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.     

Assessing the quality of intercity road transportation of passengers: An exploratory study in Brazil

In Brazil, buses represent the main mode of public transportation. However, in recent years intercity and interstate bus companies have been facing a growing competition with other forms of transportation such as bus companies competitors, illegal transportation companies, chartered buses, and, more recently, air companies. In this scenario characterized by growing competition, it is essential to evaluate the quality of road transportation of passengers. In order to contribute to the analysis of this issue, this paper presents a methodological approach to assess the quality of intercity road transportation of passengers, according to the customers’ perspective. By conducting a case study in a city of almost 500,000 inhabitants from the interior of Rio de Janeiro, an Importance–Satisfaction Analysis (ISA) and an assignment procedure were used in order to obtain: (i) the main factors (criteria) that influence the quality of service intercity road transportation of passengers, (ii) the importance degree of criteria related to road transportation of passengers, (iii) the satisfaction of the users of road transportation under the considered criteria, (iv) the critical criteria/items, and (v) the categories which best represent the quality of service intercity road transportation according to the passengers’ perspective. Finally, several possible corrective actions to improve the quality of services considering each critical item/criterion were highlighted and special recommendations were done for the critical process (ticket sales).     

A theoretical travel-time model for flexible-route buses

A theoretical model for estimating the expectation and variance of buses' running times under a flexibly-routed mode of service is proposed. The model is based on a probabilistic concept that adequately accommodates the usual randomness in the number and location of passengers served during successive vehicle trips. A few simplifications are embodied in the model but it can serve as a basis for a more refined model such as a computer simulation model that can be used in designing real bus systems.The physical setting assumed in the model is a rectangular grid road network where all houses face the side streets as in some suburban regions. Because it oversimplifies real-life situations, this assumption would need to be relaxed to make the model applicable to more general cases.Both the partially flexible-route service where some passengers are captive to fixed-route service and others are served at their doorsteps, and the fully flexible-route service where all passengers are served at their doorsteps, are studied. In each case, a very simple routing convention that can be conveniently executed by the bus drivers is assumed. The proposed travel time model confirms the intuitively correct phenomenon that when the concentration of passenger trip-ends is very high, the vehicle-route degenerates into a fixed-route in which the buses visit all possible loading points within the service area.     

Reducing bunching with bus-to-bus cooperation

Schedule-based or headway-based control schemes to reduce bus bunching are not resilient because they cannot prevent buses from losing ground to the buses they follow when disruptions increase the gaps separating them beyond a critical value. (Following buses are then overwhelmed with passengers and cannot process their work quick enough to catch up.) This critical gap problem can be avoided, however, if buses at the leading end of such gaps are given information to cooperate with the ones behind by slowing down.This paper builds on this idea. It proposes an adaptive control scheme that adjusts a bus cruising speed in real-time based on both, its front and rear spacings much as if successive bus pairs were connected by springs. The scheme is shown to yield regular headways with faster bus travel than existing control methods. Its simple and decentralized logic automatically compensates for traffic disruptions and inaccurate bus driver actions. Its hardware and data requirements are minimal.     

Passengers’ Perceived Service Quality of City Buses in Taipei: Scale Development and Measurement

Abstract

To understand fully passengers’ perceptions and expectations of the bus service quality in Taipei, business managers and governmental agencies must seek a proper scale that can reflect passengers’ opinions accurately. This study develops and tests a service quality scale designed for a city bus transit system in Taipei. Churchill’s paradigm and a focus group interview were combined into a multistage scale development procedure. Based on the procedure, Taipei city buses were selected as the example, for which a service quality scale was developed. The final scale contains four dimensions and 20 items. These four dimensions are ‘interaction with passengers’, ‘tangible service equipment’, ‘convenience of service’ and ‘operating management support’. Finally, the results of scale development and the managerial applications of the service quality scale for the city transit system are discussed.     

A self-adaptive method to equalize headways: Numerical analysis and comparison

In uncontrolled bus systems, buses tend to bunch due to the stochastic nature of traffic flows and passenger demand at bus stops. Although schedules and priori target methods introduce slack time to delay buses at control points to maintain constant headways between successive buses, too much slack required delay passengers on-board. In addition, these methods focus on regular headways and do not consider the rates of convergence of headways after disturbances. We propose a self-adaptive control scheme to equalize the headways of buses with little slack in a single line automatically. The proposed method only requires the information from the current bus at the control point and both its leading and following buses. This elegant method is shown to regulate headways faster than existing methods. In addition, compared to previous self-equalizing methods, the proposed method can improve the travel time of buses by about 12%, while keeping the waiting time of passengers almost the same.     

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.     

The allocation of buses in heavily utilized networks with overlapping routes

Many transit systems outside North America are characterized by networks with extensively overlapping routes and buses frequently operating at, or close to, capacity. This paper addresses the problem of allocating a fleet of buses between routes in this type of system; a problem that must be solved recurrently by transit planners. A formulation of the problem is developed which recognizes passenger route choice behavior, and seeks to minimize a function of passenger wait time and bus crowding subject to constraints on the number of buses available and the provision of enough capacity on each route to carry all passengers who would select it. An algorithm is developed based on the decomposition of the problem into base allocation and surplus allocation components. The base allocation identifies a feasible solution using an (approx.) minimum number of buses. The surplus allocation is illustrated for the simple objective of minimizing the maximum crowding level on any route. The bus allocation procedure developed in this paper has been applied to part of the Cairo bus system in a completely manual procedure, and is proposed to be the central element of a short-range bus service planning process for that city.     

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.     

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.     

Evaluating bus transit performance of Chinese cities: Developing an overall bus comfort model

In order to improve the level of bus service, a field study was undertaken to develop a combined bus comfort model. This paper provides a comprehensive review of the different ways to predict the bus comfort, in addition to the variable experimental techniques used. It was found some environment parameters like noise, vibration, thermal comfort and the acceleration would affect the passengers’ experience. In this model, both the measurement of objective physical parameters and subjective questionnaire survey were conducted to gather the practical environment date, as well as to distribute questionnaires on board city buses during the same trips. By comparing the subjective views of bus passengers to objective physical parameters, a combined bus comfort model was established. This model helps to calculate the concrete value of passengers’ perceived bus comfort. An effective approach integrated the comfort model, measuring instrument and the driver monitor could greatly improve the bus service quality.     

Comfort and Safety as Perceived by Wheelchair-Seated Bus Passengers

Abstract

Wheelchair-seated passengers on European and Swedish urban transit buses can travel rearwards, resting against a bulkhead, without the use of tie-down equipment. However, users sometimes disapprove of being the only passengers who have to travel rearwards, and also unrestrained. In order to investigate comfort and safety as perceived by wheelchair-seated bus passengers riding either forwards or rearwards, an experimental field study was carried out. Participating subjects were 31 wheelchair users and a group of 44 ambulant passengers. Each subject made two consecutive, identical 15-minute trips, randomly beginning either forwards or backwards, and interviews were conducted after each trip. During the trips, three-axis bus motion was recorded. The concept of categorization was used as a theoretical background and basis for discussion of the comfort and safety constructs. The results indicated that while the majority preferred the forward-facing position regarding comfort issues, a minority felt that the level of perceived safety was better. Wheelchair-seated passengers were more positive towards the rearward position than the ambulant group.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

Maximizing bus discharge flows from multi-berth stops by regulating exit maneuvers

Upon having loaded and unloaded their passengers, buses are often free to exit a multi-berth bus stop without delay. A bus need not wait to perform this exit maneuver, even if it requires circumventing one or more other buses that are still dwelling in the stop’s downstream berths. Yet, many jurisdictions impose restrictions on bus entry maneuvers into a stop to limit disruptions to cars and other buses. Buses are typically prohibited from entering a stop whenever this would require maneuvering around other buses still dwelling in upstream berths. An entering bus is instead required to wait in queue until the upstream berths are vacated.Analytical models are formulated to predict how bus discharge flows from busy, multi-berth stops are affected by allowing buses to freely exit, but not freely enter berths. These models apply when: a bus queue is always present at the stop’s entrance; buses depart the entry queue and enter the stop as per the restriction described above; and the stop is isolated from the effects of nearby traffic signals and other bus stops. We find that for these restricted-entry stops, bus-carrying capacities can often be improved by regulating the exit maneuvers as well. This turns out to be particularly true when the stop’s number of berths is large. Simulations show that these findings still hold when a stop is only moderately busy with entry queues that persist for much, but not all of the time. The simulations also indicate that removing any restrictions on bus exit maneuvers is almost always productive when stops are not busy, such that short entry queues form only on occasion, and only for short periods. We argue why certain simple policies for regulating exit maneuvers would likely enhance bus-stop discharge flows.     

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.     

Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis

As is well known, bus systems are naturally unstable. Without control, buses on a single line tend to bunch, reducing their punctuality in meeting a schedule. Although conventional schedule-based strategies that hold buses at control points can alleviate this problem these methods require too much slack, which slows buses. This delays on-board passengers and increases operating costs.It is shown that dynamic holding strategies based on headways alone cannot help buses adhere to a schedule. Therefore, a family of dynamic holding strategies that use bus arrival deviations from a virtual schedule at the control points is proposed. The virtual schedule is introduced whether the system is run with a published schedule or not. It is shown that with this approach, buses can both closely adhere to a published schedule and maintain regular headways without too much slack.A one-parameter version of the method can be optimized in closed form. This simple method is shown to be near-optimal. To put it in practice, the only data needed in real time are the arrival times of the current bus and the preceding bus at the control point relative to the virtual schedule. The simple method was found to require about 40% less slack than the conventional schedule-based method. When used only to regulate headways it outperforms headway-based methods.     

Analysis of intended bus usage

In order to plan bus operations, it is necessary for transit planners to understand what factors may influence travelers’ choice of buses for travels within a city. The proposed method involves various scenarios of a hypothetical bus operation which was rated by a group of individuals.

Analysis of Covariance technique is employed to analyze people's sensitivities to their perceived levels of bus service characteristics. The technique involves:

1. testing for the significant effects of varying levels of service characteristics upon people's intentions to use bus service, and

2. assessing differences among various population segments in their sensitivity patterns towards bus service characteristics.

Results from the application of the technique to attitudinal data collected by the Orange County Transit District indicate that bus service characteristics do influence, independently and jointly, respondents’ stated intentions to use buses.

Sensitivity pattern differed across the five homogeneous segments identified in an earlier research based on socioeconomic characteristics.

One segment (an older, predominatly male population segment with higher home ownership level and lower income than the rest of the sample) was relatively insensitive to changes in bus fare and was influenced by changes in headway independent of changes in access distance. Another segment consisting of fewer registered voters with lower education also exhibited similar independent impact of headway and access distance.

The technique is especially useful in reducing a large number of proposed alternative bus systems to a smaller set for further planning considerations by specifying the ranges within which variation of service characteristic would cause substantial changes in the intended usage responses.     

Plan-based flexible bus bridging operation strategy

Bus bridging has been widely used to connect stations affected by metro disruptions such that stranded passengers could resume their journeys. Previous studies generally assumed that a bus operates exclusively on one bridging route with given frequency, which limits the service flexibility and reduce the operational efficiency. We propose a strategy to instruct buses to operate on predefined bridging routes once they are dispatched from depots. Buses are allowed to flexibly serve different bridging routes. Each bus operates based on a bridging plan that lists the stations to serve in sequence instead of route frequencies. A two-stage model is developed to optimize the bridging plans and their assignments to buses with the objectives that balance the operational priorities between minimizing bus bridging time and reducing passenger delay. A Weight Shortest Processing Time first (WSPT) rule based heuristic algorithm is developed to solve the proposed model. The developed model is further incorporated in a rolling horizon framework to handle dynamic passenger arrivals during the disruption period. The effectiveness of the proposed strategy is demonstrated in comparison with alternative strategies in real-world case studies.     

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.     

Transit user perceptions of driverless buses

This paper reports the results of a stated preference survey of regular transit users’ willingness to ride and concerns about driverless buses in the Philadelphia region. As automated technologies advance, driverless buses may offer significant efficiency, safety, and operational improvements over traditional bus services. However, unfamiliarity with automated vehicle technology may challenge its acceptance among the general public and slow the adoption of new technologies. Using a mixed logit modeling framework, this research examines which types of transit users are most willing to ride in driverless buses and whether having a transit employee on board to monitor the vehicle operations and/or provide customer service matters. Of the 891 surveyed members of University of Pennsylvania’s transit pass benefit program, two-thirds express a willingness to ride in a driverless bus when a transit employee is on board to monitor vehicle operations and provide customer service. By contrast, only 13% would agree to ride a bus without an employee on board. Males and those in younger age groups (18–34) are more willing to ride in driverless buses than females and those in older age groups. Findings suggest that, so long as a transit employee is onboard, many transit passengers will willingly board early generation automated buses. An abrupt shift to buses without employees on board, by contrast, will likely alienate many transit users.