Prediction Model of Bus Arrival and Departure Times Using AVL and APC Data

The emphasis of this research effort was on using AVL and APC dynamic data to develop a bus travel time model capable of providing real-time information on bus arrival and departure times to passengers (via traveler information services) and to transit controllers for the application of proactive control strategies. The developed model is comprised of two Kalman filter algorithms for the prediction of running times and dwell times alternately in an integrated framework. The AVL and APC data used were obtained for a specific bus route in Downtown Toronto. The performance of the developed prediction model was tested using “hold out” data and other data from a microsimulation model representing different scenarios of bus operation along the investigated route using the VISSIM microsimulation software package. The Kalman filter-based model outperformed other conventional models in terms of accuracy, demonstrating the dynamic ability to update itself based on new data that reflected the changing characteristics of the transit-operating environment. A user-interactive system was developed to provide continuous information on the expected arrival and departure times of buses at downstream stops, hence the expected deviations from schedule. The system enables the user to assess in real time Journal of Public Transportation, Vol. 7, No. 1, 2004 4 2 transit stop-based control actions to avoid such deviations before their occurrence, hence allowing for proactive control, as opposed to the traditional reactive control, which attempts to recover the schedule after deviations occur. Introduction Recently, a growing interest has been developing in various Advanced Public Transportation Systems (APTS) solutions that mainly aim at maximizing transit system efficiency and productivity using emerging technologies. Examples of such advanced technologies include Automatic Vehicle Location (AVL) and Automatic Passenger Counting (APC) systems. Several researchers (Kalaputapu and Demetsky 1995; Lin and Zeng 1999; Wall and Dailey 1999) have used AVL (and less often APC) data to develop models specifically for bus travel time prediction. The motivation for developing these models was mostly for providing information to transit riders on expected bus arrival times with virtually no sensitivity of such models to operations control strategies. Thus, these models included very simple independent variables such as historical link travel times, upstream schedule deviations, and headway distributions, in addition to the current location of the next bus. This study develops a dynamic bus arrival/departure time prediction model, using AVL and APC information, for dynamic operations control and dissemination of real-time transit information. The study is part of a larger project that aims at developing an integrated system for dynamic operations control and real-time transit information. Currently, almost all transit operators implement control strategies, such as bus holding and expressing, after detecting schedule/headway deviations in the system, hence reactive in nature. The proposed system (shown in Figure 1) takes a proactive approach to operations control that would enable the controller to implement preventive strategies before the actual occurrence of deviations. This innovative approach requires the use of arrival/departure time models sensitive to the considered control strategies (mainly stop-based strategies). This research study focuses on developing a model of such characteristics. Prediction Model of Bus Arrival and Departure Times Using AVL and APC Data 4 3 Figure 1. Integrated Operations Control and InformationDissemination System Data The data used for this study were collected from bus route Number 5 in the Downtown Toronto area in May 2001. The route length is approximately 6.5 km, spanning 27 bus stops in each direction, 6 of which are time-point stops located at points of high passenger demand (e.g., major intersections). The route starts at the Eglinton subway station stop in the north and ends at the Treasury stop in the south during the morning peak period. At the other times of the day, the route ends further south at the Elm stop. There are 21 signalized intersections along the route, 10 of which are actuated SCOOT system signals. The schedule headway during the AM and PM peak periods is 12 minutes, increasing to 30 minutes during off peak. For the duration of the study (five weekdays in May 2001), the Toronto Transit Commission (TTC) assigned 4 buses to the route, each fitted with a GPS (Global Positioning System) receiver and an APC (Automatic Passenger Counter). Each time the bus stopped, the bus location was recorded using the GPS receiver. Also, the numbers of passengers boarding and alighting at bus stops were recorded using the APC. The route was segmented into 5 links in each direction, with each link starting and ending at two consecutive time-point stops. The Journal of Public Transportation, Vol. 7, No. 1, 2004 4 4 links range from 0.40 to 1.7 km in length, depending on the spacing between the time-point stops, and may include 2 to 8 minor bus stops. This study focused on modeling travel times along those links for the morning peak-hour bus operation. Approach As implied earlier, most of the models found in the literature (e.g., Kalaputapu and Demetsky 1995; Lin and Zeng 1999; Wall and Dailey 1999; Farhan et al. 2002) have included bus dwell times along any link in the travel time of that link (i.e., link travel time includes running plus dwell times). As such, these models cannot consider explicitly the effect of late or early bus arrivals at bus stops on the dwell times at those stops and vice versa. Ignoring such relationship yields these models insensitive to the effects of variations at upstream bus stops, such as demand surge, bus holding strategy, and bus expressing strategy, etc., on downstream bus arrivals and subsequent dwell times. The approach taken in this study addresses this issue. Conceptual Framework The link running time and bus dwell time are modeled separately in this study but in a consistent single modeling framework. It is assumed that real-time information on vehicle location, numbers of boarding and alighting passengers at bus stops, and bus arrival and departure times is known from the AVL and APC systems. The prediction modeling system consists of two separate algorithms, each based on the Kalman filter method. To predict the bus running time along a particular link at instant k+1, the first algorithm, Link Running Time Prediction Algorithm, makes use of the last three-day historical data of the bus link running time for the instant of prediction k+1, as well as the bus link running time for the previous bus on the current day at the instant k. The study used data for the previous three days only as this was deemed practical, given the limited historical data available for the study. Obviously, in real-world applications, the algorithm can make use of longer ranges of historical data. The second algorithm, Passenger Arrival Rate Prediction Algorithm, employs similar historical data of passenger arrival rate. To predict the dwell time at a particular stop, the predicted arrival rate is simply multiplied by the predicted headway (i.e., the actual arrival time of the last bus minus the predicted arrival time of the next bus) and by the passenger boarding time (assumed 2.5 seconds per passenger). Prediction Model of Bus Arrival and Departure Times Using AVL and APC Data 4 5 Separating the bus dwell time prediction from bus running time prediction in this modeling framework enhances the model’s ability to capture the effects of lateness or earliness of bus arrivals at stops on the bus dwell time at those stops, and hence the bus departure from such stops. This is simply because bus dwell time at a stop is affected by the actual arrival time of the bus at that stop, particularly for high frequency transit routes where passengers are expected to arrive at a nearly constant rate (i.e., the later the bus, the longer the dwell time and vice versa). In addition, since the model treats dwell time separately, it is sensitive to stop-based control strategies such as bus holding and expressing. In order to better understand the prediction-modeling framework, Figure 2 shows a schematic of a hypothetical transit route. The route is divided into a number of links between bus stops. When the transit bus n leaves stop i, the actual departure time is known from the AVL system. At this instant, the Kalman filter prediction algorithm for link running times will predict the next link running time RTn (i,i+1). Subsequently, the predicted arrival time of the bus at the downstream bus stop i+1 can be determined. Figure 2. Schematic of a Bus Route with Several Stops Assuming that bus n is currently at stop i AT n (i+1) = DT n (i) +RT n (i,i+1) (1)