2019/9/19

Dynamics in Traffic Analysis

September, 22 2019

Summer School by Prof. Hato

Graduate School of Information Sciences, Tohoku UniversityMasao Kuwahara

Flow conservationFundamental diagram Time-space diagram

Kinematic wave theorydifferential equationLower envelop principleVariational theory

Cumulative figure

Traffic State Estimation

Dynamic network analysisDUO, DUE

SimulationCTM (Cell Transmission Model)Block-Density method

Outline

3-dim flow representation

Queueing TheoryPoint / Physical Queue

Departure time choiceDynamic marginal cost

Fundamentals

Theory

Applied Theory

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Time-Space Diagram

space

time

space

time

speed

vehicle Red signal

trajectory

vehicle

Fundamental Diagram - Flow, Density, Speed

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

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Metropolitan Expressway

Flow [vehicles/hour/lane]

speed [km/hour]

Free flow region

Congested region

rain

A B

Bottleneck

Cumulative Counts

time

会社

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Time-space diagram

Cumulative figure

bottleneck

time

time

Cum.#

cum.# at x0

cum.# at x2

space

Three-dimensional Flow Representation

space

time

Cum.#

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

Kinematic Wave Theory

space

time

Flow Conservation

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

= functions

Kinematic Wave Theory

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Flow conservation Wave speed

Characteristic

space

timeflow

density

Characteristic

Kinematic Wave Theory

FD at (x,t)

Characteristic Curve (trajectory on which flow, density and speed are constant)

space space space

timetimetime

Kinematic Wave Theory

Non-uniform FD Uniform FD Uniform and piece-wise linear FD

slope

slope

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Solving the differential equation along Characteristic

space

time

Characteristic

• The initial density is given and does not change along the characteristic curve.

• Thus, wave speed can be known at any , if the fundamental diagram is given everywhere.

Kinematic Wave Theory

Lower Envelop Principle by Newell (1993)，Luke (1972)

Kinematic Wave Theory

space

time

ShockOn the shock, the wave speed and the density suddenly change.

Difficult the integration:

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time

Shock-Wave

Cumulative Trips

Backward Wave

Forward Wave

Flow

space

Newell

Kinematic Wave Theory

Lower Envelop Principle by Newell (1993)，Luke (1972)

Kinematic Wave Theory

Cum. #

time

x2

x1

x0

flow

densityv w

Lower Envelop Principle by Newell (1993)，Luke (1972)

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，

Variational Theory : Moving Observer

Moving Observer

space

time

If you know BP , NP can be evaluated.

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

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

Moving Observer

space

time

Relative capacity

Wave speed

Moving speed

NP NB + maxBP (relative capacity)

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space

time

NP = MinB {NB + maxBP }

Variational Theory : Evaluation of NP

Boundary

At boundary points, the cumulative counts are known.

CTM (Cell Transmission) and Block Density Models

based on Flow Conservation & Fundamental Diagram(Kinematic Wave and Lower Envelop)

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Simulation : CTM (Cell Transmission) and Block Density Models

Traffic State Estimation : Application to Intercity Motorway

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青森方面

東京方面

本宮IC

白石IC

国見IC

福島飯坂IC

福島西IC

二本松IC

Traffic State Estimation : Application to Intercity Motorway

Aomori   

Tokyo      

Shiroishi IC 

Kunimi IC

Fukushima‐iisaka IC

Fukushima‐nishi IC

Nihonmatsu IC

Motomiya IC

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全車両の走行軌跡の推定と近未来予測

感知器

感知器

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0

km

10:00 19:00時刻

probe

Loop detector

Loop detector

Boundary

Loop detector

Loop detector

Time of day

Traffic State Estimation : Application to Intercity Motorway

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probe

RED signal

time

detector

detector

Traffic State Estimation: Application to Surface Streets

probe

time

detector

detector

Traffic State Estimation: Application to Surface Streets

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Traffic State Estimation: using Backward probe

True 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 section

Traffic State Estimation: using Backward probe

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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.

Dynamic Network Analysis

Physical Queue is analysed using Lower Envelop Principle

A(t)

D(t)

one link

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Dynamic Network Analysis

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

Route Choice Principle

QueueingPoint Queue

Physical Queue (congestion propagation)

OD demandOne-to-Many OD + DUEMany-to-Many OD + DUE

Kinematic WaveLower Envelop Principle

Decomposition by absolute time

Decomposition by departure time from a single originTough Problem!

DUO (reactive) DUE (predictive)Point Queue Physical Queue Point Queue Physical Queue

One-to-Many OD

doneSimulation (CTM etc)

doneSimulation (CTM etc)

done 1993

Decomposition by departure time

done 2005

Decomposition by departure timeLower Envelop

Many-to-Many OD

done1997

Decomposition by absolute time

done2001

Decomposition by absolute timeLower Envelop

Tough! Tough!

Dynamic Network Analysis : historical development

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Flow modeling by lanes, by vehicle typesdifferent flow conditions by lanesmulti modes including motorcycles, bikes, pedestrians heterogeneity of driversanticipation, viscosity for smoother transitions

Traffic state estimation by fusing various kinds of datamore data will be available under ADAS, ADS environmentmore needs in disaster/ incident conditions (natural disasters, big events)

DUE with Many-to-Many ODone of the toughest problem kept for young researchers!

Applications to control traffic, mitigate disaster, information provision, etc.

Future Issues on Dynamics in Traffic Analysis

ADAS : Advanced Driver Assistance Systems(ADAS)ADS : Automated Driving System

A B

Bottleneck

Cum. #

time

delay

Free flow travel time

Time shiftObservation A

Observation B

Arrive at your office at the same time

Home Office

Time shift Commuting Program

Tomorrow, leave home late by time you delayed today

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