Traffic flow theory : characteristics, experimental methods, and numerical techniques PDF
Preview Traffic flow theory : characteristics, experimental methods, and numerical techniques
TRAFFIC FLOW THEORY TRAFFIC FLOW THEORY Characteristics, Experimental Methods, and Numerical Techniques DAIHENGNI DepartmentofCivilandEnvironmentalEngineering, UniversityofMassachusettsAmherst MA,USA AMSTERDAM (cid:129) BOSTON (cid:129) HEIDELBERG (cid:129) LONDON NEW YORK (cid:129) OXFORD (cid:129) PARIS (cid:129) SAN DIEGO SAN FRANCISCO (cid:129) SINGAPORE (cid:129) SYDNEY (cid:129) TOKYO Butterworth-Heinemann is an imprint of Elsevier ButterworthHeinemannisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK 225WymanStreet,Waltham,MA02451,USA Copyright©2016ElsevierInc.Allrightsreserved. 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Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluating andusinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuch informationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,including partiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assume anyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability, negligenceorotherwise,orfromanyuseoroperationofanymethods,products,instructions,orideas containedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ForinformationonallButterworthHeinemannpublications visitourwebsiteathttp://store.elsevier.com/ 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 OBE 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
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