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
2
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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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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
Dynamic traffic assignment
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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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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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
Dynamic traffic assignment
Combined dynamic traffic signal control-assignment
The ACTS Group
15
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