2019/9/19

Dynamics in Traffic Analysis
September, 22 2019
Summer School by Prof. Hato

Graduate School of Information Sciences, Tohoku University
Masao Kuwahara

1Outline
Flow conservation
Fundamental diagram

Time-space diagram

3-dim flow representation

Cumulative figure

Kinematic wave theory
differential equation
Lower envelop principle
Variational theory

Queueing Theory
Point / Physical Queue

Simulation
CTM (Cell Transmission Model)
Block-Density method

Dynamic network analysis
DUO, DUE

Traffic State Estimation

2

Fundamentals

Departure time choice
Dynamic marginal cost

TheoryApplied Theory2019/9/19

Time-Space Diagram
spacevehicle

spacevehicle

Red signal

speedtime3

Fundamental Diagram - Flow, Density, Speed

Greenshieldʼs Measurement by 16 mm Camera in Michigan in 1933
(Kuhne 2011)4

trajectorytime2019/9/19

Metropolitan Expressway
speed [km/hour]rainFree flow region

Congested region

Flow [vehicles/hour/lane]

5

Cumulative Counts

time

AB

会社

Bottleneck662019/9/19

spacebottleneck
Time-space diagram

time
Cum.#
cum.# at x0

Cumulative figure

cum.# at x2

time

7

Three-dimensional Flow Representation

spaceCum.#time8

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Kinematic Wave Theory

Flow, density, speed, cumulative count on time-space (x,t)
q(x,t) k(x,t) v(x,t)
N(x,t)
spacetime

9

Kinematic Wave Theory
Flow Conservation

Fundamental diagram (assume to exist any (x,t))= functions

10

2019/9/19

space

Kinematic Wave Theory
Characteristic

Characteristic

time

flow

Flow conservation

Wave speed

FD at (x,t)
density

11

Kinematic Wave Theory
Characteristic Curve (trajectory on which flow, density and speed are constant)spacespacespaceslope

slope
time
Non-uniform FD

12timeUniform FDtime
Uniform andpiece-wise linear FD2019/9/19

Kinematic Wave Theory
spaceSolving the differential equation along Characteristic

Characteristictime• The initial density
is given anddoes not change along the characteristic curve.
• Thus, wave speed can be known at any,
if the fundamental diagram is given everywhere.

13

Kinematic Wave Theory
Lower Envelop Principle by Newell (1993)，Luke (1972)
spacetimeOn the shock, the wave speed andthe density suddenly change.
Difficult the integration:

14Shock

2019/9/19

Kinematic Wave Theory
Lower Envelop Principle by Newell (1993)，Luke (1972)
Cumulative Trips

Forward Wave

Shock-Wave

Backward Wave

Flow

Newelltime
space

15

Kinematic Wave Theory
Lower Envelop Principle by Newell (1993)，Luke (1972)
Cum. #x2x1x0
flowv

time

16wdensity

2019/9/19

Variational Theory : Moving Observer
space

NP = NB + BP (# of overtaken)= NB + 10

Moving Observer，

If you know BP ,NP can be evaluated.

time

17

Variational Theory : Relative Capacity ( = max # of overtaken)

space

Wave speed
Moving Observer
Relative capacity
Moving speed

timeNP  NB + maxBP (relative capacity)18

2019/9/19

Variational Theory : Evaluation of NP
NP = MinB {NB + maxBP }spaceBoundarytime
At boundary points, the cumulative counts are known.

19

CTM (Cell Transmission) and Block Density Models
based on Flow Conservation & Fundamental Diagram(Kinematic Wave and Lower Envelop)202019/9/19

Simulation : CTM (Cell Transmission) and Block Density Models

21

Traffic State Estimation : Application to Intercity Motorway

222019/9/19

Traffic State Estimation : Application to Intercity Motorway

Aomori
青森方面
白石IC ICShiroishiKunimi
IC
国見IC
Fukushima‐iisaka
IC福島飯坂IC
福島西IC
Fukushima‐nishi
IC
二本松ICIC
Nihonmatsu
本宮IC ICMotomiyaTokyo
東京方面

2323

全車両の走行軌跡の推定と近未来予測
Traffic State Estimation : Application to Intercity Motorway
km感知器
Loop detector

Boundary
Loop detector

64
probe

Loop
感知器
detector0
10:00

Loop detector
Time時刻of day

19:00
24

24

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Traffic State Estimation: Application to Surface Streets

detectorprobe
RED signal

detectortime

25

Traffic State Estimation: Application to Surface Streets

detectorprobe

detector

26

time2019/9/19

Traffic State Estimation: using Backward probe27

Traffic State Estimation: using Backward probeTrue State with an Incident

Estimated State with an Incident

Backward probes can estimate traffic states• even under an incidence by observing the capacity at the incident site
• even with in / out flows in a middle of the study section28

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Traffic State Estimation : Two-dimensional Extension

Two-dimensional extension was proposed using CTM.
It can estimate the OD demand and FD parameters simultaneously with the traffic state.

29

Dynamic Network Analysis

Physical Queue is analysed using Lower Envelop Principle

A(t)
D(t)

one link30

2019/9/19

Dynamic Network Analysis
Route Choice Principle
Decomposition by absolute time
DUO ( Dynamic User Optimal) = Reactive= choose the best (shortest) route based on current traffic condition
DUE ( Dynamic User Equilibrium) = Predictive= choose the best (shortest) route actually experienced
Queueing
Point Queue
Kinematic Wave
Lower Envelop Principle

Physical Queue (congestion propagation)
OD demand

Decomposition by departure time from a single origin

One-to-Many OD + DUE
Many-to-Many OD + DUE

Tough Problem!

31

Dynamic Network Analysis : historical development
DUO (reactive)
Point Queue
One-to-Many
OD

Many-to-Many
OD

32

DUE (predictive)

Physical Queue

Point Queue

Physical Queue

done
Simulation(CTM etc)

done
Simulation(CTM etc)

done
1993
Decomposition by
departure time

done
2005
Decomposition by
departure time
Lower Envelop

done
1997
Decomposition
by absolute time

done
2001
Decomposition
by absolute time
Lower Envelop

Tough!

Tough!

2019/9/19

Future Issues on Dynamics in Traffic Analysis
Flow modeling by lanes, by vehicle types
different flow conditions by lanes
multi modes including motorcycles, bikes, pedestrians
heterogeneity of driversanticipation, viscosity for smoother transitions
Traffic state estimation by fusing various kinds of data
more data will be available under ADAS, ADS environment
more needs in disaster/ incident conditions (natural disasters, big events)
DUE with Many-to-Many OD
one of the toughest problem kept for young researchers!
Applications to control traffic, mitigate disaster, information provision, etc.
ADAS : Advanced Driver Assistance Systems(ADAS)ADS : Automated Driving System

33

Cum. #Observation A

Time shift
Arrive at your officeat the same timedelay

Time shift Commuting Program
Observation BTomorrow, leave home late by time you delayed todaytime

Free flow travel timeABOfficeHome
Bottleneck3434