bus arrival time prediction method for its application

Bus Arrival Time Prediction Method forITS ApplicationBongsoo Son1, Hyung Jin Kim1, Chi-Hyun Shin2, and Sang-Keon Lee31Dept. of Urban Plannung and Engineering, Yonsei University, Seoul, Korea{sbs,hyungkim}@yonsei.ac.kr2Dept. of Transportation Engineering, Kyonggi University, Kyunggi-do, Koreachshin@kyonggi.ac.kr3Korea Research Institute For Human Settlements, Kyunggi-do, Koreasklee@krihs.re.krAbstract. It is known that stoppage times at signalized intersections cause thebiggest errors in bus arrival time prediction for real-time Bus Information Sys-tem (BIS) services and no particular method is proven successful so far. Thisstudy developed a prediction method that compares the predicted bus traveltimes from bus stop to the stop line at signalized intersections by using Kalmanfiltering technique with the state of green time indications of traffic signals, andthen incorporates possible stoppage into a next link travel times. From fieldsurveys and in-lab simulation, the proposed method was found superior to otherconventional techniques showing an average of more than 200% improvementin prediction accuracy.1 IntroductionIn order to combat the ever-increasing congestion in urban area, traffic officials and agencies have embraced Intelligent Transportation Systems (ITS) and technologies in a proactive, systematic way. In recent years interests has grown for granting preferen-tial service to public transport such as buses, since it is desirable to favor public transit over private auto travel due to the basic role of public transport in the city. A number of different public bus preferential treatments have been implemented in many urban areas around the world to offer better service to public buses than private autos. Among bus preferential schemes such as bus gate, bus malls, bus lanes, BIS, bus pri-ority signals, etc., bus information system is one utilized in many cities to balance public and private transport. In fact, the availability of accurate, real-time information is especially useful to operators of vehicle fleets as well as passengers.However, BIS has not much impacted on the reliability of bus arrival time infor-mation. The reason for uncertainty in predicted arrival times of public buses in BIS are waiting times for green phase at the signalized intersections, dwell-times at bus stops, delays resulted from incidents, and so on. Reliability of prediction has increased recently through numerous prediction methods that try to take some of these reasons into considerations [1, 2].Bus Arrival Time Prediction Method for ITS Application 89 As can be seen from Figure 1, it is well known that waiting times at the signalized intersection cause major errors in forecasting of bus arrival times. In the figure, bus travel trajectories between bus stop i-2 and bus stop i are not constant. More specifi-cally, bus type I is associated with the buses arrived at the traffic signal i-1 during the red time period. Bus type II represents the buses arrived at the signal during the period between ending of red time and beginning of green time and experienced delay for passing the traffic signal. Bus type III is related to the buses passed the traffic signal without any delay. The three types of bus trajectories indicate that the bus arrival times at bus stop i are widely different and greatly dependent upon whether or not buses await at traffic signal i-1, so bus travel times between the two bus stops significantly vary depending upon the state of signal i-2.Fig. 1. Time-space diagram for bus trajectoriesFigures 2 and 3 show the bus travel times measured between bus stop i-2 and traf-fic signal i-1 and between traffic signal i-1 and bus stop i, respectively, during the same time period. The bus travel times between bus stop i-2 and traffic signal i-1 are severely fluctuated, while those between traffic signal i-1 and bus stop i are relatively somewhat stable. The main cause of travel time fluctuation is the fact how long the bus does wait at traffic signal i-1. From the two figures, it is very clear that that waiting times at the signalized intersection cause major errors in forecasting of bus arrival times.Up to date there is no practical and easy method that accounts for the impact cre-ated by traffic signal operation along the bus routes. This paper is an attempt to im-prove the reliability of predicted bus travel time in urban signalized intersection net-works. In the paper, we have come to the result that we can figure out the waiting times at signalized intersections under the Time-Of-Day (TOD) type operation by comparing the state of signals at that very instant if the bus arrival times at the stop line of a signalized intersection are reasonably estimated. The prediction method is described below. The data for this paper came from several sources: specific sources will be given when individual data are discussed in Section 3.90B. Son et al.Fig. 2. Real data for bus travel times between bus stop i-2 and traffic signal i-1Fig. 3. Real data for bus travel times between traffic signal i-1 and bus stop i2 The Prediction MethodThe method proposed in this paper is based upon two forecasted link travel times of buses: one from a bus stop to a stop line of intersection and another from the stop line to the next downstream bus stop which is supposed to display the remaining time until a next bus of a particular bus line arrives. Conventional techniques have usually con-sidered the distance between two successive bus stops as one link. (See Figure 4)Bus Arrival Time Prediction Method for ITS Application 91GPS SignalThe information of local bus arrival times between consecutive bus stops needed for the prediction of link travel times can be obtained from ITS devices such as GPS devices with wireless data communication modules atop buses. Then, the GPS based modules have an electronic road map and do map-match for bus stops in order to transmit data. Each link travel time is predicted using Kalman Filtering in which state equations by time are formulated [3]. A particular concern is the link travel time from signalized intersections to immediate downstream bus stop for which two state equa-tions were developed to differentiate signal-awaiting trips at the signalized intersec-tions from non-stop trips.The computer algorithm used for this method works on a rigid space-time grid. For the analysis, the site interested are broken into sections bounded by grid points {i, i-1, . . . , i-n} located at each bus stop and at each stop line of signalized intersection a shown in Figure 2. The computational procedure starts at the most upstream point of the site interested, and works downstream (i.e., the bus traveling direction).Figure 5 is a schematic diagram of the computational procedure. In the figure, amount of waiting times at each signalized intersection can be estimated by comparing the predicted bus arrival times at the subject stop lines with the state of signals (i.e., Fig. 5. Schematic diagram of bus travel time computation procedureB. Son et al.92Time-Of-Day signal operation time schedule) at that very instant. For the TOD type signalized intersection, the signal operation time schedules are readily available from the traffic officials and agencies. When stopping at signal is anticipated, the waiting time is then added to the next link travel time that is also predicted. Otherwise, the predicted bus arrival time is determined by the next link travel time, where the next link travel time can be estimated based on the information associated with the pro-ceeding buses traveled on the downstream link at the same time period.3 The Data SetThe study site is located near Seoul Metropolitan Area. The study site is an 8-lane busy urban arterial highway and approximately 2 km long with four bus stops and three-signalized intersections. The route is therefore segmented into 6 links with consecutive links sharing start and end nodes. The links range from 0.3 to 1.0 km in length. A total of sixteen different bus- lines are in operation along this route. Among them, three bus-lines are currently in BIS service.Table 1. Real data set for the bus arrival times collected from the field by manual Bus stop I – 2 Traffic signal i-1Number of bus line Arrival time Number of buslineArrival timeTravel timefrom bus stopi-2 to signal i-1333 8:00:00 333 8:02:06 0:01:56 51 8:00:28 51 8:02:19 0:01:51 820 8:00:37 820 8:02:20 0:01:43 57 8:00:56 57 8:02:28 0:01:32 736-1 8:03:27 736-1 8:05:27 0:02:00 700 8:04:58 700 8:05:38 0:00:40 1116 8:05:40 1116 8:06:00 0:00:20 333 8:06:03 333 8:08:18 0:02:15 220 8:06:22 220 8:08:27 0:02:05 51 8:08:53 51 8:09:16 0:00:23 17 8:11:39 17 8:14:18 0:02:39 220 8:11:54 220 8:12:09 0:00:15 820 8:12:11 820 8:14:23 0:02:12 116-3 8:12:29 116-3 8:14:30 0:02:01 57 8:14:37 57 8:14:56 0:00:19Bus Arrival Time Prediction Method for ITS Application 93The GPS data for the real time bus locations for the three bus-lines were obtained from SK-Entrac that the private agency provides BIS service in Korea. For the other bus-lines, the bus arrival times at signalized intersections and bus stops were directly collected from the field by manual for the three weekdays from October 14, 2003 to October 16, 2003 during the time period from 08:00 to 12:00. The signal operation time schedules were obtained from the police station. It should be noted that the signalized intersections are operated and/or controlled by the police in Korea.Table 1 shows real data set for the bus arrival times collected at two consecutive bus stops during the peak time period between 08:00 and 08:15. Average headway of buses during peak period between 08:00 and 10:00 is 44 seconds, and 57 seconds during non-peak period between 10:30 and 12:00.4 Validation TestFor the model validation test, the accuracy of the results obtained from the proposed method was measured by using three statistical errors such as Mean Relative Error (MRE), Root Squared Error (RSE) and Maximum Relative Error (MAX). Besides, the performances of proposed method were compared with those of four conventional methods such as 1) moving average method, 2) exponential smoothing method, 3) autoregressive moving average method (ARIMA) and 4) Kalman Filtering method. For these purposes, predicted bus arrival times obtained by using the four conven-tional techniques and the proposed method were compared with observed arrival times obtained from the field measurements.The results for the statistical analysis of the five methods were summarized in Table 2. As shown in the table, the proposed method is superior to the four conven-tional methods showing an average of more than 200% improvement in prediction accuracy. Among the conventional methods, Kalman Filtering method has produced the better results than the other three methods. The other methods show the same level of prediction performances in terms of statistical accuracy.Table 2. The statistical analysis results for the prediction techniques’ performancesPeriodError IndicesMoving Average Exponential Smoothing ARIMAKalman Filtering ProposedMethodMRE 0.1814 0.1809 0.19290.12800.0416 RSE 0.2163 0.2220 0.22320.15840.0586 Peak a.m. 8:00~9:00MAX 0.5703 0.5849 0.64240.32560.1400 MRE 0.2118 0.2121 0.20220.13950.0430 RSE 0.2461 0.2461 0.24160.17270.0546 Non-peak a.m. 10:30~11:30MAX0.6503 0.6056 0.62890.44490.1069B. Son et al.94Since most of signalized intersections along urban streets operate with cycle lengths of 120 seconds or more, the instance of waiting for the next green phase or non-stop passage of buses at critical intersections would create difficulty in bus arrival time forecasting efforts. It was concluded that the proposed method can offer prompt bus arrival time to bus passengers waiting at bus stops with relatively higher accuracy. Applicability of the proposed model is considered much higher in non-peak time and nighttime BIS service operation.5 ConclusionBIS is one utilized in many cities to balance public transport and private transport. The availability of accurate, real-time information is especially useful to operators of vehicle fleets as well as passengers. However, BIS has not much impacted on the reliability of bus arrival time information. It is well known that waiting times at the signalized intersection cause major errors in forecasting of bus arrival times. This paper is an attempt to improve the reliability of predicted bus travel time in urban signalized intersection networks. The emphasis of the proposed method is on estimat-ing waiting times at signalized intersections under the TOD type operation by compar-ing the state of signals at that very instant.The performances of the method proposed in this paper were measured by using three statistical errors such as MRE, RSE, and MAX. The performances of proposed method were also compared with those of four conventional methods by using the observed arrival times obtained from the field measurements. The proposed method is superior to the four conventional methods showing an average of more than 200% improvement in prediction accuracy. Among the conventional methods, Kalman Filter-ing method has produced the better results than the other three methods.References1.Wei-Hua Lin and Jian Zeng, “An Experimental Study on Real Time Bus Arrival Time Pre-diction with GPS Data”, Virginia Polytechnic Institute and State University, 1999.2.Amer Shalaby and Ali Farhan, “Bus Travel Time Prediction Model for Dynamic Opera-tions Control and Passenger Information System”, Transportation Research Board, 2003. 3.Grewal, M.S. and Andrews, A.P., “Kalman Filtering Theory and Practice”, Prentice Hall,1993.。