Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
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
1
2
2019/9/19
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)
3
4
2019/9/19
Metropolitan Expressway
Flow [vehicles/hour/lane]
speed [km/hour]
Free flow region
Congested region
rain
A B
Bottleneck
Cumulative Counts
time
会社
6
5
6
2019/9/19
Time-space diagram
Cumulative figure
bottleneck
time
time
Cum.#
cum.# at x0
cum.# at x2
space
Three-dimensional Flow Representation
space
time
Cum.#
7
8
2019/9/19
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
9
10
2019/9/19
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
11
12
2019/9/19
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:
13
14
2019/9/19
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)
15
16
2019/9/19
,
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)
17
18
2019/9/19
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)
19
20
2019/9/19
Simulation : CTM (Cell Transmission) and Block Density Models
Traffic State Estimation : Application to Intercity Motorway
21
22
2019/9/19
23
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
24
全車両の走行軌跡の推定と近未来予測
感知器
感知器
64
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
23
24
2019/9/19
probe
RED signal
time
detector
detector
Traffic State Estimation: Application to Surface Streets
probe
time
detector
detector
Traffic State Estimation: Application to Surface Streets
25
26
2019/9/19
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
27
28
2019/9/19
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
29
30
2019/9/19
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
31
32
2019/9/19
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
34
33
34