Traffic flow theory : characteristics, experimental methods, and numerical techniques

382 Pages·2015·88.465 MB·English

by  Ni, Daiheng

TRAFFIC FLOW
THEORY
TRAFFIC FLOW
THEORY
Characteristics,
Experimental Methods,
and Numerical
Techniques
DAIHENGNI
DepartmentofCivilandEnvironmentalEngineering,
UniversityofMassachusettsAmherst
MA,USA
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ISBN:978-0-12-804134-5

PREFACE
For years, I have been thinking about writing an introductory book on
traffic flow theory. The main purpose is to help readers who are new
to this subject and who do not have much knowledge of mathematics
and traffic flow. To serve this purpose, I have tried to make the con-
tents self-contained and assume minimal knowledge of mathematics and
trafficflow.
This book is derived from my lecture notes for CEE520 Traffic Flow
Theory and Simulation I (formerly offered as CEE590T Traffic Flow
Theoryonanexperimentalbasisbeforeitwasassignedapermanentcourse
number) at the University of Massachusetts Amherst. Hence, the chapters
are more like lectures, with focused topics, each of which fits in a class
meeting.Thebooktakesaunifiedperspectiveontrafficflowmodelingand
consists of five parts which are coherently connected. Each part is briefly
describedas follows.
Part I focuses on traffic flow characteristics. It starts with intelligent
transportation systems and traffic sensing technologies to illustrate how to
quantifytrafficflowandcollectsuchdata.Thisisfollowedbythreechapters
within-depthdiscussionoftrafficflowcharacteristics,onthebasisofwhich
their relationshipsare developed and a few equilibrium traffic flow models
areintroduced.
Part II is about traffic flow modeling at the macroscopic level. The goal
istosolvefortemporal-spatialevolutionoftrafficflowcharacteristicsgiven
initialandboundaryconditions.Thefirstfewchaptersprovideajumpstart
on mathematical modeling, especially partial differential equations. With
such knowledge, the domain knowledge of traffic flow is integrated into
mathematicalmodeling, resultingina first-orderquasi-linear partial differ-
ential equation problem known as the Lighthill, Whitham, and Richards
(LWR) model in the traffic flow community. Solutions to the problem
are introduced, including a graphical technique that uses the method of
characteristics and numerical techniques that involves a few discretization
schemes.
Part III is devoted to traffic flow modeling at the microscopic level.
The emphasis is on drivers’ car-following behavior involving operational
controlinthelongitudinaldirection.Aseriesofcar-followingmodelswith
differingmodelingphilosophiesandcomplexityareintroduced.Toprovide
xiii
xiv Preface
anopportunitytocross-comparetherelativeperformanceofthesemodels,a
commongroundissetupsothatthesemodelscandemonstratethemselves.
Suchaprocessiscalledbenchmarking,andthecommongroundconsistsof
twoscenarios,onemicroscopicandtheothermacroscopic.Themicroscopic
scenario is a hypothetical driving process aimed at testing these models
under various driving regimes (such as free flow and car following); the
macroscopic scenario is a set of empirical data focusing on examining the
macroscopicpropertiesofthesemodels(e.g.,howtheirimpliedfundamental
diagramscomparewith theobserved diagrams).
Part IV extends traffic flow modeling to the picoscopic level. A mod-
eling framework called a driver-vehicle-environment closed-loop system
is introduced to capture the ultrafine level of detail of traffic flow. Such
a framework involves a driver model, a vehicle model, and the driving
environment.Thedrivermodelcollectsandprocessesinformationfromits
vehicleandthedrivingenvironmentandmakescontroldecisionsonmotion
inlongitudinalandlateraldirections.Thevehiclemodelexecutesitsdriver’s
control decision and moves dynamically on the road. The driver-vehicle
unit constitutes one of the entities in the environment whose dynamic
changeaffectsdrivercontrolinthenextstep.Asanexampleofthismodeling
framework, a simple engine model and further a dynamic interactive
vehicle model are proposed, and a field theory is formulated to model
thedriver.
All things come together in Part V. With the field theoryas the basis, a
unifiedperspectivecanbecastontrafficflowtheory.Themacroscopicmod-
elsandmicroscopicmodelsintroducedthusfarcanberelatedtoeachother,
alllinkeddirectlyorindirectlytothefieldtheory.Hence,aunifieddiagram
is constructed to highlight such relations. In addition, benchmarking is
donetocross-comparetheperformanceofsomeofthemacroscopicmodels
and microscopic models in the diagram. Further, a multiscale modeling
approach is presented which involves traffic flow modeling at four levels
of detail—namely, macroscopic, mesoscopic, microscopic, and picoscopic.
The emphasis of multiscale modeling is to ensure modeling consistency—
that is, how less detailed models are derived from more detailed models
and, conversely, how more detailed models are aggregated to less detailed
models.Theproposedapproachmayestablishthetheoreticalfoundationfor
trafficmodelingand simulationat multiplescales seamlesslywithina single
system.
Thisbookisidealforusebyentry-levelgraduatestudentsintransporta-
tionengineeringas atextbookforatrafficflowtheorycourse.Inaddition,
Preface xv
civil engineering juniors and seniors may find some in-depth information
about traffic flow fundamentals in this book. Further, applied mathematics
majorsmayfindconcreteexamplesofmathematicalmodelingwithspecific
domain knowledge. Advanced readers are referred to other traffic flow
theorybooksfor in-depthcoverage; a few of themare as follows:
• G.F. Newell, Theory of Highway Traffic Flow, 1945-1965, Course
NotesUCB-ITS-CN-95-1, 1996.
• A.D.May, TrafficFlow Fundamentals,Prentice-Hall,New York,1989.
• C.F. Daganzo, Fundamentals of Transportation and Traffic Operations,
Pergamon-Elsevier,Oxford, UK, 1997.
• N. Gartner, C.J. Messer, A.K. Rathi, Revised Monograph on Traffic
Flow Theory:AState-of-the-Art Report,TRB, 2001.
• D.L.Gerlough,M.J.Huber,TrafficFlowTheory—AMonograph,TRB
SpecialReport 165, 1975.
• D.L. Gerlough,D.G. Capelle, An Introductionto Traffic Flow Theory,
HRBSpecial Report79, 1964.
• D.R. Drew, Traffic Flow Theory and Control, McGraw-Hill,
New York,1968.
• W. Leutzbach, Introduction to the Theory of Traffic Flow, Springer-
Verlag,New York,1988.
• M. Treiber, A. Kesting, Traffic Flow Dynamics, Springer, New York,
2013.
• L. Elefteriadou, An Introduction to Traffic Flow Theory, Springer,
New York,2014.
• B.S.Kerner,IntroductiontoModernTrafficFlowTheoryandControl,
Springer,New York, 2009.
I thank Professor John D. Leonard at Georgia Institute of Technology
and Professor Billy M. Williams at North Carolina State University, who
introduced me to this field and sparked my interest in traffic flow theory.
Thanks also go to former students in my traffic flow theory classes—their
insightfuldiscussionand kind encouragementmade thiswork possible.
Finally, I acknowledge my limitations. Though I have tried hard to
ensure the quality and accuracy of information, I can make mistakes.
Therefore,readers shouldusethis book withdiscretion.
Daiheng Ni
Amherst,MA
September,2015
x
v
Traffic flow theory i
A unified perspective
Part I Part II Part III Part IV Part V P
re
fa
c
e
ITS Macroscopic MMeessoossccooppiicc Microscopic Picoscopic Unified
traffic sensing modeling mmooddeelliinngg modeling modeling perspective
technologies
RRoouuttee--cchhooiiccee Driver-vehicle-
Traffic flow Conservation CCeelllluullaarr-- KKiinneettiicc mmooddeellss environment
characteristics law aauuttoommaattaa mmooddeellss closed-Loop
mmooddeellss LLaannee--cchhaannggiinngg system
mmooddeellss
GGaaapp--aacccceeppttaannccee Engine
Equilibrium 1st order Hi-order TTRRAANNSSIIMMSS PPrriiggooggiinnee mmooddeellss modeling
traffic flow models models --HHeerrmmaann
models Car-following
Vehicle
models
modeling
Single-regime:
-Greenshields LWR Driver
-Greenberg model Pipes/Forbes modeling
-Underwood GM
-Drake(NW) Gipps
-Pipes-Munjal Newell non-linear The unified
-Drew Newell simplified Field diagram
Multi-regime: Analytical Numerical IDM theory
-Edie solution solutions Van Aerde
-2-Regime Psycho-physical
-3-Regime CARSIM
Stochastic Rule-based
neural networks
…
Method of FREQ, Multiscale
characteristics, KRONOS, modeling
K-waves CTM Longitudinal
control model
(LCM)
Note: Gray areas are part of traffic flow theory but not covered in this book.
CHAPTER 1
Traffic Sensing Technologies
Safe and efficient operations of transportation systems rely heavily on
applications of advanced technologies. As a result, recent decades have
witnessed wide applications of communication, sensing, and computing
technologiesintrafficsurveillance,incidentdetection,emergencyresponse,
fleetmanagement,andtravelassistance.Figure1.1illustratesan exampleof
thesetechnologiesat an intersection.
“Intelligent transportation systems” (ITS) refers to efforts that apply
information, communication, and sensor technologies to vehicles and
transportation infrastructure in order to provide real-time information for
road users and transportation system operators to make better decisions.
ITS aim to improve traffic safety, relieve traffic congestion, reduce air
pollution, increase energy efficiency, and improve homeland security. ITS
encompass a suite of measures that address the above objectives: advanced
traffic management systems, advanced traveler information systems, ad-
vanced public transportation systems, the intelligent vehicle initiative, the
commercial vehicle operations program, etc. The recent development of
ITS emphasizes the application of dedicated short-range communications
in vehicle-to-vehicle and vehicle-to-roadside wireless communications—
that is, connected vehicle technology according to the US Department of
Transportation.
1.1 TRAFFICSENSORS
Thissectiondescribesafewtypesoftrafficsensorsthatareoftenemployedin
ITSandothertrafficsurveillanceanddatacollectionsystems.Thediscussion
ofeachtypeofsensorfocusesonhowitworks,whattrafficdataitiscapable
of collecting, itsadvantages, and its disadvantages.
1.1.1 Inductive-LoopDetector
Inductive-loop detectors are widely used at intersections with traffic-
actuatedsignals,freewayentranceswithautomaticrampmetering,highway
segments monitored by traffic counting programs, and entrances of gated
parkingfacilities.
TrafficFlowTheory Copyright©2016ElsevierInc.
http://dx.doi.org/10.1016/B978-0-12-804134-5.00001-5 Allrightsreserved. 3
4 TrafficFlowTheory
RSE
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Figure1.1 Anexampleapplicationofconnectedvehiclesatanintersection.
HowItWorks
As illustrated in Figure 1.2, an inductive-loop detection system consists of
an inductive loop, which is simply a coil of wire embedded in the road’s
pavement, and a detector, which typically sits in a signal cabinet and links
thesignalcontrollertotheinductiveloop.Thedetectordrivesanalternating
flow of current through the loop at or below the resonant frequency. All
wire conductors carrying an electrical current produce a magnetic field,
and the magnetic flux induces the electrical property called inductance.
Note that the metal body and frame provide a conductive path for the
magnetic field. Therefore, when a vehicle enters the detection zone or
crosses the loop, this produces a loading effect, which in turn causes the
loopinductanceto decrease. Thedecreased inductancecauses theresonant
frequency to increase from its nominal value. If the frequency change
exceeds the threshold set by the sensitivity setting, the detector module
will output a detect signal—that is, an “on” state. Otherwise, the detector
doesnot outputa signal—thatis, an “off” state.
The output of the detector can be used for many applications. For
example,anactuatedsignalcontrollerreliesonthedetectoroutputtodecide
whether a green indication is granted to the approach that is monitored
by the detector. As another example, when a vehicle exits a gated parking
garage,aninductiveloopisabletodetectthevehicleinadvancesothatthe