On the capacity of isolated, curbside bus stops

The maximal rates that buses can discharge from bus stops are examined. Models were developed to estimate these capacities for curbside stops that are isolated from the effects of traffic signals. The models account for key features of the stops, including their target service levels assigned to them by a transit agency. Among other things, the models predict that adding bus berths to a stop can sometimes return disproportionally high gains in capacity. This and other of our findings are at odds with information furnished in professional handbooks.     

Berth assignment planning for multi‐line bus stops

In this paper, we study an important problem that arises with the fast development of public transportation systems: when a large number of bus lines share the same bus stop, a long queue of buses often forms when they wait to get into the stop in rush hours. This causes a significant increase of bus delay and a notable drop of traffic capacity near the bus stop. Various measures had been proposed to relieve the congestions near bus stops. However, all of them require considerable financial budgets and construction time costs. In this paper, with the concept of berth assignment redesign, a simulation‐based heuristic algorithm is proposed to make full use of exiting bus berths. In this study, a trustable simulation platform is designed, and the major influencing factors for bus stop operations are considered. The concept of risk control is also introduced to better evaluate the performance of different berth arrangement plans and makes an appropriate trade‐off between the system's efficiency and stability. Finally, a heuristic algorithm is proposed to find a sub‐optimal berth assignment plan. Tests on a typical bus stop show that this algorithm is efficient and fast. The sub‐optimal berth assignment plan obtained by this algorithm could make remarkable improvements to an actual bus stop. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical model for calibrating delay at congested bus stops

Abstract

A model is proposed to calculate the overall operating and delay times spent at bus stops due to passenger boarding and alighting and the time lost to queuing caused by bus stop saturation. A formula for line demand at each stop and the interaction between the buses themselves is proposed and applied to different bus stops depending on the number of available berths. The application of this model has quantified significant operational delays suffered by users and operator due to consecutive bus arrival at stops, even with flows below bus stop capacity.     

Mitigating negative impacts of near-side bus stops on cars

Bus stops are often placed short distances upstream of signalized intersections. Buses that dwell at one of these so-called near-side stops can impede queued cars upstream from discharging through the intersection during green times. Residual car queues can form at the intersection as a result. The smaller the distance between a stop and its intersection, the greater the problem can be.Models are formulated to address this problem using kinematic wave theory. The models can be used to determine where to place a near-side stop to achieve a target level of residual car queueing. In addition, the models are used herein to develop a scheme for mitigating residual car queues by briefly detaining some buses from reaching the stop. The scheme can be applied selectively, so that the times that detained buses depart from the stop are not postponed. The buses are therefore not delayed over the longer run. Analysis indicates that this bus-holding scheme can significantly reduce car delays and queueing. Our models for placing stops and holding buses are shown to be robust to systematic and random changes in car flow.     

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.     

Development of a probabilistic model to optimize disseminated real‐time bus arrival information for pre‐trip passengers

In the advent of Advanced Traveler Information Systems (ATIS), the total wait time of passengers for buses may be reduced by disseminating real‐time bus arrival times for the next or series of buses to pre‐trip passengers through various media (e.g., internet, mobile phones, and personal digital assistants). A probabilistic model is desirable and developed in this study, while realistic distributions of bus and passenger arrivals are considered. The disseminated bus arrival time is optimized by minimizing the total wait time incurred by pre‐trip passengers, and its impact to the total wait time under both late and early bus arrival conditions is studied. Relations between the optimal disseminated bus arrival time and major model parameters, such as the mean and standard deviation of arrival times for buses and pre‐trip passengers, are investigated. Analytical results are presented based on Normal and Lognormal distributions of bus arrivals and Gumbel distribution of pre‐trip passenger arrivals at a designated stop. The developed methodology can be practically applied to any arrival distributions of buses and passengers.     

Alternative information technologies for the provision of spatial information to public transport passengers in France,Germany and Spain

In France, Germany and Spain, the availability of computer‐generated itineraries to travellers in the street is still very limited, though growing slowly. Although many French towns have an effective passenger information system via Minitel, which will calculate itineraries, this is available only from the home. The vast majority of decisions about routes for journeys by urban public transport are still made using the traditional forms of spatial information abundantly displayed at bus stops and in vehicles: usually a map of the network and diagrammatic maps of individual bus or underground lines. Unfortunately a map of the whole network is often too complicated to yield the desired information easily. Alternatively the traveller may have the difficult task of comparing several diagrammatic maps of the individual lines departing from that bus stop, none of which alone can answer his spatial query: which bus lines, if any, go to my destination? The priority for the application of the computer should be the use of a geographic information system to generate automatically two types of less‐complicated map. The ‘stop‐specific route map’ shows on one piece of paper the routes of all buses from that stop, excluding of course the portions before the stop. The ‘zone map’ shows only the bus lines which serve a specific limited zone of the city, including at a reduced scale the portions extending out to their various destinations beyond the limits of the zone itself.     

Optimal control of headway variation on transit routes

Headway control strategies have been proposed as methods for correcting transit service irregularities and thereby reducing passenger wait times at stops. This paper addresses a particular strategy which can be implemented on high frequency routes (headways under 10–12 minutes), in which buses are held at a control stop to a threshold headway. An algorithm is developed which yields the optimal control stop location and optimal threshold headway with respect to a system wait function. The specification of the wait function is based on the development of several empirical models, including a headway variation model and an average delay time model at control stops. A conclusion is reached that the headway variation does not increase linearly along a route, a common assumption made in many previous studies. Furthermore, the location of the optimal control stop and threshold value are sensitive to the passenger boarding profile, as expected. The algorithm itself appears to have practical application to conventional transit operations.     

Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors

Microeconomic optimisation of scheduled public transport operations has traditionally focused on finding optimal values for the frequency of service, capacity of vehicles, number of lines and distance between stops. In addition, however, there exist other elements in the system that present a trade-off between the interests of users and operators that have not received attention in the literature, such as the optimal selection of a fare payment system and a designed running speed (i.e., the cruising speed that buses maintain in between two consecutive stops). Alternative fare payment methods (e.g., on-board and off-board, payment by cash, magnetic strip or smart card) have different boarding times and capital costs, with the more efficient systems such as a contactless smart card imposing higher amounts of capital investment. Based on empirical data from several Bus Rapid Transit systems around the world, we also find that there is a positive relationship between infrastructure cost per kilometre and commercial speed (including stops), achieved by the buses, which we further postulate as a linear relationship between infrastructure investment and running speed. Given this context, we develop a microeconomic model for the operation of a bus corridor that minimises total cost (users and operator) and has five decision variables: frequency, capacity of vehicles, station spacing, fare payment system and running speed, thus extending the traditional framework. Congestion, induced by bus frequency, plays an important role in the design of the system, as queues develop behind high demand bus stops when the frequency is high. We show that (i) an off-board fare payment system is the most cost effective in the majority of circumstances; (ii) bus congestion results in decreased frequency while fare and bus capacity increase, and (iii) the optimal running speed grows with the logarithm of demand.     

Integrated optimization of bus priority operations in connected vehicle environment

Most previous works associated with transit signal priority merely focus on the optimization of signal timings, ignoring both bus speed and dwell time at bus stops. This paper presents a novel approach to optimize the holding time at bus stops, signal timings, and bus speed to provide priority to buses at isolated intersections. The objective of the proposed model is to minimize the weighted average vehicle delays of the intersection, which includes both bus delay and impact on nearby intersection traffic, ensuring that buses clear these intersections without being stopped by a red light. A set of formulations are developed to explicitly capture the interaction between bus speed, bus holding time, and transit priority signal timings. Experimental analysis is used to show that the proposed model has minimal negative impacts on general traffic and outperforms the no priority, signal priority only, and signal priority with holding control strategies (no bus speed adjustment) in terms of reducing average bus delays and stops. A sensitivity analysis further demonstrates the potential of the proposed approach to be applied to bus priority control systems in real‐time under different traffic demands, bus stop locations, and maximum speed limits. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths

This paper presents a dynamic user equilibrium for bus networks where recurrent overcrowding results in queues at stops. The route-choice model embedded in the dynamic assignment explicitly considers common lines and strategies with alternative routes. As such, the shortest hyperpath problem is extended to a dynamic scenario with capacity constraints where the diversion probabilities depend on the time at which the stop is reached and on the expected congestion level at that time. In order to reproduce congestion for all the lines sharing a stop, the Bottleneck Queue Model with time-varying exit capacity, introduced in Meschini et al. (2007), is extended. The above is applied to separate queues for each line in order to satisfy the First-In-First-Out principle within every attractive set, while allowing overtaking among passengers with different attractive sets but queuing single file. The application of the proposed model to a small example network clearly reproduces the formation and dispersion of passenger queues due to capacity constraints and thus motivates the implementation of the methodology on a real-size network case as the next step for future research.     

Analyzing urban bus service reliability at the stop, route, and network levels

Improving the reliability of bus service has the potential to increase the attractiveness of public transit to current and prospective riders. An understanding of service reliability is necessary to develop strategies that help transit agencies provide better services. However, few studies have been conducted analyzing bus reliability in the metropolis of China. This paper presents an in-depth analysis of service reliability based on bus operational characteristics in Beijing. Three performance parameters, punctuality index based on routes (PIR), deviation index based on stops (DIS), and evenness index based on stops (EIS), are proposed for the evaluation of bus service reliability. Reliability involves routes, stops, punctuality, deviation, and evenness. The relationship among the three parameters is discussed using a numerical example. Subsequently, through a sampling survey of bus lines in Beijing, service reliability at the stop, route, and network levels are estimated. The effects of route length, headway, the distance from the stop to the origin terminal, and the use of exclusive bus lanes are also analyzed. The results indicate low service reliability for buses in Beijing and a high correlation between service reliability and route length, headway, distance from the stop to the origin terminal, and the provision of exclusive bus lanes.     

Where Is My Bus? Impact of mobile real-time information on the perceived and actual wait time of transit riders

In order to attract more choice riders, transit service must not only have a high level of service in terms of frequency and travel time but also must be reliable. Although transit agencies continuously work to improve on-time performance, such efforts often come at a substantial cost. One inexpensive way to combat the perception of unreliability from the user perspective is real-time transit information. The OneBusAway transit traveler information system provides real-time next bus countdown information for riders of King County Metro via website, telephone, text-messaging, and smart phone applications. Although previous studies have looked at traveler response to real-time information, few have addressed real-time information via devices other than public display signs. For this study, researchers observed riders arriving at Seattle-area bus stops to measure their wait time while asking a series of questions, including how long they perceived that they had waited.The study found that for riders without real-time information, perceived wait time is greater than measured wait time. However, riders using real-time information do not perceive their wait time to be longer than their measured wait time. This is substantiated by the typical wait times that riders report. Real-time information users say that their average wait time is 7.5 min versus 9.9 min for those using traditional arrival information, a difference of about 30%. A model to predict the perceived wait time of bus riders was developed, with significant variables that include the measured wait time, an indicator variable for real-time information, an indicator variable for PM peak period, the bus frequency in buses per hour, and a self-reported typical aggravation level. The addition of real-time information decreases the perceived wait time by 0.7 min (about 13%).A critical finding of the study is that mobile real-time information reduces not only the perceived wait time, but also the actual wait time experienced by customers. Real-time information users in the study wait almost 2 min less than those arriving using traditional schedule information. Mobile real-time information has the ability to improve the experience of transit riders by making the information available to them before they reach the stop.     

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.     

Using non-real-time Automatic Vehicle Location data to improve bus services

Although real-time Automatic Vehicle Location (AVL) data is being utilised successfully in the UK, little notice has been given to the benefits of historical (non-real-time) AVL data. This paper illustrates how historical AVL data can be used to identify segments of a bus route which would benefit most from bus priority measures and to improve scheduling by highlighting locations at which the greatest deviation from schedule occurs. A new methodology which uses historical AVL data and on-bus passenger counts to calculate the passenger arrival rate at stops along a bus route has been used to estimate annual patronage and the speed of buses as they move between stops. Estimating the patronage at stops using AVL data is more cost-effective than conventional methods (such as surveys at stops which require much more manpower) but retains the benefits of accuracy and stop-specific estimates of annual patronage. The passenger arrival rate can then be used to calculate how long buses spend at stops. If the time buses spend at stops is removed from the total time it takes the bus to traverse a link, the remaining amount of time can be assumed to be the time the bus spends moving and hence the moving speed of the bus can be obtained. It was found that estimation of patronage and the speed of buses as they move between stops using AVL data produced results which were comparable with those obtained by other methods. However the main point to note is that this new method of estimating patronage has the potential to provide a larger and superior data set than is otherwise available, at very low cost.     

Rethinking bus punctuality by integrating Automatic Vehicle Location data and passenger patterns

This paper investigates punctuality at bus stops. Although it is typically evaluated from the point of view of bus operators, it must also account for users, as required in recent service quality norms. Therefore, evaluating punctuality at bus stops is highly important, but may also be a complex task, because data on both bus arrivals (or departures) and users must be taken into account and processed. Data on buses can be collected by Automatic Vehicle Location (AVL) systems, but several challenges must be addressed in order to use them effectively. Passengers data at bus stops cannot be derived from AVL, but they can be used to derive passenger patterns and need to be integrated into processed AVL data. This paper proposes a new punctuality measure defined as the fraction of passengers who will be served within an acceptably short interval after they arrive. A method is proposed to determine this measure: it provides (i) several rules to handle AVL collected data, (ii) a procedure integrating processed AVL data and potential passengers’ patterns and (iii) a hierarchical process to perform the punctuality measure on each bus route direction of a transit network, as well as for every bus stop and time period. The paper illustrates the experimentation of this method on more than 4,000,000 data of a real bus operator and represents outcomes by easy-to-read control dashboards.     

Comparing static and dynamic threshold based control strategies

This research extends a static threshold based control strategy used to control headway variation to a dynamic threshold based control strategy. In the static strategy, buses are controlled by setting a threshold value that holds buses at a control point for a certain amount of time before allowing the bus to continue along the route. The threshold remains constant each time the bus stops at the control point. The dynamic strategy involves the same principle of holding buses at a bus stop; however, a different threshold value is chosen each time the bus holds at a control point. The results indicate that in cases where the static threshold is set equal to the scheduled headway, very low headway variation and passenger system times result; however, passengers on board the bus are penalized by extra delay on the bus while waiting at the control point. The dynamic strategy reduces the penalty to passengers delayed on-board the bus at a control point at the expense of a slight increase in overall passenger system time.The results indicate that in most cases, the tradeoff of the slight increase in waiting time for the significant decrease in on-board delay penalty makes the dynamic strategy an acceptable choice.     

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.     

Real-time queue length estimation for congested signalized intersections

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic is not available once the detector is occupied by the queue. In this paper, instead of counting arrival traffic flow in the current signal cycle, we solve the problem of measuring intersection queue length by exploiting the queue discharge process in the immediate past cycle. Using high-resolution “event-based” traffic signal data, and applying Lighthill–Whitham–Richards (LWR) shockwave theory, we are able to identify traffic state changes that distinguish queue discharge flow from upstream arrival traffic. Therefore, our approach can estimate time-dependent queue length even when the signal links are congested with long queues. Variations of the queue length estimation model are also presented when “event-based” data is not available. Our models are evaluated by comparing the estimated maximum queue length with the ground truth data observed from the field. Evaluation results demonstrate that the proposed models can estimate long queues with satisfactory accuracy. Limitations of the proposed model are also discussed in the paper.