SHORT TERM TRAVEL TIME PREDICTION USINGCUMULATIVE TRAFFIC COUNTS AND UPLINK INFORMATIONCOLLECTED ON EXPRESSWAYS
Hironobu Otaka
Department of Engineering, Japan Highway Public Corporation
3-3-2 Kasumigaseki Chiyoda-ku Tokyo, 100-8979, Japan
TEL +81-3-3506-0404, FAX +81-3-3506-8870
E-mail: hironobu.otaka@jhnet.go.jp
Ryota Horiguchi
Representative Director
i-Transport Lab. Co., Ltd
2-12-404 Ageba-cho Shinjuku-ku Tokyo, 162-0824, Japan
TEL/FAX +81-3-5261-3077
E-mail: horiguchi@i-transportlab.jp
Hirokazu Akahane
Professor
Department of Engineering, Chiba Institute of Technology
2-17-1 Tsudanuma Narashino Chiba, 275-8588, Japan
TEL +81-47-478-0444, FAX +81-47-478-0474
E-mail: akahane(at)ce.it-chiba.ac.jp

ABSTRACTThis paper proposes a methodology to predict travel time in short term using uplinkinformation of equipped vehicles. The prediction is based on a simple queuing model, ofwhich traffic conditions are defined with two cumulative traffic flow curve at upstream anddownstream ends of roads. The downstream cumulative curve is drawn with traffic counter,and the upstream curve, as the imaginary cumulative flow curve, is derived by horizontallyshifting the downstream curve with the section travel time. Both cumulative curves can bepredicted by using historical data. A couple of methods to predict cumulative curve areproposed in the paper. The performance of proposed prediction methods are validated
through the experiments with observed data, which is collected on Keiyo-Road in Chiba.

INTRODUCTION
This research develops a methodology to predict travel time in short term using uplinkinformation of equipped vehicles. Travel information system on the expressways in Japannow provides travel times of major designated sections at every five minutes based on
detector speed information. The travel times are so-called ‘instantaneous’ travel time thatare simple accumulations of the travel times of ‘unit sections’ at the present time and areprovided to drivers through variable message signs (VMSs).
1

Figure.1 Ex. The travel time provided a driver through variable message signboard
Travel times of a unit section, which is covered by one detector, are estimated by assuming
uniform travel speed measured by the detector. However, the travel times may include someerror against the actual travel time, because the traffic conditions of the unit section may not
be uniform in real.
Nowadays, the ETC (electronic toll collection system) was installed on the expressway inJapan. If the issues on privacy are solved, we may expect to utilize uplink information to
identify individual vehicle for the purpose of the road administration. It must be moreaccurate to measure the section travel times with uplink information than the detector-basedones.
We have, so far, examined the advantages of uplink-based travel times over detector-based
travel times [1] and concluded that uplink-based travel times are much robust for the sizes ofunit sections than the detector-based travel times. For example, through the experiment on
Keiyo-Road, the uplink-based travel times with a long unit section of which length is 13km
will be accurate as much as the detector-based travel time with unit sections of 3km.
It is, however, pointed out that instantaneous travel times are another problems. It will differ
from the actual travel time when the traffic congestion is changing the status of itself. Thereis some time lag between the times when a driver receives information at the upstream end of
subjective section and when he/she reaches the tail of the congestion section. During thetime lag, the traffic condition may not be the same as the previous status, on which the
instantaneous travel time provided to the driver is based. This difference is coming from theintrinsic nature of instantaneous travel time and may not be removed unless the predictedtravel times are provided to the driver at the upstream end.

2VMS to provide the travel time
Traffic FlowSection ASection B

Section C

5min.

5min.

5min.

10:05

5min.

5min.

5min.

10:10

5min.

5min.

10min.

10:00(Present)

Time

Provided Travel
Time Information“15min.”Need to predict
Experienced
Travel Time
“20min.”Traffic Jam

Figure.2 Ex. Difference between actual travel time and provided information
In this paper, we will introduce a basic concept of travel time prediction at first. The
prediction is based in on simple queuing model, of which the status is determined with two
cumulative traffic flow curve at upstream and downstream ends. The downstream
cumulative curve is drawn with traffic counter, and the upstream curve, as the imaginary
cumulative flow curve, is derived by horizontally shifting the downstream curve with thesection travel time. Both cumulative curves can be predicted by using historical data.
The detail of the prediction methodology is described at second. A couple of methods topredict cumulative curve is proposed in the following chapters. Then the performance ofproposed prediction methods are validated through the experiments with observed data, whichis collected on Keiyo-Road in Chiba. At the end of this paper, we will conclude thecommendable prediction method and will state the future scope.

PROPOSED METHODOLOGIES OF PREDICTIONOUTLINE OF THE PREDICTION BASED ON QUEUING MODEL
The idea of travel time prediction [2] is based on queuing model, of which status isdetermined by two cumulative flow curves, the arrival curve A = {Ai | i = 0, 1, ...} at theupstream section and the departure curve D = {Di | i = 0, 1, ...} at the downstream section, as
shown in Figure 3Figure 3. Assuming flow conservation row, the vertical distance Nj of twocurves means the number of vehicles existing in-between two sections at time tj. Under
first-in-first-out principle, the horizontal distance Tj means the section travel time of which thevehicle arriving at the upstream section at time tj will take. Similarly, T’k , which is equal toTj, is denoted as the travel time of which the vehicle leaving out of this section at time tk hastaken. In this paper, let us call Tj as ‘arrival-based’ travel time to be predicted. On theother hand, T’j is called ‘departure-based’ travel time, which can be measured at every timeperiod.
Simple way to obtain two cumulative flow curves is to install traffic counters at both upstream
and downstream ends. It is, however, difficult to precisely estimate section travel time
because it is hard to adjust vertical levels of two 'independent' cumulative curves. When
there are some resource or sink of traffic flow within the section, the flow conservation row
will not observed any more; i.e. Nj is not equal to (Aj - Dj). Even though there are no3

resources or sinks, it is often the case that some errors may be included in each traffic countdata. The flow conservation row may not be always guaranteed with the real world data.
Upstream end

Downstream end

Cum. # of vehicles

Travel time service section

Upstream end
ADownstream end
D

Tj= T’kNjtjtkt
Time of day

Figure 3: Queuing status described by two cumulative curves.
Instead of using traffic counters at both ends, let us premise the sensor configuration as shownin Figure 4Figure 4. The sensor installed at upstream end works as a beacon that collects
uplink information to identify individual vehicle. The downstream sensor has the functionof a traffic counter and a beacon to collect uplink information, while the upstream sensor has
only the function of beacon. We may know the travel time of individual vehicle by matching
uplink information at these two sections.

Travel time service section

Traffic counter+ Uplink beacon
Downstream end

Uplink beacon
Upstream end

Figure 4: Sensor configuration assumed in this research.
With this sensor configuration, we may generate 'imaginary' cumulative flow curve of theupstream section with the subsequent procedure illustrated in Figure 5Figure 5.
i)ii)Plot the current value of the cumulative departure traffic count Dk at the downstream
section. Here, tk means the present time.
Measure the ‘departure-based’ travel time T'k by the recent uplink pairs.
4iii)

iv)

Shift Dk, the current point of D to the left (= past) by T'k, and obtain the latest point on'imaginary' arrival curve A'k. Remember that A'k represents not the present data but thesome past data.
Repeat i) - iii) for m times, where m means the number of data used for the prediction
method explained later. Then the imaginary arrival curve A' = {A'i | i = k, k-1, ...,k-m+1} is obtained

Cum. # of vehicles

Travel time mesured byuplink pairs
T’k

A’k

Dk

Imaginary curve at
upstream end
A’D

Measured curve at
downstream endttk

Time of day (discrete)

PresentFigure 5: Generation of imaginary arrival cumulative curve at upstream end.
Once the imaginary arrival cumulative curve A' is obtained, we may predict ‘arrival-based’
travel time Tk by extending two cumulative curves. The procedure of the prediction isdescribed below (Figure 6Figure 6).

Cum. # of vehiclesiii) Obtain the predicted traveltime Tk at present time.

Tki) Predict Ak at the presenttime tk.
T’kii) Predict D upto the same
cumulative counts of Ak .

A’DkTime of day (discrete)tPresent

Figure 6: Travel time prediction based on the prediction of two cumulative flow curves.
i)Since A' was estimated at the past time (tk - T'k), extend A' to the present time tk withsome time-series prediction technique, and obtain the predicted cumulative vehicle5ii)iii)

count Ak at the upstream end.
Then, extend D up to the same level of cumulative vehicle count Ak with the same
prediction method.
The horizontal distance of two predicted cumulative curve can be regarded as thepredicted ‘arrival-based’ travel time Tk at the present.

METHODOLOGIES TO PREDICT TIME SERIES DATA
There are some available methods to be applied for the prediction of cumulative flow curves.
In this research, the following three methods are evaluated of their prediction performance.
AUTO-REGRESSION (AR) MODEL
AR model predicts the future value of traffic flow q1 from the past time series {q0, q-1, ...
q-m+1, } with the following linear summation function.
q1 = a0 q0 + a1 q-1 + ... + am-1 q-m+1(eq.1)

Here, {ai | i = 0, 1, ..., m-1} are AR-coefficients to be estimated by, for instance, Levinson'salgorithm. The number of data m is to be determined so as to well approximate the futurevalue.
HISTORICAL PATTERN MATCHING
This method uses the most "similar" historical traffic flow data in place of today's future
traffic flow data. The similarity is evaluated with the distance between the two vectors,
today's observed traffic flow data and past flow data, as shown in Figure 7.
Time range to be compared
Traffic Volume

Time range to be compared

Present

Time of day

Traffic Volumei) search the most similar pattern
2) use the searched historical patternin substitute of the future value.

Time of day< predicted pattern >< historical patterns >Figure 7: Prediction using historical pattern matching

TEMPLATE PATTERN OF DAILY TRAFFIC FLOW + AR MODEL
This method applies AR-model to the differential data that subtracts "template" traffic flow
pattern from today's traffic flow, as shown in Figure 8. The template flow pattern isprepared for each day type, e.g. weekdays and holidays, by calculating the average ofhistorical traffic flow data.

6

Traffic Volume

The predictedtraffic volume

Template
pattern
Difference from template
pattern and real data /predicted of traffic volume

Present

Time of dayFigure 8: Prediction using template pattern of daily traffic flow + AR model

EXPERIMENT OF PREDICTION WITH OBSERVED DATA
In order to validate the proposed methods, the proposed methods are applied to the observed
data collected on Keiyo-Road in Chiba Prefecture. The length of the subjective section
where the travel times provided is approximately 13km, from Chiba-nishi toll barrier (TB) toFunabashi TB. The detector data at Funabashi TB and the uplinks of ETC equipped vehicles
from Chiba-nishi TB to Funabashi TB are collected for about 1 month. During this period,
the portion of the vehicles with on-board ETC equipments was 6% to the total throughput
traffic volume.
The result of some questionnaire survey says that the most of drivers with popular trip
distance may accept the error of predicted travel time within plus/minus 10minites.
Therefore, as shown in Table 1, the performance of each prediction method is evaluated interms of ‘hitting ratio’, which means the expectation whether the difference between thepredicted travel time and the 'arrival-based' travel time may be less than the allowable time, 5minutes and 10 minutes here. As a reference, the performances of the detector based travel
time are included in the table, which accumulates each travel time of 1km unit sections
estimated with detector speed and is currently provided on Keiyo-Road.
Table 1: Comparison of hitting ratio of each prediction method.
Size ofunit
section(a) AR Model(b) Pattern Matching(c) Template Pattern+ AR Model(Reference)
Detector based travel
time.

13km

1km

within5min.

within10min.

Medium - heavycongestion
withinwithin5min.
10min.

83％

94％

72％

91％

89％

98％

82％

97％

94％

99％

90％

98％

93%

99%

89%

98%

Light - heavy congestion

It is found that “(c) Template Pattern + AR Model” method are the best among the other7

methods. Figure 9 illustrates the predicted traffic flows with the method (c). The
prediction performance of traffic flow affects on the preciseness of the predicted travel time.
We may confirm the method (c) reasonably predicts the future traffic flows in the range
forward 5 - 60 minutes.

Traffic volume( unit/5min.)](c) Template Pattern + AR Model350

the truth
After 5min.
After 15min
After 30min
After 60min300250
200
150
100

0

0:00
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00

50

Figure 9: Predicted traffic flows with "template + AR-model" (18/10/2003)

Even though the prediction method use only two sensors at the upstream and the downstream
sections, the hitting ratio is better than "Detector-based travel time", which uses 13 detectors.
We may expect to reduce the construction and the maintenance cost of ATIS by using uplinkinformation and prediction methodology, while keeping the quality of the provided travel timeinformation.

CONCLUSION
This paper proposed the methodology to predict travel time in short term using uplinkinformation of equipped vehicles and traffic volume collected on Expressways. A couple ofmethods to predict travel times are proposed in this paper, and we conclude "template pattern+ AR-model" shows the satisfactory performance through the experiment with observed dataon Keiyo-Road. For the next stage, we will focus on the operational issues of the proposed
method, e.g. prediction under incidental situation, model fitting to seasonal fluctuations, etc.

REFERENCES[1] R. Horiguchi, et. al: “Analytical study on the accuracy of travel time measured with uplinkinformation”, Proceedings of 23rd Annual Meeting of Japan Society of Traffic Engineers,
2003. (in Japanese)[2] R. Horiguchi, H. Otaka, H. Akahane: “Short term travel time prediction using cumulative
traffic counts and uplink information collected on expressways”, Proceedings of 2nd ITS
Symposium in Japan, 2003. (in Japanese)8