11_ Traffic Flow Management i Road Network

8/9/2019 11_ Traffic Flow Management i Road Network

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Lecture 11Lecture 11

Traffic Flow Models, andTraffic Flow Models, and

Traffic Flow Management in Road NetworksTraffic Flow Management in Road Networks

Prof.Prof. Ismail ChabiniIsmail Chabini and Prof.and Prof. AmedeoAmedeo R.R. OdoniOdoni

1.2251.225J (ESD 205) Transportation Flow SystemsJ (ESD 205) Transportation Flow Systems

1.225, 11/28/02 Lecture 9, Page 2

Lecture 11 OutlineLecture 11 Outline

Overview of some traffic flow models: Modeling of single link: Car-following models

Dynamic macroscopic models of highway traffic

Dynamic traffic flow management in road networks: Concepts

Dynamic traffic assignment

Combined dynamic traffic signal control-assignment

The ACTS Group

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1.225, 11/28/02 Lecture 9, Page 3

Link Travel Time Models: CarLink Travel Time Models: Car--Following ModelsFollowing Models

Notation:Flown

Leader

n+1

Follower

jam

nnnk

tltxtx1

)(headway)(spacespacing)()( 11 +== ++xn+1 xn

x0 L

)()()( 11 tltxtx nnn ++ = &&&

)()(

:nvehicleofspeed txdt

tdxn

n&=

)()()(

:nvehicleoftion)(decceleraonaccelerati2

txdt

txd

dt

txdn

nn&&& ==

car-following regime: ln+1(t) is below a certain threshold

ln+1jamk

1

1.225, 11/28/02 Lecture 9, Page 4

Link Travel Time Models: CarLink Travel Time Models: Car--Following ModelsFollowing Models

Simple car-following model:))()(()()( 111 txtxatlaTtx nnnn +++ ==+ &&&&&

sec)5.1(: TtimereactionT

)37.0(: 1 safactorysensitivita

Flown

Leader

n+1

Follower

x0xn+1 xn

L

Questions about this simple car-following model:

Is it realistic?

Does it have a relationship with macroscopic models?

ln+1jamk

1

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1.225, 11/28/02 Lecture 9, Page 5

From Microscopic Models To Macroscopic ModelsFrom Microscopic Models To Macroscopic Models

))()(()( 11 yxyxayx nnn ++ = &&&&dytladyyxyxadyyx nnnn )())()(()( 111 +++ == &&&&&

++ = t nt n dytladyyx 0 10 1 )()( &&&))0()(()0()( 1111 ++++ = nnnn ltlautu

Fundamental diagram:Simple car-following model:

Proof of equivalency

)0())()(()( 11 == ++ Ttxtxatx nnn &&&&)1(max

jamk

kqq =

)0()0()()( 1111 ++++ += nnnn lautlatu0)0()0(0)(then,0)(If 1111 === ++++ nnnn laututl

1.225, 11/28/02 Lecture 9, Page 6

)11

(jamkk

au =)1()

11(

jamjam k

kak

kkakuq ===

)1(maxjamk

kqq =

aqk == then0,If

)1

)(

1()()(

1

11

jamn

nnktk

atlatu ==+

++

maxthen),1(Since qak

kaaq

jam

==

Note: ifk 0, then u . Does this make sense?

From Microscopic Model to Macroscopic ModelFrom Microscopic Model to Macroscopic Model

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1.225, 11/28/02 Lecture 9, Page 7

NonNon--linear Carlinear Car--following Modelsfollowing Models

( ) 5.111

01)()()()()(

txtx

txtxaTtxnn

nnn

++

+=+ &&&&

5.1

1

10

1)(

)(

+

=+

+

jam

n

n

ktl

tla

&

IfT= 0, the corresponding fundamental diagram is:

=

5.0

max 1jamk

kkuq

1.225, 11/28/02 Lecture 9, Page 8

Flow Models Derived from CarFlow Models Derived from Car--Following ModelsFollowing Models

( )lnnnnm

nntxtx

txtxTtxaTtx

)()(

)()()()(

1

1101

++

++

+=+ &&&&&

13

12

02

01.5

01

00

Flow vs. Densityml

=

5.0

max1

jamk

kkuq

=

jam

mk

kqq 1

=

jamk

kuq 1max

=

jamk

kkuq 1expmax

=

2

max2

1exp

jamk

kkuq

=

k

kkuq

jam

c ln

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1.225, 11/28/02 Lecture 9, Page 9

Is The Depicted Trajectory Familiar To You, andIs The Depicted Trajectory Familiar To You, and

How To Predict It?How To Predict It?Two facts:

As a vehicle travels

along the roadway, its

speed might change

The speed is lower if

surrounding traffic

density is higher

A dynamic traffic modelpredicts speeds that vary in

space and time

A macroscopic dynamictraffic flow model:

Divide the highway intoblocks of constant

densities

Model speeds within

and between blocksTime (t)

Space

(x)

k1

k2k3

k1

k1

k3

1.225, 11/28/02 Lecture 9, Page 10

DensityDensity--Flow RelationshipsFlow Relationships

Macroscopic traffic theory shows thatthere is a relationship between traffic

density and flow on a stretch of a

highway

This theory also predicts averagevehicle speed

Theory supported by real-worldmeasurements

Density-relationships: A concept familiar to you by now

An example is depicted on the

rightDensity (k)

Flow

(q)

k1k2

k3

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1.225, 11/28/02 Lecture 9, Page 11

Boundary Propagation: Upstream in Free Flow,Boundary Propagation: Upstream in Free Flow,

Down Stream CongestedDown Stream Congested

1. Two successive density blocks:

U: upstream block;

D: the downstream block

2. Depending on flow on each block, there are three cases: Two are shown below

1.225, 11/28/02 Lecture 9, Page 12

Modeling of BottlenecksModeling of Bottlenecks

Change in density-flow diagram to reflect change in capacity

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1.225, 11/28/02 Lecture 9, Page 13

Downstream in Free Flow and Upstream CongestedDownstream in Free Flow and Upstream Congested

A block with maximum flow (critical density) is created in between U and D

blocks

1.225, 11/28/02 Lecture 9, Page 14

Modeling of IncidentsModeling of Incidents

Before incident, traffic flow represented by point B.An incident acts like a temporary bottleneck if kd


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1.225, 11/28/02 Lecture 9, Page 15

Information Technology and Transportation Network OperationsInformation Technology and Transportation Network Operations

Traffic Information-Management Center

Surveillance

SystemTravel

DemandNetworkSupply

Transportation Network

User Services

- routing advice-congestion pricing

Traffic Control

-signal settings-ramp metering

1.225, 11/28/02 Lecture 9, Page 16

Traffic InformationTraffic Information--Management Systems (TIMS):Management Systems (TIMS):

Properties and MethodsProperties and Methods

TIMS should be responsive to:

future demand

potential adjustments in travel patterns due to information

provision and changes in supply network

based on projected traffic conditions to:

anticipate downstream traffic conditions, and

improve credibility

Predictions methods: Statistical: valid for short intervals only

Dynamic traffic assignment methods (models and algorithms)

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1.225, 11/28/02 Lecture 9, Page 17

Dynamic Traffic Flow MethodsDynamic Traffic Flow Methods

Traffic assignment models: require time-dependent O-D flows

incorporate driver behavior, and information provision

require link network performance models

have high computational requirements

Three modeling/algorithmic components: Travelers route-choice

Prediction of travel times when vehicle paths are known

Route-guidance provision

Two algorithmic components: Path-generation


1.225, 11/28/02 Lecture 9, Page 18

Framework for Dynamic Traffic Assignment MethodsFramework for Dynamic Traffic Assignment Methods

dynamic path flow rates

Dynamic

O-D Trip

RatesSubset of PathsSubset of Paths

UsersUsers Route Choice ModelsRoute Choice Modelspath costs

Guidance GenerationGuidance Generation

Link PerformanceLink Performance

ModelsModels

link travel times

Dynamic Network Loading ModelDynamic Network Loading Model link volumes

GenerationGeneration

of Optimal Pathsof Optimal Paths

Path FilterPath Filter

generated

paths

path costs

new paths

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1.225, 11/28/02 Lecture 9, Page 19

Types of DTA ModelsTypes of DTA Models

Microscopic traffic models (MITSIM): Traffic is represented at the vehicle level Vehicles are moved using car-following and lane changing

models

Mesoscopic traffic models (MesoTS/DynaMIT): Traffic is represented at the vehicle level

Speed is obtained using models that relate macroscopictraffic flow variables

Macroscopic (or flow-based) traffic models: Traffic is represented as continuous variables

Speed is obtained using models that relate macroscopictraffic flow variables

Analytical (flow-based) traffic models: macroscopic models witha good mix of lot of math, computer science and traffic flowunderstanding

1.225, 11/28/02 Lecture 9, Page 20

A Small RealA Small Real--Word Network Model: AmsterdamWord Network Model: Amsterdam

Beltway NetworkBeltway Network

196 nodes, 310 links, 1134 O-D pairs and 1443 pathsMorning peak: 2 hours and 20 minutesDiscretization intervals: 2357 (3.50 sec each)Various types of users:

Fixed routes

Minimum perceived cost routes

Minimum experienced cost routes

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1.225, 11/28/02 Lecture 9, Page 21

Computer Resources Used in Analytical ModelComputer Resources Used in Analytical Model

Link variables: 25 MbytesPath variables: 34 MbytesAverage time for one loading: about 3 minutesSaving ratio compared to known analytical methods: 1000Results are encouraging for real-time deploymentAnalytical approach: 45 times faster than real time

1.225, 11/28/02 Lecture 9, Page 22

Interdependence of Control and AssignmentInterdependence of Control and Assignment

Consequences of the conventional approach: Sub-optimal signal settings;

Inconsistent traffic flow predictions.

Dynamic Traffic

Control

Dynamic Traffic

Assignment

Dynamic

Traffic

Flow

Dynamic

Signal

Setting

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1.225, 11/28/02 Lecture 9, Page 23

A Case Study (cont.)A Case Study (cont.)

Controls current existing pre-timed control

Webster equal-saturation control

Smith P0 Control

One-level Cournot control

Bi-level Stackelberg control

System-optimal Monopoly control

Route Choices A set of pre-determined paths (4 paths) for each O-D pair

Total of 400 paths Demand is model using C-Logit

Results from Back Bay Case StudyResults from Back Bay Case Study

Controls Total Travel Time(mins)

Existing 11784Webster 11781Smith P0 11566Cournot 10642Stackelberg 10504Monopoly 10325

Gap from System-Optimum(%)

14.12

14.1

12.02

3.07

1.73

0

1.225, 11/28/02 Lecture 9, Page 24

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1.225, 11/28/02 Lecture 9, Page 25

Current Research Interests of ACTS GroupCurrent Research Interests of ACTS Group

Algorithms and Computation in Transportation Systems (ACTS) Group: A group formed by Prof. Ismail Chabini and his graduate advisees

Has been around for 5 years now

Field of Interest: Design and computer implementation of models and algorithms for

transportation network analysis and operations

Modeling and real-time management of traffic flows on road networks

Applications to solve increasingly important societal problems such ascongestion, air quality, energy, safety, and emergency

Critical Characteristics of Problems: Real-time operation

Dynamics Large networks

Intelligence and subsystems integration

Complex interactions involving humans

1.225, 11/28/02 Lecture 9, Page 26

Related Ongoing Research ProjectsRelated Ongoing Research Projects

NSF CAREER (and NSF ETI): High Performance Computing and NetworkOptimization Methods with Applications to Intelligent Transportation Systems (~ $350k)

NSF-NYSDOT: Deployment of ITS technologies (~ $350k)

US DOT: Design and Implementation of Computer Models and Algorithms for DynamicNetwork Flow Problems (~$300k)

Ford Motor Company: Emissions Modeling and Control, and Parallel Traffic Modelsand Applications to Safety (~ $330k)

CMI (with colleagues from MIT and Cambridge University): The SentientVehicle (~ $400k)

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Some Research Contributions of the ACTS Group:Some Research Contributions of the ACTS Group:

Routing Problems in TimeRouting Problems in Time--Dependent NetworksDependent Networks

Developed the fastest known algorithms for a variety of routing problemsin time-dependent networks

Algorithms are based on the Decreasing-Order-of-Time (DOT) algorithm,described in paper 2.2, which finds all-to-one shortest paths for all times

Algorithm DOT has been a breakthrough in this area, and was shown to bea degree of magnitude faster than previously known algorithms

Implementations of algorithm DOT exploiting high performancecomputing platforms and hierarchical structures of transportation networks

resulted in further gains in computational speed

The developed algorithms are essential building blocks of real-time trafficmanagement methods, and have significantly expanded the boundary of

network sizes for which these methods are deployable

It is now computationally possible to deploy real-time traffic managementmethods to medium-size networks, which are a degree of magnitude larger

1.225, 11/28/02 Lecture 9, Page 27

Some Research Contributions of the ACTS Group:Some Research Contributions of the ACTS Group:

Methods and Tools for Traffic Flow Modeling and ManagementMethods and Tools for Traffic Flow Modeling and Management

Developed new models, faster algorithms and computer implementationsto solve a class of traffic flow modeling and management problems

They are the fastest known tools in the literature, and run much faster thanreal-time on medium-size real-life networks

Developed new traffic management algorithms, which have the potential tosignificantly improve travel-times through effective real-time dynamic

adjustment of traffic signals and provision of route guidance strategies

The developed models, algorithms and software tools contribute to creatinga knowledge and computational base needed to build and deploy real-time

traffic management systems to alleviate congestion

The algorithms and software systems have unique capabilities, and havebeen sought by industry. Some are the subject of patent applications

In projects sponsored by CMI and Ford-MIT initiatives, the developedmethods are being used to design new solutions to problems related to air

pollution, energy consumption, and safety

1.225, 11/28/02 Lecture 9, Page 28

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1.225, 11/28/02 Lecture 9, Page 29

Lecture 11 SummaryLecture 11 Summary

Overview of some traffic flow models: Modeling of single link: Car-following models

Dynamic macroscopic models of highway traffic

Dynamic traffic flow management in road networks: Concepts


Combined dynamic traffic signal control-assignment

The ACTS Group

15

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11_ Traffic Flow Management i Road Network