Time control point strategy coupled with transfer coordination in bus schedule design

A schedule consisting of an appropriate arrival time at each time control point can ensure reliable transport services. This paper develops a novel time control point strategy coupled with transfer coordination for solving a multi‐objective schedule design problem to improve schedule adherence and reduce intermodal transfer disutility. The problem is formulated using a robust mixed‐integer nonlinear programming model. The mixed‐integer nonlinear programming model is equivalently transformed into a robust mixed‐integer linear programming model, which is then approximated by a deterministic mixed‐integer linear programming model through Monte Carlo simulation. Thus, the optimal scheduled arrival time at each time control point can be precisely obtained using cplex . Numerical experiments based on three bus lines and the mass rapid transit system in Singapore are presented, and the results show that the schedule determined using the developed model is able to provide not only reliable bus service but also a smooth transfer experience for passengers. Copyright © 2016 John Wiley & Sons, Ltd.     

Real-time control of buses for schedule coordination at a terminal

Recently, bus transit operators have begun to adopt technologies that enable bus locations to be tracked from a central location in real-time. Combined with other technologies, such as automated passenger counting and wireless communication, it is now feasible for these operators to execute a variety of real-time strategies for coordinating the movement of buses along their routes. This paper compares control strategies that depend on technologies for communication, tracking and passenger counting, to those that depend solely on local information (e.g., time that a bus arrived at a stop, and whether other connecting buses have also arrived). We also develop methods to forecast bus arrival times, which are most accurate for lines with long headways, as is usually the case in timed transfer systems. These methods are tested in simulations, which demonstrate that technology is most advantageous when the schedule slack is close to zero, when the headway is large, and when there are many connecting buses.     

The impact of real-time information on bus ridership in New York City

In the past few years, numerous mobile applications have made it possible for public transit passengers to find routes and/or learn about the expected arrival time of their transit vehicles. Though these services are widely used, their impact on overall transit ridership remains unclear. The objective of this research is to assess the effect of real-time information provided via web-enabled and mobile devices on public transit ridership. An empirical evaluation is conducted for New York City, which is the setting of a natural experiment in which a real-time bus tracking system was gradually launched on a borough-by-borough basis beginning in 2011. Panel regression techniques are used to evaluate bus ridership over a three year period, while controlling for changes in transit service, fares, local socioeconomic conditions, weather, and other factors. A fixed effects model of average weekday unlinked bus trips per month reveals an increase of approximately 118 trips per route per weekday (median increase of 1.7% of weekday route-level ridership) attributable to providing real-time information. Further refinement of the fixed effects model suggests that this ridership increase may only be occurring on larger routes; specifically, the largest quartile of routes defined by revenue miles of service realized approximately 340 additional trips per route per weekday (median increase of 2.3% per route). Although the increase in weekday route-level ridership may appear modest, on aggregate these increases exert a substantial positive effect on farebox revenue. The implications of this research are critical to decision-makers at the country’s transit operators who face pressure to increase ridership under limited budgets, particularly as they seek to prioritize investments in infrastructure, service offerings, and new technologies.     

Hybrid model for prediction of bus arrival times at next station

Effective prediction of bus arrival times is important to advanced traveler information systems (ATIS). Here a hybrid model, based on support vector machine (SVM) and Kalman filtering technique, is presented to predict bus arrival times. In the model, the SVM model predicts the baseline travel times on the basic of historical trips occurring data at given time‐of‐day, weather conditions, route segment, the travel times on the current segment, and the latest travel times on the predicted segment; the Kalman filtering‐based dynamic algorithm uses the latest bus arrival information, together with estimated baseline travel times, to predict arrival times at the next point. The predicted bus arrival times are examined by data of bus no. 7 in a satellite town of Dalian in China. Results show that the hybrid model proposed in this paper is feasible and applicable in bus arrival time forecasting area, and generally provides better performance than artificial neural network (ANN)–based methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Attitudes of bus operators towards real-time transit information tools

Although it is apparent that providing useful information has a positive effect on transit riders, no studies to date have investigated bus operators’ reactions to real-time arrival information and other potential rider information tools. In this study, the project team surveyed 253 bus operators to determine their views and values concerning the existing use of real-time information and to ask about future transit rider information applications. Almost all operators (93 and 91 % on two separate questions) were positive or neutral to the provision of real-time information. In addition, operators were receptive to building other new information applications, with all applications in the survey being supported by at least 60 % of the bus operators. The two most widely supported potential applications in the survey were additional tools to help blind and deaf-blind riders (89 % of bus operators favored) and an application that would aid riders in identifying physical stop, shelter and bus issues such as graffiti, broken parts or a need for lights (88 % of bus operators). Applications displaying data about past performance or current bus capacity received the least support (66 and 61 % respectively). This research gives a better understanding of the impact of rider information tools on bus operators, including the views and values of the operators, and the harms and benefits of such tools.     

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.     

An analysis of the commuter departure time decision

Transportation planners and transit operators alike have become increasingly aware of the need to diffuse the concentration of peak period travel in an effort to improve gasoline economy and reduce peak load requirements. An evaluation of the potential effectiveness of strategies directed to achieve this end requires an understanding of factors which affect commuter trip timing decisions. The research discussed in this article addresses this particular problem through the development and estimation of a commuter departure time (to work) choice model.A number of conclusions were drawn based on the departure time model results and related analyses. It was found that work schedule flexibility, mode, occupation, income, age, and transportation level of service all influence departure time choice. The uncertainty in work arrival time and the consequences of various work arrival times may also be determinants of commuter departure time choice.The estimated model represents improvements over previous work in that it more explicitly considers work arrival time uncertainty and travelers' perceived loss associated with varying work arrival times, and additional socio-demographic factors which can potentially affect departure time choice. Furthermore, the estimated model includes consideration of transit commuters, in addition to single occupant auto and carpool work travelers. The inclusion of transit commuters represents a particularly important contribution for policy analysis, since the model could potentially be used to study the effect of service and employment policies on transit system peak load requirements.     

Bus arrival time prediction at bus stop with multiple routes

Provision of accurate bus arrival information is vital to passengers for reducing their anxieties and waiting times at bus stop. This paper proposes models to predict bus arrival times at the same bus stop but with different routes. In the proposed models, bus running times of multiple routes are used for predicting the bus arrival time of each of these bus routes. Several methods, which include support vector machine (SVM), artificial neural network (ANN), k nearest neighbours algorithm (k-NN) and linear regression (LR), are adopted for the bus arrival time prediction. Observation surveys are conducted to collect bus running and arrival time data for validation of the proposed models. The results show that the proposed models are more accurate than the models based on the bus running times of single route. Moreover, it is found that the SVM model performs the best among the four proposed models for predicting the bus arrival times at bus stop with multiple routes.     

Bus running time prediction using a statistical pattern recognition technique

Abstract

Given that real-time bus arrival information is viewed positively by passengers of public transit, it is useful to enhance the methodological basis for improving predictions. Specifically, data captured and communicated by intelligent systems are to be supplemented by reliable predictive travel time. This paper reports a model for real-time prediction of urban bus running time that is based on statistical pattern recognition technique, namely locally weighted scatter smoothing. Given a pattern that characterizes the conditions for which bus running time is being predicted, the trained model automatically searches through the historical patterns which are the most similar to the current pattern and on that basis, the prediction is made. For training and testing of the methodology, data retrieved from the automatic vehicle location and automatic passenger counter systems of OC Transpo (Ottawa, Canada) were used. A comparison with other methodologies shows enhanced predictive capability.     

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.     

Bus arrival time calculation model based on smart card data

Bus arrival time is usually estimated using the boarding time of the first passenger at each station. However, boarding time data are not recorded in certain double-ticket smart card systems. As many passengers usually swipe the card much before their alighting, the first or the average alighting time cannot represent the actual bus arrival time, either. This lack of data creates difficulties in correcting bus arrival times. This paper focused on developing a model to calculate bus arrival time that combined the alighting swiping time from smart card data with the actual bus arrival time by the manual survey data. The model was built on the basis of the frequency distribution and the regression analysis. The swiping time distribution, the occupancy and the seating capacity were considered as the key factors in creating a method to calculate bus arrival times. With 1011 groups of smart card data and 360 corresponding records from a manual survey of bus arrival times, the research data were divided into two parts stochastically, a training set and a test set. The training set was used for the parameter determination, and the test set was used to verify the model’s precision. Furthermore, the regularity of the time differences between the bus arrival times and the card swiping times was analyzed using the “trend line” of the last swiping time distribution. Results from the test set achieved mean and standard error rate deviations of 0.6% and 3.8%, respectively. The proposed model established in this study can improve bus arrival time calculations and potentially support state prediction and service level evaluations for bus operations.     

Optimal slack time for timed transfers at a transit terminal

At transit terminals where two routes interchange passengers, total system costs may be reduced by allowing some “slack” time in the vehicle schedules to decrease the probability of missed connections. Transfer cost functions are formulated and used to determine optimal slack time for simple systems with transfers between one bus route and one rail line. Some analytic results are derived for empirical discrete and Gumbel distributions of bus arrival times. Relations between the optimal slack times and headways, transfer volumes, passenger time values, bus operating costs, and standard deviations of bus and train arrivals are also developed numerically using normally distributed arrivals. However, the proposed numerical approach can optimize slack times for any observed arrival distributions. The results provide some guidelines on desirable slack times and show that schedule coordination between the two routes is not worth attempting when standard deviations of arrivals exceed certain levels. Possible extensions of this work are suggested in the last section.     

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.     

An application-oriented model of passenger waiting time based on bus departure time intervals

This paper develops an application-oriented model to estimate waiting times as a function of bus departure time intervals. Bus stops are classified into Type A and B depending on whether they are connected with urban rail transit systems. Distributions of passenger arrival rates are analyzed based on field data for Beijing. The results indicate that the best fits for the distribution of passenger arrival rates for Type A and B bus stops are the lognormal distribution and gamma distribution, respectively. By analyzing relationships between passenger arrival rates and bus departure time intervals, it is demonstrated that parameters of the passenger arrival rate distribution can be expressed by the average and coefficient of variation of bus departure time intervals in functional relationships. The validation shows that the model provides a reliable estimation of the average passenger waiting time based on readily available bus departure time intervals.     

Metro disruption management: Optimal initiation time of substitute bus services under uncertain system recovery time

Determining the initiation time of substitute bus (SB) services is critical for metro disruption management, especially under uncertain recovery time. This study develops a mathematical formulation to determine the optimal initiation time (OIT) of SB services by trading-off their initiation cost and passenger delay cost, thereby minimizing the total system cost. Given the probability distribution of metro disruption duration, we determine the OIT by formulating an optimization problem to minimize the expected total system cost. We then conduct sensitivity analyses of the initiation cost of SB services, passenger value of time, and SB services rate. The results show that SB services ought to be activated only if the metro incident lasts longer than a certain time interval, depending on the factors mentioned earlier, and the OIT should advance with the predicted incident duration. This paper derives analytical results for the case of linear passenger arrival, and determines the results numerically for the case of non-linear passenger arrival when analytical closed-form solutions are not available. The findings will facilitate transit operators to develop response plans in the aftermath of a metro disruption.     

Dispatching control at transfer stations in multi‐hub transit networks

Among dispatching control approaches, the holding option has attracted the most attention in bus control. However, holding a vehicle at a transfer station may exacerbate the delays because more passengers might accumulate at downstream stations and may also affect other connecting routes at other transfer stations. Our problem is to minimize the total costs of dispatching ready vehicles at each transfer station along coordinated routes in a multi‐hub transit network. The total costs include the waiting cost for on‐board passengers, the missed connection costs for late arrival passengers at the subject transfer station and possible transfer costs at downstream transfer stations. We develop a heuristic algorithm to optimize the holding times based on real time information about late vehicles. The results show that ready vehicles should be held longer when the arrival variances of late vehicles are small or when many late connecting passengers are expected.     

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.     

Investigating the impact of stochastic vehicle arrivals to optimal stop spacing and headway for a feeder bus route

Stop spacing and service frequency (i.e., the inverse of headway) are key elements in transit service planning. The trade‐offs between increasing accessibility and reducing travel time, which affect transit system performance, need to be carefully evaluated. The objective of this study is to optimize stop spacing and headway for a feeder bus route, considering the relationship between the variance of inter‐arrival time (VIAT), which yields the minimum total cost (including user and operator costs). A solution algorithm, called successive substitution, is adapted to efficiently search for the optimal solutions. In a numerical example, the developed model is applied to planning a feeder bus route in Newark, New Jersey. The results indicate that the optimal stop spacing should be longer that those suggested by previous studies where the impact of VIAT was ignored. Reducing VIAT via certain operational control strategies (i.e., holding/stop‐skipping, transit signal priority) may shorten stop spacing and improve accessibility. Copyright © 2014 John Wiley & Sons, Ltd.     

Bus rapid transit operation analysis using the Downs–Thomson paradox

The purpose of the paper is to analyze effectiveness before and after implementation of the bus rapid transit operation. The paper includes a speed analysis based on the Downs–Thomson paradox, and a reliability analysis based on variance analysis of arrival time. According to the speed analysis, some road sections are now under phase 2 in the Downs–Thomson paradox, which is a state in which the bus speeds are greater than the auto speeds. In the future, it is predicted that autos and buses will reach an equilibrium speed which is in phase 3 of the multi‐modal equilibrium theory. According to the reliability analysis of arrival time at each bus stop, in roads of median arterial bus lanes, the variance of arrival time is generally smaller than after the scheme implemented in 8 months later. Copyright © 2010 John Wiley & Sons, Ltd.     

A hybrid scheme for real‐time prediction of bus trajectories

The uncertainty associated with public transport services can be partially counteracted by developing real‐time models to predict downstream service conditions. In this study, a hybrid approach for predicting bus trajectories by integrating multiple predictors is proposed. The prediction model combines schedule, instantaneous and historical data. The contribution of each predictor as well as values of respective parameters is estimated by minimizing the prediction error using a linear regression heuristic. The hybrid method was applied to five bus routes in Stockholm, Sweden, and Brisbane, Australia. The results indicate that the hybrid method consistently outperforms the timetable and delay conservation prediction method for different route layouts, passenger demands and operation practices. Model validation confirms model transferability and real‐time applicability. Generating more accurate predictions can help service users adjust their travel plans and service providers to deploy proactive management and control strategies to mitigate the negative effects of service disturbances. Copyright © 2017 John Wiley & Sons, Ltd.