Autonomous Driving in the Framework of ThreePhase Traffic Theory
Glossary
 Autonomous Driving

An autonomous driving vehicle is a selfdriving vehicle that can move without a driver. Autonomous driving is realized through the use of an automated system in a vehicle: The automated system has control over the vehicle in traffic flow. For this reason, autonomous driving vehicle is often also called automated driving (or automatic driving) vehicle.
 Autonomous Driving in Framework of ThreePhase Traffic Theory

An autonomous driving in the framework of the threephase traffic theory is the autonomous driving for which there is no fixed time headway to the preceding vehicle. This means the existence of an indifference zone in carfollowing for the autonomous driving vehicle.
 Bottleneck

Traffic breakdown occurs mostly at road bottlenecks. A road bottleneck can be a result of roadworks, on and offramps, a decrease in the number of freeway lanes, road curves and road gradients, traffic signal, etc.
 Main Prediction of ThreePhase Traffic Theory

The main...
Notes
Acknowledgments
I would like to thank Sergey Klenov for the help and useful suggestions. We thank our partners for their support in the project “MECView – Object detection for autonomous driving based on Mobile Edge Computing,” funded by the German Federal Ministry of Economic Affairs and Energy.
Bibliography
 Automated Highway Systems (2007) http://www.seminarsonly.com/Civil Engineering/automatedhighwaysystems.php
 Automated Highway Systems (2012) https://seminarprojects.blogspot.de/2012/01/detailedreportonautomatedhighway.html
 Automatisches Fahren (2012) http://www.tuvpt.de/index.php?id=foerderung000
 Barlović R, Santen L, Schadschneider A, Schreckenberg M (1998) Metastable states in cellular automata for traffic flow. Eur Phys J B 5:793–800ADSCrossRefGoogle Scholar
 Bellomo N, Coscia V, Delitala M (2002) On the mathematical theory of vehicular traffic flow I. Fluid dynamic and kinetic modelling. Math Mod Meth App Sc 12:1801–1843MathSciNetzbMATHCrossRefGoogle Scholar
 Bengler K, Dietmayer K, Farber B, Maurer M, Stiller C, Winner H (2014) Three decades of driver assistance systems: review and future perspectives. IEEE Intell Transp Sys Mag 6:6–22CrossRefGoogle Scholar
 Borsche R, Kimathi M, Klar A (2012) A class of multiphase traffic theories for microscopic, kinetic and continuum traffic models. Comput Math Appl 64:2939–2953MathSciNetzbMATHCrossRefGoogle Scholar
 Bose A, Ioannou P (2003) Mixed manual/semiautomated traffic: a macroscopic analysis. Transp Res C 11:439–462CrossRefGoogle Scholar
 Brockfeld E, Kühne RD, Skabardonis A, Wagner P (2003) Toward benchmarking of microscopic traffic flow models. Trans Res Rec 1852:124–129CrossRefGoogle Scholar
 Chen D, Ahn S, Chitturi M, Noyce DA (2017) Towards vehicle automation: roadway capacity formulation for traffic mixed with regular and automated vehicles. Transp Res B 100:196–221CrossRefGoogle Scholar
 Chowdhury D, Santen L, Schadschneider A (2000) Statistical physics of vehicular traffic and some related systems. Phys Rep 329:199–329ADSMathSciNetCrossRefGoogle Scholar
 Daganzo CF (1997) Fundamentals of transportation and traffic operations. Elsevier Science Inc., New YorkCrossRefGoogle Scholar
 Davis LC (2004a) Multilane simulations of traffic phases. Phys Rev E 69:016108ADSMathSciNetCrossRefGoogle Scholar
 Davis LC (2004b) Effect of adaptive cruise control systems on traffic flow. Phys Rev E 69:066110ADSMathSciNetCrossRefGoogle Scholar
 Davis LC (2006a) Controlling traffic flow near the transition to the synchronous flow phase. Phys A 368:541–550CrossRefGoogle Scholar
 Davis LC (2006b) Effect of cooperative merging on the synchronous flow phase of traffic. Phys A 361:606–618CrossRefGoogle Scholar
 Davis LC (2007) Effect of adaptive cruise control systems on mixed traffic flow near an onramp. Phys A 379:274–290CrossRefGoogle Scholar
 Davis LC (2008) Driver choice compared to controlled diversion for a freeway double onramp in the framework of threephase traffic theory. Phys A 387:6395–6410CrossRefGoogle Scholar
 Davis LC (2014) Nonlinear dynamics of autonomous vehicles with limits on acceleration. Phys A 405:128–139MathSciNetzbMATHCrossRefGoogle Scholar
 Davis LC (2016) Improving traffic flow at a 2to1 lane reduction with wirelessly connected, adaptive cruise control vehicles. Phys A 451:320–332CrossRefGoogle Scholar
 Delis AI, Nikolos IK, Papageorgiou M (2015) Macroscopic traffic flow modeling with adaptive cruise control: development and numerical solution. Comput Math Appl 70:1921–1947MathSciNetCrossRefGoogle Scholar
 Dharba S, Rajagopal KR (1999) Intelligent cruise control systems and traffic flow stability. Transp Res C 7:329–352CrossRefGoogle Scholar
 Elefteriadou L (2014) An introduction to traffic flow theory. Springer optimization and its applications, vol 84. Springer, BerlinGoogle Scholar
 Elefteriadou L, Roess RP, McShane WR (1995) Probabilistic nature of breakdown at freeway merge junctions. Transp Res Rec 1484:80–89Google Scholar
 European Roadmap Smart Systems for Automated Driving (2015) https://www.smartsystemsintegration.org/public/documents/
 Ferrara A, Sacone S, Siri S (2018) Freeway traffic modelling and control. Springer, Berlin. https://doi.org/10.1007/9783319759616CrossRefzbMATHGoogle Scholar
 Gao K, Jiang R, Hu SX, Wang BH, Wu QS (2007) Cellularautomaton model with velocity adaptation in the framework of Kerner’s threephase traffic theory. Phys Rev E 76:026105ADSCrossRefGoogle Scholar
 Gao K, Jiang R, Wang BH, Wu QS (2009) Discontinuous transition from free flow to synchronized flow induced by shortrange interaction between vehicles in a three phase traffic flow model. Phys A 388:3233–3243CrossRefGoogle Scholar
 Gartner NH, Messer CJ, Rathi A (eds) (1997) Special report 165: revised monograph on traffic flow theory. Transportation Research Board, Washington, DCGoogle Scholar
 Gartner NH, Messer CJ, Rathi A (eds) (2001) Traffic flow theory: a stateoftheart report. Transportation Research Board, Washington, DCGoogle Scholar
 Gasnikov AV, Klenov SL, Nurminski EA, Kholodov YA, Shamray NB (2013) Introduction to mathematical simulations of traffic flow. MCNMO, Moscow (in Russian)Google Scholar
 Gazis DC (2002) Traffic theory. Springer, BerlinzbMATHGoogle Scholar
 Gipps PG (1981) Behavioral carfollowing model for computer simulation. Trans Res B 15:105–111CrossRefGoogle Scholar
 Haight FA (1963) Mathematical theories of traffic flow. Academic, New YorkzbMATHGoogle Scholar
 Han Y, Ahn S (2018) Stochastic modeling of breakdown at freeway merge bottleneck and traffic control method using connected automated vehicle. Transp Res B 107:146–166CrossRefGoogle Scholar
 Hausken K, Rehborn H (2015) Gametheoretic context and interpretation of Kerner’s threephase traffic theory. In: Hausken K, Zhuang J (eds) Game theoretic analysis of congestion, safety and security. Springer series in reliability engineering. Springer, Berlin, pp 113–141Google Scholar
 He S, Guan W, Song L (2010) Explaining traffic patterns at onramp vicinity by a driver perception model in the framework of threephase traffic theory. Phys A 389:825–836CrossRefGoogle Scholar
 Helbing D (2001) Traffic and related selfdriven manyparticle systems. Rev Mod Phys 73:1067–1141ADSCrossRefGoogle Scholar
 Helbing D, Hennecke A, Treiber M (1999) Phase diagram of traffic states in the presence of inhomogeneities. Phys Rev Lett 82:4360–4363ADSCrossRefGoogle Scholar
 Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) (2000) Traffic and granular flow’ 99. Springer, HeidelbergzbMATHGoogle Scholar
 Helbing D, Treiber M, Kesting A, Schönhof M (2009) Theoretical vs. empirical classification and prediction of congested traffic states. Eur Phys J B 69:583–598ADSCrossRefGoogle Scholar
 Highway Capacity Manual (2000) National research council. Transportation Research Board, Washington, DCGoogle Scholar
 Highway Capacity Manual (2010) National research council. Transportation Research Board, Washington, DCGoogle Scholar
 Hoogendoorn S, van Lint H, Knoop VL (2008) Macroscopic modeling framework unifying kinematic wave modeling and threephase traffic theory. Trans Res Rec 2088:102–108CrossRefGoogle Scholar
 Ioannou PA (ed) (1997) Automated highway systems. Plenum Press, New YorkzbMATHGoogle Scholar
 Ioannou P, Chien CC (1993) Autonomous Intelligent Cruise Control. IEEE Trans Veh Technol 42:657–672CrossRefGoogle Scholar
 Ioannou PA, Kosmatopoulos EB (2000) Adaptive control. In: Webster JG (ed) Wiley encyclopedia of electrical and electronics engineering. Wiley, New York. https://doi.org/10.1002/047134608X.W1002CrossRefGoogle Scholar
 Ioannou PA, Sun J (1996) Robust adaptive control. Prentice Hall, Inc., Upper Saddle RiverzbMATHGoogle Scholar
 Jiang R, Wu QS (2004) Spatialtemporal patterns at an isolated onramp in a new cellular automata model based on threephase traffic theory. J Phys A Math Gen 37:8197–8213ADSMathSciNetzbMATHCrossRefGoogle Scholar
 Jiang R, Wu QS (2005) Toward an improvement over KernerKlenovWolf three phase cellular automaton model. Phys Rev E 72:067103ADSCrossRefGoogle Scholar
 Jiang R, Wu QS (2007a) Dangerous situations in a synchronized flow model. Phys A 377:633–640CrossRefGoogle Scholar
 Jiang R, Wu QS (2007b) Dangerous situations in a synchronized flow model. Phys A 377:633–640CrossRefGoogle Scholar
 Jiang R, Hu MB, Wang R, Wu QS (2007) Spatiotemporal congested traffic patterns in macroscopic version of the KernerKlenov speed adaptation model. Phys Lett A 365:6–9ADSCrossRefGoogle Scholar
 Jiang R, Hu MB, Zhang HM, Gao ZY, Jia B, Wu QS, Yang M (2014) Traffic experiment reveals the nature of carfollowing. PLoS One 9:e94351ADSCrossRefGoogle Scholar
 Jiang R, Hu MB, Zhang HM, Gao ZY, Jia B, Wu QS (2015) On some experimental features of carfollowing behavior and how to model them. Transp Res B 80:338–354CrossRefGoogle Scholar
 Jiang R, Jin CJ, Zhang HM, Huang YX, Tian JF, Wang W, Hu MB, Wang H, Jia B (2017) Experimental and empirical investigations of traffic flow instability. Transp Res Proc 23:157–173CrossRefGoogle Scholar
 Jin CJ, Wang W (2011) The influence of nonmonotonic synchronized flow branch in a cellular automaton traffic flow model. Phys A 390:4184–4191CrossRefGoogle Scholar
 Jin CJ, Wang W, Jiang R, Gao K (2010) On the firstorder phase transition in a cellular automaton traffic flow model without a slowtostart effect. J Stat Mech 2010:P03018CrossRefGoogle Scholar
 Jin CJ, Wang W, Jiang R, Zhang HM, Wang H, Hu MB (2015) Understanding the structure of hypercongested traffic from empirical and experimental evidences. Transp Res C 60:324–338CrossRefGoogle Scholar
 Kerner BS (1998a) Traffic flow: experiment and theory. In: Schreckenberg M, Wolf DE (eds) Traffic and granular flow’97. Springer, Singapore, pp 239–267Google Scholar
 Kerner BS (1998b) Theory of congested traffic flow. In: Rysgaard R (ed) Proceedings of the 3rd symposium on highway capacity and level of service, vol 2. Road Directorate, Ministry of Transport, Denmark, pp 621–642Google Scholar
 Kerner BS (1998c) Empirical features of selforganization in traffic flow. Phys Rev Lett 81:3797–3400ADSzbMATHCrossRefGoogle Scholar
 Kerner BS (1999a) Congested traffic flow: observations and theory. Trans Res Rec 1678:160–167CrossRefGoogle Scholar
 Kerner BS (1999b) Theory of congested traffic flow: selforganization without bottlenecks. In: Ceder A (ed) Transportation and traffic theory. Elsevier Science, Amsterdam, pp 147–171Google Scholar
 Kerner BS (1999c) The physics of traffic. Phys World 12:25–30CrossRefGoogle Scholar
 Kerner BS (2000) Experimental features of the emergence of moving jams in free traffic flow. J Physics A: Math Gen 33:L221–L228ADSzbMATHCrossRefGoogle Scholar
 Kerner BS (2001) Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories. Netw Spat Econ 1:35–76CrossRefGoogle Scholar
 Kerner BS (2002a) Synchronized flow as a new traffic phase and related problems for traffic flow modelling. Math Comput Model 35:481–508MathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS (2002b) Empirical macroscopic features of spatialtemporal traffic patterns at highway bottlenecks. Phys Rev E 65:046138ADSCrossRefGoogle Scholar
 Kerner BS (2004) The physics of traffic. Springer, BerlinCrossRefGoogle Scholar
 Kerner BS (2007a) Method for actuating a trafficadaptive assistance system which is located in a vehicle, USA patent US 20070150167A1. https://google.com/patents/US20070150167A1; USA patent US 7451039B2 (2008)
 Kerner BS (2007b) Betriebsverfahren für ein fahrzeugseitiges verkehrsadaptives Assistenzsystem, German patent publication DE 102007008253A1. https://register.dpma.de/DPMAregister/pat/PatSchrifteneinsicht?do cId=DE102007008253A1
 Kerner BS (2007c) Betriebsverfahren für ein fahrzeugseitiges verkehrsadaptives Assistenzsystem, German patent publication DE 102007008257A1. https://register.dpma.de/DPMAregister/pat/PatSchrifteneinsicht?do cId=DE102007008257A1
 Kerner BS (2008) Betriebsverfahren für ein fahrzeugseitiges verkehrsadaptives Assistensystem, German patent publication DE 102007008254A1Google Scholar
 Kerner BS (2009) Introduction to modern traffic flow theory and control. Springer, BerlinzbMATHCrossRefGoogle Scholar
 Kerner BS (2013) Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory: a brief review. Phys A 392:5261–5282MathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS (2015a) Microscopic theory of trafficflow instability governing traffic breakdown at highway bottlenecks: growing wave of increase in speed in synchronized flow. Phys Rev E 92:062827ADSCrossRefGoogle Scholar
 Kerner BS (2015b) Failure of classical traffic flow theories: a critical review. Elektrotechnik und Informationstechnik 132:417–433CrossRefGoogle Scholar
 Kerner BS (2016) Failure of classical traffic flow theories: stochastic highway capacity and automatic driving. Phys A 450:700–747MathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS (2017a) Breakdown in traffic networks: fundamentals of transportation science. Springer, BerlinzbMATHCrossRefGoogle Scholar
 Kerner BS (2017b) Traffic networks, breakdown in. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC, Springer, Berlin. https://doi.org/10.1007/97836422773757011CrossRefGoogle Scholar
 Kerner BS (2017c) Physics of autonomous driving based on threephase traffic theory. arXiv:1710.10852v3. http://arxiv.org/abs/1710.10852
 Kerner BS (2017d) Traffic breakdown, modeling approaches to. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC, Springer, Berlin. https://doi.org/10.1007/97836422773755592CrossRefGoogle Scholar
 Kerner BS (2018a) Traffic congestion, spatiotemporal features of. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC, Springer, BerlinGoogle Scholar
 Kerner BS (2018b) Physics of automated driving in framework of threephase traffic theory. Phys Rev E 97:042303ADSCrossRefGoogle Scholar
 Kerner BS (2018c) Autonomous driving in framework of threephase traffic theory. Procedia Comput Sci 130:785–790. https://doi.org/10.1016/j.procs.2018.04.136CrossRefGoogle Scholar
 Kerner BS, Klenov SL (2002) A microscopic model for phase transitions in traffic flow. J Phys A Math Gen 35:L31–L43ADSMathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS, Klenov SL (2003) Microscopic theory of spatiotemporal congested traffic patterns at highway bottlenecks. Phys Rev E 68:036130ADSCrossRefGoogle Scholar
 Kerner BS, Klenov SL (2006) Deterministic microscopic threephase traffic flow models. J Phys A Math Gen 39:1775–1809ADSMathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS, Klenov SL (2009) Phase transitions in traffic flow on multilane roads. Phys Rev E 80:056101ADSCrossRefGoogle Scholar
 Kerner BS, Klenov SL (2018) Traffic breakdown, mathematical probabilistic approaches to. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC, Springer, BerlinGoogle Scholar
 Kerner BS, Rehborn H (1996) Experimental properties of complexity in traffic flow. Phys Rev E 53:R4275–R4278ADSCrossRefGoogle Scholar
 Kerner BS, Rehborn H (1997) Experimental properties of phase transitions in traffic flow. Phys Rev Lett 79:4030–4033ADSCrossRefGoogle Scholar
 Kerner BS, Klenov SL, Wolf DE (2002) Cellular automata approach to threephase traffic theory. J Phys A Math Gen 35:9971–10013ADSMathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS, Klenov SL, Hiller A (2006a) Criterion for traffic phases in single vehicle data and empirical test of a microscopic threephase traffic theory. J Phys A Math Gen 39:2001–2020ADSzbMATHCrossRefGoogle Scholar
 Kerner BS, Klenov SL, Hiller A, Rehborn H (2006b) Microscopic features of moving traffic jams. Phys Rev E 73:046107ADSCrossRefGoogle Scholar
 Kerner BS, Klenov SL, Hiller A (2007) Empirical test of a microscopic threephase traffic theory. Non Dyn 49:525–553zbMATHCrossRefGoogle Scholar
 Kerner BS, Klenov SL, Schreckenberg M (2011) Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow. Phys Rev E 84:046110ADSCrossRefGoogle Scholar
 Kerner BS, Klenov SL, Hermanns G, Schreckenberg M (2013a) Effect of driver overacceleration on traffic breakdown in threephase cellular automaton traffic flow models. Phys A 392:4083–4105MathSciNetzbMATHCrossRefGoogle Scholar
 Kerner BS, Rehborn H, Schäfer RP, Klenov SL, Palmer J, Lorkowski S, Witte N (2013b) Traffic dynamics in empirical probe vehicle data studied with threephase theory: spatiotemporal reconstruction of traffic phases and generation of jam warning messages. Phys A 392:221–251CrossRefGoogle Scholar
 Kerner BS, Klenov SL, Schreckenberg M (2014) Probabilistic physical characteristics of phase transitions at highway bottlenecks: incommensurability of threephase and twophase trafficflow theories. Phys Rev E 89:052807ADSCrossRefGoogle Scholar
 Kerner BS, Koller M, Klenov SL, Rehborn H, Leibel M (2015) The physics of empirical nuclei for spontaneous traffic breakdown in free flow at highway bottlenecks. Phys A 438:365–397CrossRefGoogle Scholar
 Kesting A, Treiber M, Schönhof M, Helbing D (2007) Extending adaptive cruise control to adaptive driving strategies. Transp Res Rec 2000:16–24CrossRefGoogle Scholar
 Kesting A, Treiber M, Schönhof M, Helbing D (2008) Adaptive cruise control design for active congestion avoidance. Transp Res C 16:668–683CrossRefGoogle Scholar
 Kesting A, Treiber M, Helbing D (2010) Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity. Phil Trans Royal Society Series A 368:4585–4605ADSzbMATHCrossRefGoogle Scholar
 Klenov SL (2010) Kerner’s threephase traffic theory – a new theoretical basis for development of intelligent transportation systems. In: Kozlov VV (Ed) Proceedings of Moscow institute of physics and technology (State University), vol 2, pp 75–90 (in Russian)Google Scholar
 Knorr F, Schreckenberg M (2013) The comfortable driving model revisited: traffic phases and phase transitions. J Stat Mech 2013:P07002MathSciNetCrossRefGoogle Scholar
 Kokubo S, Tanimoto J, Hagishima A (2011) A new cellular automata model including a decelerating damping effect to reproduce Kerner’s threephase theory. Phys A 390:561–568CrossRefGoogle Scholar
 Krauß S (1998) Microscopic modeling of traffic flow: investigation of collision free vehicle dynamics. Ph.D. thesis, University of Cologne, Germany. http://earchive.informatik.unikoeln.de/319/
 Krauß S, Wagner P, Gawron C (1997) Metastable states in a microscopic model of traffic flow. Phys Rev E 55:5597–5602ADSCrossRefGoogle Scholar
 Kuhn TS (2012) The structure of scientific revolutions, 4th edn. The University of Chicago Press, Chicago/LondonCrossRefGoogle Scholar
 Kukuchi S, Uno N, Tanaka M (2003) Impacts of shorter perceptionreaction time of adapted cruise controlled vehicles on traffic flow and safety. Transp Eng 129:146–154CrossRefGoogle Scholar
 Lee HK, Kim BJ (2011) Dissolution of traffic jam via additional local interactions. Phys A 390:4555–4561MathSciNetCrossRefGoogle Scholar
 Lee HK, Barlović R, Schreckenberg M, Kim D (2004) Mechanical restriction versus human overreaction triggering congested traffic states. Phys Rev Lett 92:238702ADSCrossRefGoogle Scholar
 Leutzbach W (1988) Introduction to the theory of traffic flow. Springer, BerlinCrossRefGoogle Scholar
 Levine W, Athans M (1966) On the optimal error regulation of a string of moving vehicles. IEEE Trans Automat Contr 11:355–361CrossRefGoogle Scholar
 Li PY, Shrivastava A (2002) Traffic flow stability induced by constant time headway policy for adaptive cruise control vehicles. Transp Res C 10:275–301CrossRefGoogle Scholar
 Li XG, Gao ZY, Li KP, Zhao XM (2007) Relationship between microscopic dynamics in traffic flow and complexity in networks. Phys Rev E 76:016110ADSCrossRefGoogle Scholar
 Liang CY, Peng H (1999) Optimal adaptive cruise control with guaranteed string stability. Veh Syst Dyn 32:313–330CrossRefGoogle Scholar
 Liang CY, Peng H (2000) String stability analysis of adaptive cruise controlled vehicles. JSME Jnt J Ser C 43:671–677Google Scholar
 Lin TW, Hwang SL, Green P (2009) Effects of timegap settings of adaptive cruise control (ACC) on driving performance and subjective acceptance in a bus driving simulator. Saf Sci 47:620–625CrossRefGoogle Scholar
 Mahnke R, Kaupužs J, Lubashevsky I (2005) Probabilistic description of traffic flow. Phys Rep 408:1–130ADSCrossRefGoogle Scholar
 Mahnke R, Kaupužs J, Lubashevsky I (2009) Physics of stochastic processes: how randomness acts in time. WileyVCH, WeinheimzbMATHGoogle Scholar
 Mamouei M, Kaparias I, Halikias G (2018) A framework for user and systemoriented optimisation of fuel efficiency and traffic flow in Adaptive Cruise Control. Transp Res C 92:27–41CrossRefGoogle Scholar
 Marsden G, McDonald M, Brackstone M (2001) Towards an understanding of adaptive cruise control. Transp Res C 9:33–51CrossRefGoogle Scholar
 Martinez JJ, CanudasdoWit C (2007) A safe longitudinal control for adaptive cruise control and stopandgo scenarios. IEEE Trans Control Syst Technol 15:246–258CrossRefGoogle Scholar
 Maurer M, Gerdes JC, Lenz B, Winner H (eds) (2015) Autonomes Fahren. Springer, BerlinGoogle Scholar
 May AD (1990) Traffic flow fundamentals. PrenticeHall, Inc., New JerseyGoogle Scholar
 Meyer G, Beiker S (2014) Road vehicle automation. Springer, BerlinCrossRefGoogle Scholar
 Nagatani T (2002) The physics of traffic jams. Rep Prog Phys 65:1331–1386ADSCrossRefGoogle Scholar
 Nagel K, Wagner P, Woesler R (2003) Still flowing: approaches to traffic flow and traffic jam modeling. Oper Res 51:681–716MathSciNetzbMATHCrossRefGoogle Scholar
 Neto JPL, Lyra ML, da Silva CR (2011) Phase coexistence induced by a defensive reaction in a cellular automaton traffic flow model. Phys A 390:3558–3565CrossRefGoogle Scholar
 Newell GF (1982) Applications of queuing theory. Chapman Hall, LondonCrossRefGoogle Scholar
 Ngoduy D (2012) Application of gaskinetic theory to modelling mixed traffic of manual and ACC vehicles. Transpormetrica 8:43–60CrossRefGoogle Scholar
 Ngoduy D (2013) Instability of cooperative adaptive cruise control traffic flow: a macroscopic approach. Commun Nonlinear Sci Numer Simul 18:2838–2851ADSMathSciNetzbMATHCrossRefGoogle Scholar
 Ntousakis IA, Nokolos IK, Papageorgiou M (2015) On microscopic modelling of adaptive cruise control systems. Transp Res Procedia 9:111–127CrossRefGoogle Scholar
 Papageorgiou M (1983) Application of automatic control concepts in traffic flow modeling and control. Springer, BerlinzbMATHCrossRefGoogle Scholar
 Perraki G, Roncoli C, Papamichail I, Papageorgiou M (2018) Evaluation of a model predictive control framework for motorway traffic involving conventional and automated vehicles. Trans Res C 92:456–471CrossRefGoogle Scholar
 Persaud BN, Yagar S, Brownlee R (1998) Exploration of the breakdown phenomenon in freeway traffic. Trans Res Rec 1634:64–69CrossRefGoogle Scholar
 Pottmeier A, Thiemann C, Schadschneider A, Schreckenberg M (2007) Mechanical restriction versus human overreaction: accident avoidance and twolane simulations. In: Schadschneider A, Pöschel T, Kühne R, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’05. Proceedings of the international workshop on traffic and granular flow. Springer, Berlin, pp 503–508CrossRefGoogle Scholar
 Qian YS, Feng X, JunWei Zeng JW (2017) A cellular automata traffic flow model for threephase theory. Phys A 479:509–526MathSciNetCrossRefGoogle Scholar
 Rajamani R (2012) Vehicle dynamics and control, mechanical engineering series. Springer US, BostonzbMATHCrossRefGoogle Scholar
 Rehborn H, Klenov SL (2009) Traffic prediction of congested patterns. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer, Berlin, pp 9500–9536CrossRefGoogle Scholar
 Rehborn H, Koller M (2014) A study of the influence of severe environmental conditions on common traffic congestion features. J Adv Transp 48:1107–1120CrossRefGoogle Scholar
 Rehborn H, Palmer J (2008) ASDA/FOTO based on Kerner’s threephase traffic theory in north RhineWestphalia and its integration into vehicles. In: Intelligent vehicles symposium, IEEE, Eindhoven, Netherlands, pp 186–191. ISSN: 19310587. https://doi.org/10.1109/IVS.2008.4621192
 Rehborn H, Klenov SL, Palmer J (2011a) An empirical study of common traffic congestion features based on traffic data measured in the USA, the UK, and Germany. Phys A 390:4466–4485CrossRefGoogle Scholar
 Rehborn H, Klenov SL, Palmer J (2011b) Common traffic congestion features studied in USA, UK, and Germany based on Kerner’s threephase traffic theory. In: IEEE intelligent vehicles symposium (IV), IEEE, BadenBaden, Germany, pp 19–24. https://doi.org/10.1109/IVS.2011.5940394
 Rehborn H, Klenov SL, Koller M (2017) Traffic prediction of congested patterns. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC, Springer, BerlinGoogle Scholar
 Rempe F, Franeck P, Fastenrath U, Bogenberger K (2016) Online freeway traffic estimation with real floating car data. In: Proceedings of 2016 IEEE 19th international conference on Intelligent Transportation Systems (ITSC), Rio de Janeiro, pp 1838–1843Google Scholar
 Roncoli C, Papageorgiou M, Papamichail I (2015) Traffic flow optimisation in presence of vehicle automation and communication systems – part I: a firstorder multilane model for motorway traffic. Transp Res C 57:241–259CrossRefGoogle Scholar
 Saifuzzaman M, Zheng Z (2014) Incorporating humanfactors in carfollowing models: a review of recent developments and research needs. Transp Res C 48:379–403CrossRefGoogle Scholar
 Schadschneider A, Chowdhury D, Nishinari K (2011) Stochastic transport in complex systems. Elsevier Science Inc., New YorkzbMATHGoogle Scholar
 Sharon G, Levin MW, Hanna JP, Rambha T, Boyles SD, Stone P (2017) Network wide adaptive tolling for connected and automated vehicles. Transp Res C 84:142–157CrossRefGoogle Scholar
 Shladover SE (1995) Review of the state of development of advanced vehicle control systems (AVCS). Veh Syst Dyn 24:551–595CrossRefGoogle Scholar
 Shladover SE, Su D, Lu XT (2012) Impacts of cooperative adaptive cruise control on freeway traffic flow. Transp Res Rec 2324:63–70CrossRefGoogle Scholar
 Siebel F, Mauser W (2006) Synchronized flow and wide moving jams from balanced vehicular traffic. Phys Rev E 73:066108ADSMathSciNetzbMATHCrossRefGoogle Scholar
 Suzuki H (2003) Effect of adaptive cruise control (ACC) on traffic throughput: numerical example on actual freeway corridor. JSAE Rev 24:403–410CrossRefGoogle Scholar
 Swaroop D, Hedrick JK (1996) String stability for a class of nonlinear systems. IEEE Trans Automat Contr 41:349–357zbMATHCrossRefGoogle Scholar
 Swaroop D, Hedrick JK, Choi SB (2001) Direct adaptive longitudinal control of vehicle platoons. IEEE Trans Veh Technol 50:150–161CrossRefGoogle Scholar
 Takayasu M, Takayasu H (1993) Phase transition and 1/f type noise in one dimensional asymmetric particle dynamics. Fractals 1:860–866zbMATHCrossRefGoogle Scholar
 Talebpour A, Mahmassani HS (2016) Influence of connected and autonomous vehicles on traffic flow stability and throughput. Transp Res C 71:143–163CrossRefGoogle Scholar
 Tian JF, Jia B, Li XG, Jiang R, Zhao XM, Gao ZY (2009) Synchronized traffic flow simulating with cellular automata model. Phys A 388:4827–4837CrossRefGoogle Scholar
 Tian JF, Yuan ZZ, Jia B, Treiber M, Jia B, Zhang WY (2012) Cellular automaton model within the fundamentaldiagram approach reproducing some findings of the threephase theory. Phys A 391:3129–3139CrossRefGoogle Scholar
 Tian JF, Jiang R, Jia B, Gao ZY, Ma SF (2016a) Empirical analysis and simulation of the concave growth pattern of traffic oscillations. Transp Res B 93:338–354CrossRefGoogle Scholar
 Tian JF, Jiang R, Li G, Treiber M, Jia B, Zhu CQ (2016b) Improved 2D intelligent driver model in the framework of threephase traffic theory simulating synchronized flow and concave growth pattern of traffic oscillations. Transp Rec F 41:55–65CrossRefGoogle Scholar
 Tian JF, Li G, Treiber M, Jiang R, Jia N, Ma SF (2016c) Cellular automaton model simulating spatiotemporal patterns, phase transitions and concave growth pattern of oscillations in traffic flow. Transp Rec B 93:560–575CrossRefGoogle Scholar
 Tian JF, Zhu CQ, Jiang R (2018) Cellular automaton models in the framework of threephase traffic theory. In: Meyers RA (ed) Encyclopedia of complexity and system science. Springer Science+Business Media LLC, Springer, BerlinGoogle Scholar
 Treiber M, Helbing D (2001) Microsimulations of freeway traffic including control measures. Automatisierungstechnik 49:478–484CrossRefGoogle Scholar
 Treiber M, Kesting A (2013) Traffic flow dynamics. Springer, BerlinzbMATHCrossRefGoogle Scholar
 van Arem B, van Driel CJG, Visser R (2006) The impact of cooperative adaptive cruise control on traffic flow characteristics. IEEE Trans Intell Transp Syst 7:429–436CrossRefGoogle Scholar
 Van Brummelen J, O’Brien M, Gruyer D, Najjaran H (2018) Autonomous vehicle perception: the technology of today and tomorrow. Transp Res C 89:384–406CrossRefGoogle Scholar
 VanderWerf J, Shladover SE, Kourjanskaia N, Miller M, Krishnan H (2001) Modeling effects of driver control assistance systems on traffic. Transp Res Rec 1748:167–174CrossRefGoogle Scholar
 VanderWerf J, Shladover SE, Miller MA, Kourjanskaia N (2002) Effects of adaptive cruise control systems on highway traffic flow capacity. Transp Res Rec 1800:78–84CrossRefGoogle Scholar
 Varaiya P (1993) Smart cars on smart roads: problems of control. IEEE Trans Autom Control 38:195–207MathSciNetCrossRefGoogle Scholar
 Wang R, Jiang R, Wu QS, Liu M (2007) Synchronized flow and phase separations in singlelane mixed traffic flow. Phys A 378:475–484CrossRefGoogle Scholar
 Wang R, Li Y, Work DB (2017) Comparing traffic state estimators for mixed human and automated traffic flows. Transp Res C 78:95–110CrossRefGoogle Scholar
 Whitham GB (1974) Linear and nonlinear waves. Wiley, New YorkzbMATHGoogle Scholar
 Wiedemann R (1974) Simulation des Verkehrsflusses. University of Karlsruhe, KarlsruheGoogle Scholar
 Wu JJ, Sun HJ, Gao ZY (2008) Longrange correlations of density fluctuations in the KernerKlenovWolf cellular automata threephase traffic flow model. Phys Rev E 78:036103ADSCrossRefGoogle Scholar
 Xiang ZT, Li YJ, Chen YF, Xiong L (2013) Simulating synchronized traffic flow and wide moving jam based on the brake light rule. Phys A 392:5399–5413CrossRefGoogle Scholar
 Yang H, Lu J, Hu XJ, Jiang J (2013) A cellular automaton model based on empirical observations of a driver’s oscillation behavior reproducing the findings from Kerner’s threephase traffic theory. Phys A 392:4009–4018MathSciNetzbMATHCrossRefGoogle Scholar
 Yang H, Zhai X, Zheng C (2018) Effects of variable speed limits on traffic operation characteristics and environmental impacts under carfollowing scenarios: simulations in the framework of Kerner’s threephase traffic theory. Phys A. https://doi.org/10.1016/j.physa.2018.05.032ADSCrossRefGoogle Scholar
 Zhang P, Wu CX, Wong SC (2012) A semidiscrete model and its approach to a solution for a wide moving jam in traffic flow. Phys A 391:456–463CrossRefGoogle Scholar
 Zhou J, Peng H (2005) Range policy of adaptive cruise control vehicles for improved flow stability and string stability. IEEE Trans Intell Transp Syst 6:229–237CrossRefGoogle Scholar
 Zhou M, Qu X, Jin S (2017) On the impact of cooperative autonomous vehicles in improving freeway merging: a modified intelligent driver modelbased approach. IEEE Trans Intell Transp Syst 18:1422–1428Google Scholar