisation problem to minimise costs for both passengers and operators, making it possible to evaluate the effects of reducing operator cost against passenger cost. A case study based on demand data for Hiroshima City confirms that the current bus network is close to the Pareto front, if the total costs to both passengers and operators are adopted as objective functions. However, the sensitivity analysis with regard to the OD pattern fluctuation indicates that passenger and operator costs in the current network are not always close to the Pareto front. Finally, the results suggests that, regardless of OD pattern fluctuation, reducing operator costs will increase passenger cost and increase inequity in service levels among passengers.     

Timetable optimization models and methods for minimizing passenger waiting time at public transit terminals

This paper focuses on developing mathematical optimization models for the train timetabling problem with respect to dynamic travel demand and capacity constraints. The train scheduling models presented in this paper aim to minimize passenger waiting times at public transit terminals. Linear and non-linear formulations of the problem are presented. The non-linear formulation is then improved through introducing service frequency variables. Heuristic rules are suggested and embedded in the improved non-linear formulation to reduce the computational time effort needed to find the upper bound. The effectiveness of the proposed train timetabling models is illustrated through the application to an underground urban rail line in the city of Tehran. The results demonstrate the effectiveness of the proposed demand-oriented train timetabling models, in terms of decreasing passenger waiting times. Compared to the baseline and regular timetables, total waiting time is reduced by 6.36% and 10.55% respectively, through the proposed mathematical optimization models.     

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).     

Modeling the interaction between buses,passengers and cars on a bus route using a multi-agent system

This paper models part of a public transport network (PTN), specifically, a bus route, as a small-size multi-agent system (MAS). The proposed approach is applied to a case study considering a ‘real world’ bus line within the PTN in Auckland, New Zealand. The MAS-based analysis uses modeling and simulation to examine the characteristics of the observed system – autonomous agents interacting with one another – under different scenarios, considering bus capacity and frequency of service for existing and projected public transport (PT) demand. A simulation model of a bus route is developed, calibrated and validated. Several results are attained, such as when the PT passenger load is not close to bus capacity, this load has no effect on average passenger waiting time at bus stops. The model proposed can be useful to practitioners as a tool to model the interaction between buses and other agents.     

Analysis of real-time control strategies in a corridor with multiple bus services

Control strategies have been widely used in the literature to counteract the effects of bus bunching in passenger‘s waiting times and its variability. These strategies have only been studied for the case of a single bus line in a corridor. However, in many real cases this assumption does not hold. Indeed, there are many transit corridors with multiple bus lines interacting, and this interaction affects the efficiency of the implemented control mechanism.This work develops an optimization model capable of executing a control scheme based on holding strategy for a corridor with multiple bus lines.We analyzed the benefits in the level of service of the public transport system when considering a central operator who wants to maximize the level of service for users of all the bus lines, versus scenarios where each bus line operates independently. A simulation was carried out considering two medium frequency bus lines that serve a set of stops and where these two bus lines coexist in a given subset of stops. In the simulation we compared the existence of a central operator, using the optimization model we developed, against the independent operation of each line.In the simulations the central operator showed a greater reduction in the overall waiting time of the passengers of 55% compared to a no control scenario. It also provided a balanced load of the buses along the corridor, and a lower variability of the bus headways in the subset of stops where the lines coexist, thus obtaining better reliability for all types of passengers present in the public transport system.     

An analytic investigation of optimal bus size

The use of smaller buses offers passengers a better service frequency for a given service capacity, but costs more to operate per seat provided. Within this trade-off there is an optimal bus size which maximises social benefit. A mathematical model is described which can be solved analytically to provide an explicit relationship between optimal bus size and factors such as operating cost, level of demand, and demand elasticities. The model includes: passenger demand varying with the generalised cost of travel according to a constant elasticity; the effect of changes in bus occupancy on average waiting times and on operating speed; the financial constraint that farebox revenue must equal operating cost less subsidy; an allowance for external benefits associated with generated demand, and for the effect of the flow of buses on traffic congestion; and an operating cost increasing linearly with bus size. The optimal size varies with the square root of demand, and with the unit cost to the power of 0.1 to 0.2. It also increases slowly with the proportion of cost covered by subsidy. For typical urban operating conditions in the United Kingdom the optimal size for a monopoly service lies between 55 and 65 seats assuming the observed relationship between cost and size; it is possible that changes in working practices could make smaller buses relatively cheaper to operate, so reducing the optimal size, but it seems unlikely to fall below 40 seats.     

Flexing service schedules: Assessing the potential for demand-adaptive hybrid transit via a stated preference approach

This paper assesses the demand for a flexible, demand-adaptive transit service, using the Chicago region as an example. We designed and implemented a stated-preference survey in order to (1) identify potential users of flexible transit, and (2) inform the service design of the flexible transit mode. Multinomial logit, mixed-logit, and panel mixed-logit choice models were estimated using the data obtained from the survey. The survey instrument employed a d_p-efficient design and the Google Maps API to capture precise origins and destinations in order to create realistic choice scenarios. The stated-preference experiments offered respondents a choice between traditional transit, car, and a hypothetical flexible transit mode. Wait time, access time, travel time, service frequency, cost, and number of transfers varied across the choice scenarios. The choice model results indicate mode-specific values of in-vehicle travel time ranging between $16.3 per hour (car) and $21.1 per hour (flexible transit). The estimated value of walking time to transit is $25.9 per hour. The estimated value of waiting time at one’s point of origin for a flexible transit vehicle is $11.3 per hour; this value is significantly lower than the disutility typically associated with waiting at a transit stop/station indicating that the ‘at-home’ pick-up option of flexible transit is a highly desirable feature. The choice model results also indicate that respondents who use active-transport modes or public transit for their current commute trip, or are bikeshare members, were significantly more likely to choose flexible and traditional transit than car commuters in the choice experiments. The implications of these and other relevant model results for the design and delivery of flexible, technology-enabled services are discussed.     

Secrets of success: assessing the large increases in transit ridership achieved by Houston and San Diego transit providers

This paper summarizes and updates the findings from an earlier study by the same authors of transit systems in Houston (all bus) and San Diego (bus and light rail). Both systems achieved unusually large increases in transit ridership during a period in which most transit systems in other metropolitan areas were experiencing large losses. Based on ridership models estimated using cross section and time series data, the paper quantifies the relative contributions of policy variables and factors beyond the control of transit operators on ridership growth. It is found that large ridership increases in both areas are caused principally by large service increases and fare reductions, as well as metropolitan employment and population growth. In addition, the paper provides careful estimates of total and operating costs per passenger boarding and per passenger mile for Houston's bus operator and San Diego's bus and light rail operators. These estimates suggest that the bus systems are more cost-effective than the light rail system on the basis of total costs. Finally, the paper carries out a series of policy simulations to analyze the effects of transit funding levels and metropolitan development patterns on transit ridership and farebox recovery ratio.     

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.     

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.     

An analysis of public bus transit performance in Indian cities

Maintaining and enhancing public transit service in Indian cities is important, to meet rapidly growing mass mobility needs, and curb personal motor vehicle activity and its impacts at low cost. Indian cities rely predominantly on buses for public transport, and are likely to continue to do so for years. However, the public bus transit service is inadequate, and unaffordable for the urban poor. The paper explores the factors that contribute to and affect efforts to improve this situation, based on an analysis of the financial and operational performance of the public bus transit service in the four metropolitan centres and four secondary cities during the 1990s. Overall, there were persistent losses, owing to increasing input costs and declining productivity. The losses occurred despite rapidly increasing fares, and ridership declined. The situation, and the ability to address it, is worse in the secondary cities than the metropolitan centres. We suggest a disaggregated approach based on the needs and motivations of different groups in relation to public transit, along with improved operating conditions and policies to internalize costs of personal motor vehicle use, to address the challenge of providing financially viable and affordable public bus transit service.     

Crowding in public transport systems: Effects on users,operation and implications for the estimation of demand

The effects of high passenger density at bus stops, at rail stations, inside buses and trains are diverse. This paper examines the multiple dimensions of passenger crowding related to public transport demand, supply and operations, including effects on operating speed, waiting time, travel time reliability, passengers’ wellbeing, valuation of waiting and in-vehicle time savings, route and bus choice, and optimal levels of frequency, vehicle size and fare. Secondly, crowding externalities are estimated for rail and bus services in Sydney, in order to show the impact of crowding on the estimated value of in-vehicle time savings and demand prediction. Using Multinomial Logit (MNL) and Error Components (EC) models, we show that alternative assumptions concerning the threshold load factor that triggers a crowding externality effect do have an influence on the value of travel time (VTTS) for low occupancy levels (all passengers sitting); however, for high occupancy levels, alternative crowding models estimate similar VTTS. Importantly, if demand for a public transport service is estimated without explicit consideration of crowding as a source of disutility for passengers, demand will be overestimated if the service is designed to have a number of standees beyond a threshold, as analytically shown using a MNL choice model. More research is needed to explore if these findings hold with more complex choice models and in other contexts.     

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.     

Equity-oriented skip-stopping schedule optimization in an oversaturated urban rail transit network

In this study, we focus on improving system-wide equity performance in an oversaturated urban rail transit network based on multi-commodity flow formulation. From the system perspective, an urban rail transit network is a distributed system, where a set of resources (i.e., train capacity) is shared by a number of users (i.e., passengers), and equitable individuals and groups should receive equal shares of resources. However, when oversaturation occurs in an urban rail transit network during peak hours, passengers waiting at different stations may receive varying shares of train capacity leading to the inequity problem under train all-stopping pattern. Train skip-stopping pattern is an effective operational approach, which holds back some passengers at stations and re-routes their journeys in the time dimension based on the available capacity of each train. In this study, the inequity problem in an oversaturated urban rail transit network is analyzed using a multi-commodity flow modeling framework. In detail, first, discretized states, corresponding to the number of missed trains for passengers, are constructed in a space-time-state three-dimensional network, so that the system-wide equity performance can be viewed as a distribution of all passengers in different states. Different from existing flow-based optimization models, we formulate individual passenger and train stopping pattern as commodity and network structure in the multi-commodity flow-modeling framework, respectively. Then, we aim to find an optimal commodity flow and well-designed network structure through the proposed multi-commodity flow model and simultaneously achieve the equitable distribution of all passengers and the optimal train skip-stopping pattern. To quickly solve the proposed model and find an optimal train skip-stopping pattern with preferable system-wide equity performance, the proposed linear programming model can be effectively decomposed to a least-cost sub-problem with positive arc costs for each individual passenger and a least-cost sub-problem with negative arc costs for each individual train under a Lagrangian relaxation framework. For application and implementation, the proposed train skip-stopping optimization model is applied to a simple case and a real-world case based on Batong Line in the Beijing Subway Network. The simple case demonstrates that our proposed Lagrangian relaxation framework can obtain the approximate optimal solution with a small-gap lower bound and a lot of computing time saved compared with CPLEX solver. The real-world case based on Batong Line in the Beijing Subway Network compares the equity and efficiency indices under the operational approach of train skip-stopping pattern with those under the train all-stopping pattern to state the advantage of the train skip-stopping operational approach.     

Distributed algorithm for empty vehicles management in personal rapid transit (PRT) network

In this paper, an original heuristic algorithm of empty vehicles management in personal rapid transit network is presented. The algorithm is used for the delivery of empty vehicles for waiting passengers, for balancing the distribution of empty vehicles within the network, and for providing an empty space for vehicles approaching a station. Each of these tasks involves a decision on the trip that has to be done by a selected empty vehicle from its actual location to some determined destination. The decisions are based on a multi‐parameter function involving a set of factors and thresholds. An important feature of the algorithm is that it does not use any central database of passenger input (demand) and locations of free vehicles. Instead, it is based on the local exchange of data between stations: on their states and on the vehicles they expect. Therefore, it seems well‐tailored for a distributed implementation. The algorithm is uniform, meaning that the same basic procedure is used for multiple tasks using a task‐specific set of parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterizing,measuring, and managing transit service quality

Recent studies to evaluate the quality of transit service are generating a good amount of renewed interest in an old idea, the passenger's perspective; this new interest stems from recognizing that transit service quality should be characterised, measured, and managed by parameters capturing both passenger and transit operator perspectives. However, although the selected parameters are user‐oriented in their input, the output may not be as user‐oriented as considered, and the number or the percentage of passengers is often neglected. As a result, the findings are often misleading because the perspectives of transit operators dominate. Therefore, academics and practitioners must rethink their strategies of quality analysis of public transportation by stressing more on the role of passengers. These challenges are addressed in this paper with a practical, simple, and holistic framework, for Transit Quality (TRANSQUAL). This framework provides for the involvement of all stakeholders in the characterisation, measurement, and management of the stages of quality monitoring, which is jointly analyzed at different planning levels. In the characterization stage, the framework supports the selection of parameters to be monitored. The measurement stage sets and measures four quality areas in terms of percentage of passengers who expect a predefined level of service, for whom the service is designed, who receive the planned service, and who perceive the service as delivered. The management stage computes the differences between these percentages, points out criticalities, and recommends corrective actions. These stages are investigated in‐depth, integrated, and discussed in a real‐life case study. Copyright © 2016 John Wiley & Sons, Ltd.     

On seat capacity in traffic assignment to a transit network

Seating or standing make distinct on‐board states to a transit rider, yielding distinct discomfort costs, with potential influence on the passenger route choice onto the transit network. The paper provides a transit assignment model that captures the seating capacity and its occupancy along any transit route. The main assumptions pertain to: the seat capacity by service route, selfish user behaviour, a seat allocation process with priority rules among the riders, according to their prior state either on‐board or at boarding. To each transit leg from access to egress station is associated a set of ‘service modes’, among which the riders are assigned in a probabilistic way, conditionally on their priority status and the ratio between the available capacity and the flow of them. Thus the leg cost is a random variable, with mean value to be included in the trip disutility. Computationally efficient algorithms are provided for, respectively, loading the leg flows and evaluating the leg costs along a transit line. At the network level, a hyperpath formulation is provided for supply‐demand equilibrium, together with a property of existence and an method of successive averages equilibration algorithm. It is shown that multiple equilibria may arise. Copyright © 2010 John Wiley & Sons, Ltd.