An Analysis of Traffic BreakdownPhenomena Using a Platoon-

based Traffic Flow Model

Kyoto University Yasuhiro SHIOMI

30/6/2009 The Joy of the Journey:Celebrating the Life and Work of Ryuichi Kitamura

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Contents of my talk

1. The reason why I choose Kitamura sensei

2. Current research related to Kitamura sensei- Research of my colleagues- My PhD studies

3. The influence and teach of Kitamura sensei

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Self Introduction

Apr, 2000 Kyoto University

Apr, 2001 First meeting with Kitamura sensei(in the class, “Statistics”)

Oct, 2002 Second meeting with Sensei(in the class, “Traffic Engineering”, co-organized by Prof. Iida)

Apr, 2003 Join “Kitamura Lab.”

Apr, 2004 Graduate school of Engineering, Kyoto University

2005-2007 TA of Sensei class (“Traffic Management Engineering”)

Sep, 2008 Doctor of Engineering, Kyoto University(Supervised by Kitamura sensei)

Oct, 2008- Assistant Professor, Kyoto University (ITS Lab.)

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Why I choose “Kitamura Lab” ?

(Choosing Kitamura lab is the best decision I have ever made.)

“I was interested in urban problems, especially in transportationsystem.”

“I knew Kitamura sensei and Kikuchi sensei, who was assistantprofessor in Kitamura lab. “

Inspiration

Because …

The member of Kitamura lab. 2003

Yusak

Doctor

Senbil YanoArief Arthit Hashiue Ikeda Maeda

M2

Nishiuchi

Researcher

Bayarma Matsuda Nishino

MurakamiAshikawa Hara Ushiwaka Pirapol Nakano Nakamura

M1

InagakiAssoc. Prof. Yoshii Assist. Prof. Kikuchi

Secretary

Prof. Kitamura

B4

ShiomiSakamoto Koi Hanada Yamaoka

STAFF

A study for the amusement activitiesin the public realm by the suburbs residence

(2001)

Kei Maeda

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A study for the amusement activitiesin the public realm by the suburbs residence

Maeda

u What makes our life “true” well-being?u The death of suburban residential area.à The necessity of “Oldenburg’s the third place”

u Analyzing Keihanshin area-PT data (1990)u Questionnaire for customers of “Izakaya (pubs)” in urban andsuburban area.

Hypothesis Suburbs, where “Oldenburg’s the third place” arelacked, are not attractive place for resident.

Conclusion2. In reality, suburban residence had lessamusement activities due to time constraint.

1. Some “Oldenburg’s third place” could be foundalso in suburban area.

A study on the perception of the publicspace in the city

(2003)

Risa Koi

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A study on the perception of the public spacein the city

Koi

u In typical suburban area, some public space where thecommunity and social welfare can mature were equipped.u There are fewer social welfare and community in suburban areas.

u “Public” = Diversity in (people + faculty + activity) + Historyu Questionnaire asking which factors affect the cognition of “public”feeling.

Hypothesis People never aware the “public” feelings in thesuburban areas.

Typical urban areaTypical suburban area

A study on the perception of the public spacein the city

Koi

Hypothesis People never aware the “public” feelings in thesuburban areas.

Conclusion

2. Residence in suburban area were less sociablethan in urban area.

1. Residence in urban area tend to perceive urbanspace as “public”, whereas residence in suburbanarea tend to perceive suburban area as “public”.

u In typical suburban area, some public space which can createcommunity and social welfare were equipped.

u There are few social welfare and community in suburban areas.

Worldviews, lifestyle and sustainability:A search for a primordial determinant of

environmental friendliness(2005)

Kyotaro Sakamoto

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Worldviews, lifestyle and sustainability:A search for a primordial determinant of

environmental friendlinessSakamoto

WorldviewsAn individual’s way of thinking and attitude, whichhave strong influence to the social recognition andbehavior

FatalistIndividuals

Egalitarian Hierarchistu Questionnaire about worldviewsand attitude towards transportation,environment, residential area andsociety was done in some areas

1. Strong relationship between individuals’worldviews and attitudes towards residential area.

2. The utility of market research for public worksbased on the worldviews was discussed.

Conclusion

Platoon-based Traffic Flow Model toEstimate Traffic Breakdown Probability

on Freeway Bottlenecks

Kyoto University Yasuhiro SHIOMIKyoto University Toshio YOSHII

Kyoto University Ryuichi KITAMURA

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9/24/2008 at Kitamura sensei’s office

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Background (i)-Traffic Capacity

u In reality, this is not so simple issue….

u “Traffic Capacity” is defined as the maximum number of vehiclesthat can pass a point per unit of time.

In this concept, traffic congestion occursonly when traffic demand exceeds the maximum flow rate.

Planning Design Operation

u “Traffic Capacity” has played important roles in...

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Background(ii)-Stochastic Phenomena

u “Traffic Breakdown” occurs stochastically to the traffic volume.

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20

40

60

80

100

120

0

150

300

450

7 8 9 10 11 12

Time

15m

in

-ave

rage

spee

d[k

m/h

]

15m

in

-tra

ffic

volu

me

[pcu

/15m

in/l

ane]

traffic volume

15 min average speed

free flow

congested flow

Transition from non-congested stateto congested state

The traffic volume can bestochastically defined

*Divided-two lane section in Tokai-hokuriku Expressway, 48.43 kp (2003)Traffic Volume [veh/hour]

Rela

tive

Freq

uenc

yof

Traf

ficBr

eakd

own

[%]

10

0

30

20

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Probability ofbreakdown

Traffic volume0Traffic

CapacityTraffic

Capacity

Increase the trafficcapacity (Ex. Add a lane)

1.0

Decrease thebreakdown probability

(Ex.???)

Background(iii)-Stochastic Capacity

u The concept of “stochastic capacity/ breakdown probability” havebeen suggested. (Brilon et al. (2005), Kuhne (2007) and so on…)

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Probability ofbreakdown

Traffic volume0Traffic

CapacityTraffic

Capacity

Increase the trafficcapacity (Ex. Adda lane)

1.0

Decrease thebreakdown probability

(Ex.???)

Objective of this study

u The concept of “stochastic capacity/ breakdown probability” wassuggested. (Brilon et al. (2005), Kuhne (2007) and so on…)

To investigate new freeway operation schemesbased on the concept of stochastic capacity

To establish the traffic flow modelrepresents traffic breakdown stochastically

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Viewpoint of this study (i) - Heterogeneity

Heterogeneity of vehicles in traffic flow

u Why does traffic phenomena have stochastic nature???

u Desired speeds vary among vehicles.ex) Trucks or sports cars

Young drivers or senior driversWith time limit or without time limit

Desired Speed: the speed a driver would choosefor a certain section without any obstacles.

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Viewpoint of this study (ii) - Platoons

Time

Space

0

LA platoon of four vehicles

u Due to the desired speed distribution,platoons are formed in stochastic manner.

Viewpoint of this study (iii) - Platoons

Deceleration wave can propagate upstream, whichcauses traffic breakdown.

Deceleration wave will not propagate upstream.Small Platoons

Bottleneck

Large Platoons

Bottleneck

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u It is pointed out that platoons cause traffic breakdown (e.g. Koshi, 1986)

Each platoon has breakdown probability,influenced by its platoon size.

CONJECTURE

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Frameworks of this study

Platoon-breakdownprobability

- Road structural condition- Traffic inflow rate- Desired speed distribution

INPUTS OUTPUTSStochastic capacityTraffic Inflow Rate

vsBreakdown Probability

Platoon condition at bottlenecks- Platoon size- The speed of a lead vehicle

Estimation

Platoon behaviormodel

Platoon formationmodelInverse

estimation

Summary of the result

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p Breakdown probability to the traffic inflow rate was defined.p Desired speed distribution was estimated in unbiased way.

• Reducing the variance of DSD and installing pace cars areeffective way to reduce breakdown probability.

• The relationship between traffic flow rate and breakdownprobability could be explained by desired speed distribution.

0

0.25

0.5

0.75

1

1500 1600 1700 1800

Brea

kdow

npr

obab

ility

Inflow rate[veh/h]

No pace car

Pace car with 60km/hone per ten vehicles

Pace car with 70km/h,one per the vehicles

Improve thetraffic breakdown

Kitamura sensei’s teaching

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p In many cases, I could not answer correctly.

p To think by myself is worth. Just “information” is meaningless.

“What is traffic capacity?”“What is traffic congestion?“

“What is a platoon?“

p Through the PhD research,“what I was asked by Kitamura sensei” are…

Impressive talk of Kitamura sensei

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p At the end of his class, “traffic management engineering”, forbefore under graduate 3rd year students, 2006.

p Fortunately, I joined his class as a teaching assistant.

Kitamura sensei to the student in the class:

“In the future when you become a civil engineer and engage in landdevelopment, please keep this promise at least:

don’t cut this existing tree. ”

“

”

Thank you for your attention.

Assumptions in traffic flow

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Platoon formation model

Exit

EntrancetimeT6T1 T2 T3 T4 T5

A platoon

L

Trajectory

Inputs Desired speed distribution

Each vehicle’s entrance time

v6v1 v2 v3 v4 v5The desired speedis given randomly

Following vehicleFreely driving vehicle

If the vehiclecatches up with a

front vehicle, itmust follow at the

same speed

Platoon Formation

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p This model outputs “lead vehicle speed and platoon-size distribution”

Platoon formation model

[ ] )()()|(Prob 1 vpvpvf,kv klead

ii −⋅⋅= â

)|( âvf : PDF of desired speed distribution (parameter vector β)

: Probability that k-1 vehicles catch up with a vehicle atspeed v

)(1 vpk−

: Probability that a vehicle with DS v becomes the lead)(vplead

()Τϕ/Φ41 20.64 Τφ1 0 −0 1 359.04 230.96 Τµ ()∏ ∫∞

=

∞

=

−1 ,

)()(k

vd

lead

kii

duufvp

()Τϕ/Φ41 18.06 Τφ1 0 −0 1 334.56 90.08 Τµ ()

()Τϕ/Φ41 18.06 Τφ1 0 −0 1 492.72 120.8 Τµ ()

⋅

= ∫∏ ∫+

+

−

=

∞

−

vdk

jvdk

iki

iji

duufduufvp,

, 0

1

11 )()()(

di,i-k(v): Variable related toinflow rate andthe bottleneck outflow rate

Desired speed distribution

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p The parameter vector β can be estimatedby applying maximum likelihood estimation

()Τϕ/Φ41 36.55 Τφ1 0 −0 1 400.32 331.04 Τµ ()[ ]∏=

==N

iii kvL

1

* |~

,~Probmaxarg âââ

iv~

: the size of the observed platoon i

N : Observed number of platoons

ik~

: the speed of the lead vehicle of the observedplatoon i

Platoon formation model

Assumptions in platoon flow

Traffic detector

vtopvtop v2 f(vtop)v2 v3 f(v2)vtop

• Assumption 1: Speed transition within a platoon can betreated as Markov Chain

• Assumption 2: Traffic Breakdown à under 40 km/h

Speed Transition Probability Matrix29

Platoon behavior model

=

nnnn

n

SSSSSS

SSSSSS

ppp

ppp

L

MOMM

L

L

10

11101

001

P ()Τϕ/Φ41 40.39 Τφ1 0 −0 1 551.52 168.8 Τµ ()()Τϕ/Φ41 40.39 Τφ1 0 −0 1 655.92 168.8 Τµ ()11,1, ePp −⋅= kleadlead

plt vkvp

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Description of breakdown probability

()Τϕ/Φ41 33.23 Τφ1 0 −0 1 167.28 397.28 Τµ ()[ ]{ } ()Τϕ/Φ41 45.09 Τφ1 0 −0 1 597.84 397.28 Τµ ()()Τϕ/Φ41 45.09 Τφ1 0 −0 1 754.8 397.28 Τµ ()∑ ∑ ⋅⋅⋅=i v

leadplt

leadplt

leadBD

top

ivpivtQivQP Pââ |,,,|,ProbN|

• Breakdown probability at a bottleneck can be expressed as:

Where,

: Time of a platoon with (vlead, i) to pass through a BN()Τϕ/Φ41 53.71 Τφ1 0 −0 1 196.32 94.64 Τµ ()ivt leadplt ,

[ ]∑ ∑

⋅

=

i v

Qivi

QN

,|,Prob â

: The number of observable platoons per unit of timeN

Q: given, β: inversely estimated, P: observed

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Numerical example

0

0.25

0.5

0.75

1

1500 1600 1700 1800

Brea

kdow

npr

obab

ility

Inflow rate[veh/h]

No pace car

Pace car with 60km/hone per ten vehicles

Pace car with 70km/h,one per the vehicles

Improve thetraffic breakdown

EntranceBottleneck

5km• Single-lane section of 5km is considered.

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Conclusion

0

0.25

0.5

0.75

1

1500 1600 1700 1800

Brea

kdow

npr

obab

ility

Inflow rate[veh/h]

No pace car

Pace car with 60km/hone per ten vehicles

Pace car with 70km/h,one per the vehicles

Improve thetraffic breakdown

EntranceBottleneck

5km• Single-lane section of 5km is considered.