Traffic Information Provision Suitable for TV Broadcasting Basedon Macroscopic Fundamental Diagram from Floating Car Data
Ryota Horiguchi, Morihisa Iijima and Hisatomo Hanabusa

Abstract—This paper describes the feasibility study on the
traffic information provision which is suitable for TV
broadcasting by using floating car data (FCD). Recent
telematics services provide traffic information via on-board car
navigation units or portable navigation devices which facilitate
interactive use but for limited number of users. On the other
hand, the information provision via TV broadcasting has large
number of viewer and may seems have significant influence on
their travel behaviors especially in the case of singular traffic
conditions. However the way of expression of traffic
information via broadcasting has limitation in the interaction
and the sparse resolution on TV monitors. In this paper, we willpropose the mesh-wised traffic indices in terms of the fluidity
and the singularity in traffic conditions based on themacroscopic fundamental diagram (MFD) of traffic flows. Afterthe discussion on the theoretical framework, the preliminary
studies using taxi probe data in Tokyo will be presented.

I. INTRODUCTIONT

HIS paper describes the feasibility study on the traffic
information provision which is suitable for TV
broadcasting by using floating car data (FCD).
Recent telematics service provides traffic information via
an on-board car navigation unit or a portable navigation
device which facilitates interactive use. In Japan, carmanufacturers provide their own telematics services based on
FCD combining with VICS, the sensor based traffic
information system in Japan.
The information provision via a navigation unit producesmuch 'personalized' knowledge which reflects the user's
preference, alternative routes to the destination, vehicle
queues near the current position, etc. However, it is only
provided to the limited number of drivers who correctly telltheir destinations to the navigation units. Although there is no
statistics, it is believed that the number of such drivers issmall so that the influence of the telematics would be limited.
Another limitation of the present telematics is justproviding the information to the on-trip drivers who havealready chosen vehicles in place of the public transportation.
This means the present telematics does not reduce the traffic

demand. It is said the possible mitigation of traffic congestion
will not be high without any traffic demand management.
On the other hand, the information provision via TV
broadcasting has large number of viewer and may seems havesignificant influence on their travel behaviors. If traffic
information will be provided as well as the weather forecastin the morning news, many people will watch it in habit andwill consider the suitable transportation mode before theyleave home.
However the way of expression of traffic information via
broadcasting has limitations. Because of a lack of theinteraction, the displayed content of the traffic information
will be shared in public to exclude the dependence on thelocation, the travel purpose or the destination of each viewer.
Furthermore, since one broadcasting center covers wide
area as large as whole region or metropolis, the link-based
display like car navigation units becomes messy if we aregoing to stuff all of the link iformation on TV monitors withsparse resolution. The present traffic information provisionon TV uses of the deformed map image only covering
highways and major arterial roads, as shown in Fig. 1, but it
may lose plenty of the valuable information of the congestion
on surface streets. Even if we assume high density monitors
which can show the clear picture of whole road network, therich information may not always help the quick
comprehension of traffic conditions within the limited display
duration.
In this paper, let us propose the mesh-wised traffic
information which will be provided onto TV monitors for thequick comprehension of the rough skech of regional traffic
conditions. in terms of the fluidity and the singularity intraffic conditions for more suitable expression of urban traffic
conditions on TV monitors. In order to collect wider andmore precise traffic information as much as we can, the use of

Fig. 1. An example of the deformed map for the traffic information on
TV monitor (left), and the actual road network of the same region.

floating car data will be discussed for how to derive thoseindices. After the discussion on the theoretical framework,
the preliminary studies using taxi probe data in Tokyo will bepresented.
II. MESH-WISED TRAFFIC INFORMATION
A. Traffic Conditions Based on MFD estimated with FCD
The fundamental diagram (FD) of traffic flows is thewell-known relationship among the flow (q), the density (k)and the space-mean speed (v) of the traffic on a simple section.
It is frequently seen that q is approximated with the concave
function of k.
The idea of FD for the flow on a simple section can beextended to network flows. Daganzo formulated the idea as
macroscopic fundamental diagram (MFD) for homogenously
congested areas relating 'production' (Q: the product of
average flow and network length) and 'accumulation' (K: theproduct of density and network length) [1]. Theoretically, theMFD of a certain area will be found independently from thetravel demand. It is basically to be estimated with the travel
speeds of all vehicles running in the area, but it is difficult toknow them in practice. Even though we do not know the
movement of entire vehicles, however, Geroliminis andDaganzo [2] suggested MFD can be estimated from FCD
with the field experiment data in Yokohama.
To confirm how MFD will be estimated, we haveexamined with the FCD of taxis running on the surface streetsin Tokyo city center. The size of the area depends on thevolume of FCD and the homogeneity of the traffic condition.
If we use smaller mesh, the homogeneity will be higher but
the volume of FCD will be lower. This is undesirable forsteady service. Similar discussion can be found on theaggregation period. In the following study, let us use squaremesh of 1km in length and breadth and 1 hour aggregationinterval.
Fig. 2 shows the aggregated Q-K values for the weekdays
and the holidays in one mesh. The vertical axis (Q) represents
the total trip distance of whole floating cars, while theAggregated Q-K relationship in MFD（Tokyo Mesh#533936_00, 5:00~20:00）

Aggregated flow [veh*km/hr

8.0
7.0

Approximated curve for holidays

6.0
5.0
4.0
3.0
Approximated curve for weekdays

2.0
1.0
0.0
0.00

0.05

0.10

0.15

0.20

Area average density [veh]Weekdays

Holidays

y=-72.4x^2+41.9xy=-70.6x^2+48.1x

Fig. 2. The aggregated flow-density plot for the weekdays and thehorizontal axis (K) means the total travel time.
The number of the taxis operating as floating cars in Tokyo
city center was approximately 3000. In this case, we have
only used in-service taxi trips for a month. We have overlaid
the approximated quadratic curves, both of which show theconcave form. If those in-service taxi trips always represent
some constant portion of whole trips, the approximated curveof each day will be consistent with other days. However the
weekdays and the holidays apparently reveal different curves.
We may agree the proportion of the in-service taxis within thewhole traffic on weekdays will differ from the holidays. Thisimplies we have to prepare different MFDs for each day
according to the volume of the running floating cars.
It seems curious there are no plots in the congested area,
the right half side of the concave. This comes from two
possible reasons; 1) the in-service taxis have the tendency to
avoid congestion and can run faster than the other cars, or 2)
there are always non-congested sections in the area even in
the peak period and the aggregation including such section
will counterbalance the contribution of the congestion.
Although we cannot conclude the sufficient reason, it will beapproved that the MFD in the figure has the nature withwhich the ‘fluidity’ of the aggregated traffic condition
declines in proportion how it is far from the origin, since thetangent of each point on MFD means the average travel speed
in the area.
B. Concept of the Mesh-wised Traffic Information
The concept of the mesh-wised traffic information
provision is quite different from the conventional telematics
services. The conventional link-based traffic information will
be mainly used to estimate the travel time or to find better
alternative route to the destination with the aim to increase theusers' benefit.
On the other hand, the mesh-wised information does not
represent the traffic condition of any certain road but
quantifies the average fluidity and the singularity of thetraffic conditions for all roads in the mesh by using MFD. It isaiming to suppress the traffic demand by letting the people
recognize the whole picture of the real traffic condition andconsider ceasing driving when the traffic condition is heavy.
As for the mesh-wised traffic information, let us propose
two indices, the fluidity index and the singularity index.
1) Fluidity index
The fluidity index quantifies how close the aggregatedtraffic condition is to the origin of MFD. In place of using the
average travel speed in a mesh, the reason why we introduce
such quantification is the low sensitivity of the travel speed
on MFD. As we discussed in the previous section, theaggregated Q-K values mostly appear in the left half of thequadratic curve. The range of the travel speed may not widelyvary.
On the contraly, the Q-K values widely distributed along
the quadratic curve. The traffic condition far from the MFD
origin, i.e. with low fluidity index, may indicate some degreeof the congestion in the area. Fig. 3 shows an example of theFig. 4. Mesh-wised 'singularity' index at the same time of Fig. 3.

Fig. 3. Mesh-wised 'fluidity' index in Tokyo city center.

fluidity index of each mesh in Tokyo city center. The redcolor means low fluidity with heavy congestion and the blue
color does high fluidity. People will see the distribution of thecongestion over the city and may roughly understand thetraffic condition around their habitat or business places.
2) Singularity index
In order to understand the traffic condition correctly, it isimportant to know not only how congested but also how
different from the ordinary. For this purpose, let us introduce
another index to highlight the singularity of the traffic
condition of the mesh. The singularity index is an extensionof the quantity of information for traffic congestion proposedby Horiguchi [3] which calculates the entropy of theaggregated traffic condition of certain time period according
to the probability density function of traffic conditions.
Even though a mesh has low fluidity index at certain time,
it may have low singularity index when the extent of thecongestion is ordinary level for that time. If the mesh has highfluidity index to the contrary, it may have high singularity
when the traffic is unusually light because of theextraordinary demand reduction in some disasters orincidents.
Fig. 4 shows an example of the mesh-wised singularity
index at the same time of Fig. 3. In this picture, the red color
means high singularity and the blue means low. By
comparing those two pictures, people will see how thecongestion in the south area of Tokyo is extraordinary.
C. Operation on the Aggregated Q-K plot on MFD
In order to quantify the aggregated Q-K condition on MFD
in terms of the fluidity and the singularity, let us propose thefollowing operation.
1) Approximation with quadratic curve
For the first step, let us approximate the aggregated Q-Kvalues with concave function in order to represent the'average' relationship. In this case, we borrow the quadratic
curve from the Greenshield's formula [4], i.e.
Q  aK 2  bK (a  0, b  0)
Where, Q : aggregated flow

(1)

K : aggregated densitya, b: parameters
The parameters a and b are determined to minimize thesquare error between the approximated curve and the values.
It is said the Greenshield’s formula does not describe
traffic accurately especially for heavy congestion. However,the distribution of the aggregated traffic conditions will not
spread over the heavy congested area, as shown in Fig. 2, theuse of the quadratic formula may be less problematic and let
us allow to take the advantage of the easiness for theoperation described later.
2) Transformation of Q-K plot
The singularity index intends to express how rare a traffic
condition is with the entropy in the information mathematics.
For the calculation of the entropy, we need to know the
probability density function of traffic conditions.
However, it is difficult to identify the function for theaggregated Q-K values which distributes around the concave
curve. Therefore, let us allow to transform Q-K plot onto well
posed two-dimensional normal distribution which is suitable
for the entropy calculation.
In this study, we introduce ‘t’-axis in accordance with thequadratic curve and ‘d’-axis meaning the distance from thequadratic curve. For the preparation, the quadratic function(1) is transformed to the parametric expression (2).
b K   a t(2)
2
Q  b t 2  taHere, t is the parameter changing along the quadratic curvewith the range [0, 1]. The point where 't = 0' is the origin andthe point where 't=1' is the right intercept on k-axis.
Let us next introduce the scaling factor s to modify thequadratic curve as follows.
b K   a st(3)
2
Q  b s t 2  t

a









For given point (Ki, Qi), we may calculate si to let thescaled curve pass the point and ti corresponding to the pointon the scaled curve as follows.
Qi
(4)
si 
2
aK i  bK iti 

a 2 K i3  abK i2
 bQi

(5)

Then find the point (K*i, Q*i) of which t-parameter is equals
to ti on the original quadratic curve with the equation (2).
We may now calculate the distance di between (ki, qi) and(k*i, q*i) with the following equation.



2



 4a

a

d i   i  K i  t i   
Qi  4 t i2  t i 
2
b


b

1
i  
 1

2

(6)

( si  1)( si  1)

2

Fig. 5 illustrates the operation described with the equations(1)-(6). Fig. 6 shows the transformed plot from Q-K onto t-dplane according to each time of day. By introducing thosetransformations, we may approximate the t-d plot of eachtime with two-dimensional normal distribution.

Q
t=0.5

Q=si(aK2+bK)

2

Q=aK +bK(Ki, Qi)(si, ti)di(K*i, Q*i)(1, ti)

t=0

t=1
-b/a

-b/2a

d: difference fron approx. curv

0.4
0.2
0.0
0.05

0.1

0.15

0.2

0.25

-0.4
-0.6
t: fluidity
5~7am

7~11am11am~3pm

3~7pm

7~9pm

Fig. 6. The transformed t-d plot from Q-K values for the weekdays.

2(8)

Where, t, d : the mean values of t and d,t, d : the unbiased standard deviations of t and d,: the correlation coefficients between t and d.
For given (ti,di), the generation probability P(ti,di) is
calculated as the integral of p(t,d) around (ti,di). Here, let us
allow the approximation as the equation (9) by taking the tiny
widths t and d to avoid the complication in the integral of
the normal distribution.
(9)Pt i , d i   p t i , d i td (0  t  1, 0  d  1)
The singularity index Ii for (ti,di) is now given by theentropy of P(ti,di) as follows.
I i   log P t i , d i (10)From the definition of entropy, Ii will be larger when thegeneration probability p(ti,di) is getting small.
III. CASE STUDIES IN TOKYO CITY CENTER

Transformation of MFD onto t-d space(weekdays, mesh#533936_00)-0.2

 t  t 
2  (t   t )(d   d )  d   d 



 
    t d d t exp
 2(1   2 )K

Fig. 5. Transformation of aggregated Q-K values to t-d values.

03) Calculation of fluidity index
The parameter t represents the extent how far from theorigin of MFD along the approximated curve. Within therange [0, 1], 't=0' means 'no traffic', 't=1' means 'fully jammed'
condition, and 't=0.5' means 'critical' condition. It is obvious
as the t-value gets higher, the fluidity of the traffic will besmaller. Therefore, let us introduce the fluidity index f as
follow;f  1 t(7)4) Calculation of singularity index
In order to quantify the singularity of the traffic condition,
let us regard that the t-d plot of each time of day follows thetwo-dimensional normal distribution p(t,d) represented by theequation (8).
1p t , d  2 t  d (1   2 )0.3

For the demonstration purpose, the fluidity and thesingularity indices were calculated for some interested days.
In the following examples, we have used the FCD ofapproximately 3000 in-service taxis operating in the Tokyo
city center. The FCD from the empty trips and the traverse on
expressways were filtered.
The period of the data collection is from September toNovember in 2009. Same as the example in the chapter II, thesize of the mesh is 1 km in length and breadth and theaggregation period is 1 hour. The meanings of the color are
also the same as well. For convenience, only major arterial
roads are figured on the pictures of mesh-wised indices toknow the location of the map.
Fig. 7 is an example for the 'ordinary' weekday (Wed. Oct.
7, 2010). We may see, from the fluidity pictures in the upper
row, the congestion arises at around the fringe of the city
center (8~9 am) at first, then penetrates into the center later

a) Fluidity Index

7~8am

8~9am

9~10am10-11am

7~8am

8~9am

9~10am10-11amb) Singularity Index

Fig. 7. The fluidity and the singularity indices for the 'ordinary' weekday (Wed., Oct. 7, 2010)a) Fluidity Index

7~8am

8~9am

9~10am10-11am

7~8am

8~9am

9~10am10-11amb) Singularity Index

Fig. 8. The fluidity and the singlarity indices for the 'singlar' day that the typhoon hits Japan (Thu., Oct. 8, 2010)(9~10 am). The movement of the congestion well fits to ourknowledge about the commuting travel demand.
On the other hand, from the singularity pictures in thelower row, we may not find any significant area where thehigh singularity meshes are concentrated. This implies thecongestion in Fig. 7 was almost 'average' level.
Fig. 8 shows the indices for the next day of Fig. 7. In themorning on this day, the Typhoon No.18 hit Japan and many
trains suspended the service because of the strong wind.
Especially, the railway lines which had to pass the bridges on
the river in the eastern part of Tokyo were suspended longtime after the typhoon had gone.
The fluidity index for this situation shows serious
congestion widely spreading over the Tokyo city center in themorning peak period. The singularity index highlights thatthe congestions in the eastern part and the southern part wereextraordinary.
Fig. 9 shows the indices for the day of the Tokyo City
Marathon was held. More than 30,000 runners started fromthe western part at 9 am and were running in all over the
Tokyo city center. As the race proceeded, the roads were
gradually closed to exclude vehicles.
In this case, the singularity index highlights the congestionin Asakusa area surrounded by the red circles. The east end of
this area is bounded by Sumida River. Therefore, the drivers
who pass through this area had less alternative routes andmight cause unusual congestion comparing with the otherarea on the marathon course.

a) Fluidity Index

Start

Goal

11~10am12~1pm

1~2pm

2~3pm

11~10am12~1pm

1~2pm

2~3pm

b) Singularity Index

Fig. 9. The fluidity and the sigularity indices for the 'singlar' day that the Tokyo City Marathon was held. (Sun., Mar. 22, 2009)

IV. CONCLUSIONSIn this paper, we have proposed the mesh-wised
measurement index in terms of the fluidity and the singularityof the area traffic conditions based on the macroscopic
fundamental diagram. The fluidity index quantifies how
smooth the traffic in the area flows and the singularity index
shows how extraordinary the traffic condition from theaverage.
For the purpose of demonstration, we have studied thefluidity and the singularity indices for a couple of interestdays by using the FCD with more than 3000 in-service taxis
operating in the Tokyo city center. The case study
demonstrates that the mesh-wised fluidity index can express
the rough distribution of congestions over the city and thesingularity index can highlight the unusually congested area
because of whether anomalies, big events, etc.
We believe that the mesh-wised traffic information will be
more preferable for the broadcasting on TV than theconventional link-wised traffic information in terms of thearea-wide comprehension of congestion. It will affect thetravel behaviors of huge number of people to avoid the car
use in the extraordinary traffic condition.
There are, however, some remaining issues. The mostessential one is the validity of the mesh-wised traffic
information. It is possible that taxi trips may not be
representative for entire trips. For this issue, the mesh-wised
indices with taxi are to be compared with the ones withpassenger car in order to be checked the correspondency
between them.
Another one would be the discussion on the suitable
resolution in terms of mesh size and aggregation time period.
The resolution should be fine as much as possible to know the
dynamic changes in queue building up or resolving. However,

too fine resolution troubles the steadiness of information
provision. We have used 1 km square mesh and 1 houraggregation period in this study, but it is not a generalsolution.
Our future works will concern with the following tasks;
1) The aggregation of traffic conditions to distinguish thedirection of traffic.
2) Data fusion with the other spatial data source such aswhether, accident reports, etc. to interpret the traffic
conditions.
3) Statistical analysis to find the similarity on the changing
pattern of the index for the preparation of 'traffic forecast'service.
ACKNOWLEDGMENT
We would like to thank Mr. Kobayashi in Japan
Broadcasting Company (NHK) for his valuable suggestions.
Also thank Fujitsu Ltd. to provide us their taxi prove data forthe research use.
REFERENCES
[1]

[2]

[3]

[4]

C. F. Daganzo, “Urban gridlock: macroscopic modeling and mitigation
approaches,” Transportation Research B 41, 49-62; “corrigendum”
Transportation Research B 41, 379, 2007.
N. Geroliminis and C. F. Daganzo, “Existence of urban-scale
macroscopic fundamental diagrams: some experimental findings,”
Working paper, Volvo Center of Excellence on Future Urban Transport,
Univ. of California, Berkeley, 2007.
R. Horiguchi and K. Wada, "Effective probe data transmittal with
detection of congestion pattern," Proceedings of 11th World Congresson Intelligent Transport Systems, Nagoya, October, 2004.
B. D. Greenshields, "A study of traffic capacity," Highway Research
Board Proceedings 14, 1935, pp. 448-477.