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M.Gh. Negoita et al. (Eds.): KES 2004, LNAI 3215, pp. 88–94, 2004.

© Springer-Verlag Berlin Heidelberg 2004

Bus Arrival Time Prediction Method for

ITS Application

Bongsoo Son1, Hyung Jin Kim1, Chi-Hyun Shin2, and Sang-Keon Lee3

1Dept. of Urban Plannung and Engineering, Yonsei University, Seoul, Korea

{sbs,hyungkim}@yonsei.ac.kr2Dept. of Transportation Engineering, Kyonggi University, Kyunggi-do, Korea

[email protected] Research Institute For Human Settlements, Kyunggi-do, Korea

[email protected]

Abstract. It is known that stoppage times at signalized intersections cause the

biggest errors in bus arrival time prediction for real-time Bus Information Sys-

tem (BIS) services and no particular method is proven successful so far. This

study developed a prediction method that compares the predicted bus travel

times from bus stop to the stop line at signalized intersections by using Kalman

filtering technique with the state of green time indications of traffic signals, and

then incorporates possible stoppage into a next link travel times. From field

surveys and in-lab simulation, the proposed method was found superior to otherconventional techniques showing an average of more than 200% improvement

in prediction accuracy.

1 Introduction

In 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 periodbetween 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.

Time

Distance

Bus Stop

i-2

Bus Type I Bus Type II Bus Type IIICar

Bus Stop

i

Signal

i-1

Time

Distance

Bus Stop

i-2

Bus Type I Bus Type II Bus Type IIICar

Bus Stop

i

Signal

i-1

Fig. 1. Time-space diagram for bus trajectories

Figures 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 bycomparing 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.



B. Son et al.90

0:00:00

0:00:43

0:01:26

0:02:10

0:02:53

8 : 0 0 : 1 0

8 : 0 6 : 0 3

8 : 1 4 : 3 7

8 : 1 8 : 0 9

8 : 2 7 : 2 1

8 : 3 6 : 2 1

8 : 4 5 : 0 1

8 : 5 2 : 3 7

8 : 5 6 : 5 5

9 : 0 2 : 4 3

9 : 0 9 : 0 1

9 : 1 3 : 0 0

9 : 2 1 : 1 0

9 : 2 9 : 3 7

9 : 3 5 : 5 1

9 : 4 6 : 3 7

9 : 4 9 : 5 5

9 : 5 7 : 4 9

1 0 : 3 7 : 2 0

1 0 : 4 5 : 4 8

1 0 : 5 1 : 3 8

1 1 : 0 2 : 5 7

1 1 : 0 8 : 5 2

1 1 : 1 9 : 3 8

1 1 : 2 5 : 3 1

1 1 : 3 1 : 3 7

1 1 : 4 2 : 2 1

1 1 : 4 8 : 0 3

Fig. 2. Real data for bus travel times between bus stop i-2 and traffic signal i-1

0:00:00

0:00:43

0:01:26

0:02:10

0:02:53

8 : 0 0

: 1 4

8 : 0 8

: 1 8

8 : 1 5

: 2 6

8 : 2 2

: 1 8

8 : 3 5

: 2 9

8 : 4 8

: 0 2

8 : 5 6

: 5 8

9 : 0 2

: 2 5

9 : 0 9

: 4 6

9 : 1 8

: 4 0

9 : 2 7

: 1 0

9 : 3 7

: 4 8

9 : 4 6

: 5 4

9 : 5 4

: 4 0

1 0 : 3 1 : 4 0

1 0 : 4 0 : 3 4

1 0 : 4 9 : 3 1

1 0 : 5 7 : 0 8

1 1 : 0 6 : 0 6

1 1 : 1 7 : 2 4

1 1 : 2 5 : 5 4

1 1 : 3 1 : 4 2

1 1 : 4 2 : 2 3

1 1 : 4 8 : 5 6

Fig. 3. Real data for bus travel times between traffic signal i-1 and bus stop i

2 The Prediction Method

The 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)




Stop line

GPS Signal

Reception error range

Bus stop

Stop line

GPS Signal

Reception error range

Bus stop

Fig. 4. Data transmitting no des and concept of links

The 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 procedure



B. Son et al.92

Time-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 nextlink 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 Set

The 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 consecutivelinks 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-1

Number of bus line Arrival time Number of busline Arrival time

Travel time

from bus stop

i-2 to si nal i-1

333 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 0:02:12116-3 8:12:29 116-3 8:14:30 0:02:01

57 8:14:37 57 8:14:56 0:00:19




The 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 Test

For 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’ performances

PeriodError

Indices

Moving

Average

Exponential

SmoothingARIMA

Kalman

Filtering

Proposed

Method

MRE 0.1814 0.1809 0.1929 0.1280 0.0416

RSE 0.2163 0.2220 0.2232 0.1584 0.0586Peak

a.m. 8:00~9:00

MAX 0.5703 0.5849 0.6424 0.3256 0.1400MRE 0.2118 0.2121 0.2022 0.1395 0.0430

RSE 0.2461 0.2461 0.2416 0.1727 0.0546

Non-peak

a.m.

10:30~11:30 MAX 0.6503 0.6056 0.6289 0.4449 0.1069



B. Son et al.94

Since 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 Conclusion

BIS 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 thereliability 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.

References

1. 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.

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