Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling

References

• Acha-Daza J. A., Hall F. L. Graphical comparison of predictions for speed given by catastrophe theory and some classic models. Transportation Res. Record (1993) 1398:119–124Google Scholar
• Ansorge R. What does the entropy condition mean in traffic flow theory? Transportation Res. B (1990) 24:133–143Crossref, Google Scholar
• Aw A., Rascle M. Resurrection of second order models of traffic flow. SIAM J. Appl. Math. (2000) 60:916–938Crossref, Google Scholar
• Aw A., Klar A., Materne T., Rascle M. Derivation of continuum traffic flow models from microscopic follow-the-leader models. SIAM J. Appl. Math. (2002) 63(1):259–278Crossref, Google Scholar
• Bachmann E. Leistungsfähigkeit von Strassen und Plätzen. Strasse und Verkehr (1938) 24:237–246In GermanGoogle Scholar
• Bando M., Hasebe K., Nakayama A., Shibata A., Sugiyama Y. Structure stability of congestion in traffic dynamics. Japan J. Indust. Appl. Math. (1994) 11(2):203–223Crossref, Google Scholar
• Bando M., Hasebe K., Nakayama A., Shibata A., Sugiyama Y. Dynamical model of traffic congestion and numerical simulation. Physical Rev. E (1995) 51(2):1035–1042Crossref, Google Scholar
• Barlovic R., Santen L., Schadschneider A., Schreckenberg M. Metastable states in CA models for traffic flow. Eur. Physical J. B (1998) 5(3):793–800Crossref, Google Scholar
• Barrett C. L., Wolinsky M., Olesen M. W., Wolf D. E., Schreckenberg M., Bachem A. Emergent local control properties in particle hopping traffic simulations. Traffic and Granular Flow (1996) (World Scientific, Singapore) 169–173Google Scholar
• Ben-Naim E., Krapivsky P. L. Stationary velocity distributions in traffic flows. Physical Rev. E (1997) 56(6):6680–6686Crossref, Google Scholar
• Biham O., Middleton A., Levine D. Self-organization and a dynamical transition in traffic-flow models. Physical Rev. A (1992) 46:R6124–R6127Crossref, Google Scholar
• Bogomolny E. B., Gerland U., Schmit C. Models of intermediate spectral statistics. Physical Rev. E (1999) 59:R1315–R1318Crossref, Google Scholar
• Bottom J. A. Consistent anticipatory route guidance. (2000) . Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MAGoogle Scholar
• Brankov J. G., Priezzhev V. B., Schadschneider A., Schreckenberg M. The Kasteleyn model and a cellular automaton approach to traffic flow. J. Physics A Math. General (1996) 29:L229–L235Crossref, Google Scholar
• Brilon W., Wu N., Brilon W. , Huber F., Schreckenberg M., Wallentowitz H. Evaluation of cellular automata for traffic flow simulation on freeway and urban streets. Traffic and Mobility: Simulation–Economics–Environment (1999) (Springer, Heidelberg, Germany) 163–180Crossref, Google Scholar
• Burgers J. M.The Nonlinear Diffusion Equation (1974) (Reidel, Dordrecht, The Netherlands) Crossref, Google Scholar
• Cassidy M. J. Bivariate relations in nearly stationary highway traffic. Transportation Res. B (1998) 32:49–59Crossref, Google Scholar
• Ceder A. A time-sequence analysis of a two-regime traffic flow model. Proc. 7th Internat. Sympos. Transportation Traffic Theory (1977) Kyoto, Japan:145–165Google Scholar
• Cheybani S., Kertesz J., Schreckenberg M. Nondeterministic Nagel-Schreckenberg traffic model with open boundary conditions. Physical Rev. E (2001) 63:1–9Crossref, Google Scholar
• Chowdhury D., Santen L., Schadschneider A. Statistical physics of vehicular traffic and some related systems. Physics Rep. (2000a) 329(4–6):199–329Crossref, Google Scholar
• Chowdhury D., Kertész J., Nagel K., Santen L., Schadschneider M. Comment on: “Critical behavior of a traffic flow model.”. Physical Rev. E (2000b) 61(3):3270–3271Crossref, Google Scholar
• Chronopolous A., Michalopoulos P. Traffic flow simulation through parallel processing. Final research report. (1991) . Technical report, Center for Transportation Studies, University of Minnesota, Minneapolis, MNGoogle Scholar
• Coifman B., Lyddy D., Skabardonis A. The Berkeley Highway Laboratory—Building on the I-880 field experiment. 2000 IEEE Intelligent Transportation Systems Proc. (2000) Dearborn, MI:5–10Crossref, Google Scholar
• Cremer M., Ludwig J. A fast simulation model for traffic flow on the basis of Boolean operations. Math. Comput. in Simulation (1986) 28:297–303Crossref, Google Scholar
• Cremer M., May A. D. An extended traffic model for freeway control. (1985) . Technical research report UCB-IST-RR-85-7, Institute of Transportation Studies, University of California, Berkeley, CAGoogle Scholar
• Daganzo C. F. The cell transmission model: A simple dynamical representation of highway traffic consistent with the hydrodynamic theory. Transportation Res. B (1994) 28(4):269–287Crossref, Google Scholar
• Daganzo C. F. Requiem for second-order fluid approximations of traffic flow. Transportation Res. B (1995a) 29:277–286Crossref, Google Scholar
• Daganzo C. F. The cell transmission model. Part II: Network traffic. Transportation Res. B (1995b) 29:79–93Crossref, Google Scholar
• Daganzo C. F. A behavioral theory of multi-lane traffic flow. I: Long homogeneous freeway sections. (1999) . Technical research report UCB-IST-RR-99-6, Institute of Transportation Studies, University of California, Berkeley, CAGoogle Scholar
• Daganzo C. F., Cassidy M. Personal communication. (2001) Google Scholar
• Daganzo C. F., Cassidy M., Bertini R. L. Possible explanations of phase transitions in highway traffic. Transportation Res. A (1999) 33:365–379Google Scholar
• DLR Multisat Web Services. (2002) . http://www.multisat.dlr.deGoogle Scholar
• DLR/VF Institute for Transportation Research. (2001) . ivf.dlr.de/clearingGoogle Scholar
• DYNAMIT Massachusetts Institute of Technology, Cambridge, MA. (1999) . its.mit.eduGoogle Scholar
• Dyson F. J. Statistical theory of energy levels of complex systems, parts I–III. J. Math. Physics (1962) 3:140–175Crossref, Google Scholar
• Edie L. C. Car-following and steady-state theory for noncongested traffic. Oper. Res. (1961) 9:66–77Link, Google Scholar
• Eissfeldt N., Schrader R. Calculation of street traffic emissions with a queuing model. J. Comput. Tech. (2001) . SubmittedGoogle Scholar
• Gawron C. An iterative algorithm to determine the dynamic user equilibrium in a traffic simulation model. Internat. J. Modern Physics C (1998) 9(3):393–407Crossref, Google Scholar
• Gawron Ch. Simulation-based traffic assignment. (1999) . Ph.D. thesis, University of Cologne, Cologne, GermanyGoogle Scholar
• Gazis D. C., Herman R., Montroll E. W., Rothery R. W. Nonlinear follow-the-leader models of traffic flow. Oper. Res. (1961) 9:545–560Link, Google Scholar
• Gerlough D. L., Burggraf F., Ward E. M. Simulation of freeway traffic by an electronic computer. Proc. 35th Annual Meeting (1956) (Highway Research Board, National Research Council, Washington, DC) 543–547Google Scholar
• Gerlough D. L., Huber M. J. Traffic flow theory. (1975) . Special report 165. Transportation Research Board, National Research Council, Washington, DCGoogle Scholar
• Gipps P. G. A behavioural car following model for computer simulation. Transportation Res. B (1981) 15:105–111Crossref, Google Scholar
• Gipps P. G. A model for the structure of lane-changing decisions. Transportation Res. B (1986) 20B(5):403–414Crossref, Google Scholar
• Godunov S. K. A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics. Math. Sbornik (1959) 47:271–306In RussianGoogle Scholar
• Gray L., Griffeath D. The ergodic theory of traffic jams. J. Statist. Physics (2001) 105(3–4):413–452Crossref, Google Scholar
• Greenshields B. D. A study of traffic capacity. Proc. Highway Res. Board (1935) 14Washington, DC:448–477Google Scholar
• Haberman R.Mathematical Models in Mechanical Vibrations, Population Dynamics, and Traffic Flow (1977) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• Haight F. A.Mathematical Theories of Traffic Flow (1963) (Academic Press, New York) Google Scholar
• Hall F. L., Agyemang-Duah K. Freeway capacity drop and the definition of capacity. Transportation Res. Record (1991) 1320:91–98Google Scholar
• Hall F. L., Hurdle V. F., Banks J. H. A synthesis of recent work on the nature of speed-flow and flow-occupancy (or density) relationships on freeways. Transportation Res. Record (1992) 1365:12–18Google Scholar
• Helbing D. Gas-kinetic derivation of Navier-Stokes-like traffic equations. Physical Rev. E (1996) 53(3):253–282Crossref, Google Scholar
• Helbing D.Verkehrsdynamik (1997) (Springer, Berlin, Germany) . In GermanCrossref, Google Scholar
• Helbing D. Traffic and related self-driven many-particle systems. Rev. Modern Physics (2001) 73:1067–1141Crossref, Google Scholar
• Helbing D., Huberman B. A. Coherent moving states in highway traffic. Nature (1998) 396:738–740Crossref, Google Scholar
• Helbing D., Tilch B. Generalized force model of traffic dynamics. Physical Rev. E (1998) 58:133–138Crossref, Google Scholar
• Helbing D., Treiber M. Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Physical Rev. Lett. (1998) 81(14):3042–3045Crossref, Google Scholar
• Herman R., Montroll E. W., Potts R. B., Rothery R. W. Traffic dynamics: Analysis of stability in car following. Oper. Res. (1959) 7:86–106Link, Google Scholar
• Janz S. Mikroskopische minimalmodelle des strassenverkehrs. (1998) . Master's thesis, University of Cologne, Cologne, Germany. In GermanGoogle Scholar
• Jost D. Breakdown and recovery in traffic flow models. (2002) . Master's thesis, ETH Zurich, Switzerland. e-collection. ethbib.ethz.chGoogle Scholar
• Jost D., Nagel K. Probabilistic traffic flow breakdown in stochastic car following models. (2003) . Paper 03-4266, Transportation Research Board Annual Meeting, Washington, DC. sim.inf.ethz.ch/papers. Shorter version to be published in Transportation Res. RecordGoogle Scholar
• Kates R., Bogenberger K., Hoops M., Schreckenberg M., Wolf D. E. Mesoscopic simulation with ANIMAL. Traffic and Granular Flow '97 (1998) (Springer, Berlin, Germany) 453–467Google Scholar
• Kerner B. S. Experimental features of self-organization in traffic flow. Physical Rev. Lett. (1998) 81:3797–3800Crossref, Google Scholar
• Kerner B. S. Congested traffic flow: Observations and theory. Transportation Res. Record (1999a) 1678:160–167Crossref, Google Scholar
• Kerner B. S., Helbing D., Hermann H. J., Schreckenberg M., Wolf D. E. Phase transitions in traffic flow. Traffic and Granular Flow '99 (1999b) (Springer, Berlin, Germany) 253–284Google Scholar
• Kerner B. S. The physics of traffic. Physics World (1999c) 8:25–30Crossref, Google Scholar
• Kerner B. S., Klenov S. L.J. Physics A: Math. General (2002) 35:L31–L43Crossref, Google Scholar
• Kerner B. S., Konhäuser P. Cluster effect in initially homogeneous traffic flow. Physical Rev. E (1993) 48(4):R2335–R2338Crossref, Google Scholar
• Kerner B. S., Konhäuser P. Structure and parameters of clusters in traffic flow. Physical Rev. E (1994) 50(1):54–83Crossref, Google Scholar
• Kerner B. S., Osipov X. Cluster effect in initially homogeneous traffic flow. J. Physics A: Math. General (2002) 35:L31–L43Crossref, Google Scholar
• Kerner B. S., Rehborn H. Experimental features and characteristics of traffic jams. Physical Rev. E (1996a) 53(2):R1297–R1300Crossref, Google Scholar
• Kerner B. S., Rehborn H. Experimental properties of complexity in traffic flow. Physical Rev. E. (1996b) 53(5):R4275–R4278Crossref, Google Scholar
• Kerner B. S., Rehborn H. Experimental properties of phase transitions in traffic flow. Physical Rev. Lett. (1997) 79(20):4030–4033Crossref, Google Scholar
• Kerner B. S., Klenov S. L., Wolf D. E. Cellular automata approach to three-phase traffic theory. J. Physics A: Math. General (2002) 35(47):9971–10013Crossref, Google Scholar
• Kikuchi M., et al. (2001) . Video presented at Traffic and Granular Flow (TGF)'01, Nagoya, JapanGoogle Scholar
• Klar A., Wegener R. Enskog-like kinetic models for vehicular traffic. J. Statist. Physics (1997) 87(1–2):91–114Crossref, Google Scholar
• Klar A., Wegener R. Kinetic derivation of macroscopic anticipation models for vehicular traffic. SIAM J. Appl. Math. (2000) 60(5):1749–1766Crossref, Google Scholar
• Knospe W., Santen L., Schadschneider A., Schreckenberg M., Helbing D., Hermann H. J., Schreckenberg M., Wolf D. E. CA models for traffic flow: Comparison with empirical single-vehicle data. Traffic and Granular Flow '99 (1999a) (Springer, Berlin, Germany) 366–376Google Scholar
• Knospe W., Santen L., Schadschneider A., Schreckenberg M. Single-vehicle data of highway traffic. Physical Rev. E (1999b) 60:6480–6490Crossref, Google Scholar
• Knospe W., Santen L., Schadschneider A., Schreckenberg M. Towards a realistic microscopic description of highway traffic. J. Physics A Math. General (2000) 33:L477–L485Crossref, Google Scholar
• Knospe W., Santen L., Schadschneider A., Schreckenberg M. Single-vehicle data of highway traffic: Microscopic description of traffic phases. Physical Rev. E (2002) 65(056133):1–16Google Scholar
• Koshi M., Iwasaki M., Ohkura I. Some findings and an overview of vehicular flow characteristics. Proc. 8th Internat. Sympos. Transportation Traffic Theory (1983) (Elsevier, Amsterdam, The Netherlands, and Toronto, Ontario, Canada) 403–426Google Scholar
• Krauß S. Microscopic modelling of traffic flow: Investigation of collision free vehicle dynamics. (1998) . Ph.D. thesis, University of Cologne, Cologne, GermanyGoogle Scholar
• Krauß S., Wagner P., Gawron C. Metastable states in a microscopic model of traffic flow. Physical Rev. E (1997) 55:5597–5605Crossref, Google Scholar
• Krbalek M., Seba P., Wagner P. Headways in traffic flow—Remarks from a physical perspective. Physical Rev. E (2001) 64(066110):1–7Google Scholar
• Kühne R. D., Volmuller J., Hamerslag R. Macroscopic freeway model for dense traffic stop-start waves and incident detection. Proc. 9th Internat. Sympos. Transportation Traffic Theory (1984) (VNU Science Press, Utrecht, The Netherlands) 21–42Google Scholar
• Lax P. D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves, no. 11. Regional Conference Series Appl. Math (1973) (Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA) Crossref, Google Scholar
• Lebacque J. P. The Godunov scheme and what it means for first order traffic flow models. (1995) . Technical report 95-48, Centre de'Enseignement et de Recherche en Mathmatiques, Informatique et Calcul Scientifique (CERMICS), Marne la Vallée, France. cermics.enpc.fr/reports/Google Scholar
• Lebacque J. P., Lesort J. B., Ceder A. Macroscopic traffic flow models: A question of order. Transportation and Traffic Theory (1999) (Pergamon Press, Amsterdam, The Netherlands) 3–25Google Scholar
• Lee H. Y., Lee H.-W., Kim D. Origin of synchronized traffic flow on highways and its dynamic phase transitions. Physical Rev. Lett. (1998) 81(5):1130–1133Crossref, Google Scholar
• Lee H. Y., Lee H.-W., Kim D. Macroscopic traffic models from microscopic car-following models. Physical Rev. E (2001) 64(056126):1–12Google Scholar
• Leo C. J., Pretty R. L. Numerical simulation of macroscopic continuum traffic models. Transportation Res. B (1992) 23:79–94Google Scholar
• Leutzbach W.Introduction to the Theory of Traffic (1988) (Springer, Berlin, Germany) Crossref, Google Scholar
• Lighthill M. J., Whitham J. B. On kinematic waves. I: Flow movement in long rivers. II: A theory of traffic flow on long crowded roads. Proc. Royal Soc. A (1955) 229:281–345Crossref, Google Scholar
• Lubashevsky I. A., Mahnke R., Helbing D., Hermann H. J., Schreckenberg M., Wolf D. E. Order parameter as an additional state variable of unstable traffic flow. Traffic and Granular Flow '99 (1999) (Springer, Berlin, Germany) 377–382Google Scholar
• Lubashevsky I. A., Mahnke R. Order-parameter model for unstable multilane traffic flow. Physical Rev. E (2000) 62(5):6082–6093Crossref, Google Scholar
• Mahmassani H. S., Hu T., Jayakrishnan R., Gartner N. H., Improta G. Dynamic traffic assignment and simulation for advanced network informatics (DYNASMART). Urban Traffic Networks: Dynamic Flow Modeling and Control (1995) (Springer, Berlin/New York) Google Scholar
• Mahut M. Speed-maximizing car following models and macroscopic curves based on save stopping rules. (1999) . Preprint number 990351, Transportation Research Board Annual Meeting, Washington, DCGoogle Scholar
• Mehta M. L.Random Matrices (1991) 2nd ed.(Academic Press, San Diego, CA) Google Scholar
• Michalopoulos P. G., Lin J., Beskos D. E. Integrated modelling and numerical treatment of traffic flow. Appl. Math. Modelling (1987) 2:447–457Crossref, Google Scholar
• Mika H. S., Kreer J. B., Yuan L. S. Dual-mode behaviour of freeway traffic. Highway Res. Records (1969) 279:1–13Google Scholar
• Mitarai N., Nakanishi H. Spatio-temporal structure of traffic flow in a system with an open boundary. Physical Rev. Lett. (2000) 85:1766–1769Crossref, Google Scholar
• Muñoz J. C., Daganzo C. F. Structure of the transition zone behind freeway queues. Transportation Sci. (2003) 37(3):312–329Link, Google Scholar
• Nagel K. Life-times of simulated traffic jams. Internat. J. Modern Physics C (1994) 5(3):567–580Crossref, Google Scholar
• Nagel K. Particle hopping models and traffic flow theory. Physical Rev. E (1996) 53(5):4655–4672Crossref, Google Scholar
• Nagel K. From particle hopping models to traffic flow theory. Transportation Res. Records (1999) 1644:1–9Crossref, Google Scholar
• Nagel K., Paczuski M. Emergent traffic jams. Physical Rev. E (1995) 51:2909–2918Crossref, Google Scholar
• Nagel K., Schreckenberg M. A cellular automaton model for freeway traffic. J. Physique I France (1992) 2:2221–2229Crossref, Google Scholar
• Nagel K., Kayatz C., Wagner P., Sugiyama Y., et al. Breakdown and recovery in traffic flow models. Traffic and Granular Flow '01. (2003) (Springer, Heidelberg, Germany) . In pressCrossref, Google Scholar
• Nagel K., Wolf D. E., Wagner P., Simon P. Two-lane traffic rules for cellular automata: A systematic approach. Physical Rev. E (1998) 58(2):1425–1437Crossref, Google Scholar
• Nagel K., Stretz P., Pieck M., Leckey S., Donnelly R., Barrett C. L. TRANSIMS traffic flow characteristics. (1997) . Los Alamos unclassified report (LA-UR) 97-3530. Los Alamos National Laboratory, Los Alamos, NM. transims.tsasa.lanl.govGoogle Scholar
• Namazi A., Eissfeldt N., Wagner P., Schadschneider A. Boundary-induced phase transitions in a space-continuous traffic model with non-unique flow-density relation. Eur. Physical J. B (2002) 30(4):559–570Crossref, Google Scholar
• Nelson P., Gartner N. H., Messer C. J., Rathi A. Kinetic theories. Monograph on Traffic Flow Theory (1997) . http://www.tfhrc.gov/its/tft/tft.htmGoogle Scholar
• Nelson P. Synchronized traffic flow from a modified Lighthill-Whitham model. Physical Rev. E (2000) 62(2):R6052–R6055Crossref, Google Scholar
• Newell G. F. Mathematical models of freely moving traffic. J. Oper. Res. Soc. Amer. (1955) 3:176–188Link, Google Scholar
• Newell G. F. Nonlinear effects in the dynamics of car following. Oper. Res. (1961) 9(2):209–229Link, Google Scholar
• Newell G. F. Theories of instability in dense highway traffic. J. Oper. Res. Soc. Japan (1962) 5:9–54Google Scholar
• Newell G. F. Instability in dense highway traffic, a review. Second Sympos. Theory Traffic Flow (1963) (OECD, London, U.K) 73–83Google Scholar
• Newell G. F. A simplified car-following theory: A lower order model. Transportation Res. B (2002) 36:195–205Crossref, Google Scholar
• Owren B., Zennaro M. Derivation of efficient, continuous, explicit Runge-Kutta methods. SIAM J. Sci. Statist. Comput. (1992) 13:1488–1501Crossref, Google Scholar
• Payne H. J., Bekey G. A. Models of freeway traffic and control. Mathematical Models of Public Systems (1971) (Simulation Council, La Jolla, CA) 51–61no. 28. Simulation Council ProcGoogle Scholar
• Payne H. J., Levine W. S. A critical review of macroscopic freeway model. Research Directions in Computer Control of Urban Traffic Systems (1979) (American Society of Civil Engineers, New York) 251–265Google Scholar
• Persaud B. N., Hall F. L. Catastrophe theory and patterns in 30-second freeway traffic data—Implications for incident detection. Transportation Res. A (1989) 23A(2):103–113Crossref, Google Scholar
• Popkov V., Schütz G. M. Steady-state selection in driven diffusive systems with open boundaries. Europhysics Lett. (1999) 48:257–263Crossref, Google Scholar
• Prigogine I., Herman R. A Boltzmann-like approach to the statistical theory of traffic flow. Theory of Traffic Flow (1961) (Elsevier, Amsterdam, The Netherlands) 158–164Google Scholar
• Prigogine I., Herman R.Kinetic Theory of Vehicular Traffic (1971) (Elsevier, New York) Google Scholar
• Rajewsky N., Schreckenberg M. Exact results for one-dimensional cellular automata with different types of updates. Physica A (1997) 245(1–2):139–144Crossref, Google Scholar
• Reiss H., Hammerich A. D., Montroll E. W. Thermodynamic treatment of nonphysical systems: Formalism and an example (single-lane traffic). J. Statist. Physics (1986) 42(3/4):647–687Crossref, Google Scholar
• Reuschel A. Fahrzeugbewegung in der Kolonne bei gleichförmig beschleunigtem oder verzögertem Leitfahrzeug. Zeitschrift des österreichischen Ingenieur und Architektenvereins (1950) . 7/8, 9/10; 59–62, 73–77. Vienna, Austria. In GermanGoogle Scholar
• Richards P. I. Shockwaves on the highway. Oper. Res. (1956) 4:42–51Link, Google Scholar
• Rickert M., Nagel K. Dynamic traffic assignment on parallel computers in TRANSIMS. Future Generation Comput. Systems (2001) 17(5):637–648Crossref, Google Scholar
• Rickert M., Nagel K., Schreckenberg M., Latour A. Two lane traffic simulations using cellular automata. Physica A (1996) 231(4):534–550Crossref, Google Scholar
• Rosswog S., Wagner P. Towards a macroscopic modelling of the complexity in traffic flow. Physical Rev. E (2002) 65(036106):1–9Google Scholar
• Roters L., Lübeck S., Usadel K. D. Critical behavior of a traffic flow model. Physical Rev. E (1999) 59(3):2672–2676Crossref, Google Scholar
• Ruhe M.Luftgestütztes Verkehrsmonitoring (2002) . ivf.dlr.de/berlin/projekte/luftgest_verkmonitor.htmGoogle Scholar
• Santen L., Appert C. Boundary induced phase transitions in driven lattice gases with metastable states. Physical Rev. Lett. (2001) 86:2498–2501Crossref, Google Scholar
• Sasvari M., Kertesz J. Cellular automata models of single lane traffic. Physical Rev. E (1997) 56(4):4104–4110Crossref, Google Scholar
• Sauermann G., Herrmann H. J., Wolf D. E., Schreckenberg M. A 1d traffic model with threshold parameters. Traffic Granular Flow '97 (1998) (Springer, Heidelberg, Germany) 481–486Google Scholar
• Schadschneider A., Schreckenberg M. Traffic flow models with “slow-to-start” rules. Ann. Physics (1997) 6(7):541–551Crossref, Google Scholar
• Sheffi Y.Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (1985) (Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
• SMARTEST Simulation modelling applied to road transport European scheme tests. . www.its.leeds.ac.uk/projects/smartest/ index.htmlGoogle Scholar
• Sparmann U. Forschung Straßenbau und Straßenverkehrstechnik. Spurwechselvorgänge auf zweispurigen BAB-Richtungsfahrbahnen (1978) (Bundesminister für Verkehr, Bonn-Bad Godesberg, Germany) . no. 263Google Scholar
• Stauffer D.Introduction to Percolation Theory (1985) (Taylor & Francis, London, U.K., and Philadelphia, PA) Crossref, Google Scholar
• Stauffer D. Computer simulations of cellular automata. J. Physics A (1991) 24:909–927Crossref, Google Scholar
• Takayasu M., Takayasu H. Phase transition and 1/f type noise in one dimensional asymmetric particle dynamics. Fractals (1993) 1:860–866Crossref, Google Scholar
• Tomer E., Safonov L., Havlin S. Presence of many stable non-homogeneous states in an inertial car-following traffic model. Physical Rev. Lett. (2000) 84:382–385Crossref, Google Scholar
• TRANSIMSTRansportation ANalysis and SIMulation System. transims.tsasa.lanl.govGoogle Scholar
• Treiber M., Hennecke A., Helbing D. Derivation, properties, and simulation of a gas-kinetic-based, non-local traffic model. Physical Rev. E (1999a) 59:239–253Crossref, Google Scholar
• Treiber M., Hennecke A., Helbing D., Helbing D., Hermann H. J., Schreckenberg M., Wolf D. E. Microscopic simulation of congested traffic. Traffic and Granular Flow '99 (1999b) (Springer, Berlin, Germany) 366–376Google Scholar
• Treiterer J., Myers J. A., Buckley D. J. The hysteresis phenomenon in traffic flow. Proc. 6th ISTT (1974) Sydney, Australia(Elsevier, New York) 13–38Google Scholar
• Troutbeck R. J., Brilon W., Gartner N. H., Messer C. J., Rathi A. Unsignalized intersection theory. Monograph on Traffic Flow Theory (1997) . TFHRC. http://www.tfhrc.gov/its/tft/tft.htmGoogle Scholar
• von Neumann J. Edited and completed by A. W. Burks. Theory of Self-Reproducing Automata (1966) (University of Illinois Press, Urbana, IL) Google Scholar
• Wagner P., Nagel K., Wolf D. E. Realistic multi-lane traffic rules for cellular automata. Physica A (1997) 234:687–698Crossref, Google Scholar
• Wehner B.Die Leistungsfähigkeit von Strassen, Forschungsarbeiten aus dem Strassenwesen (1939) (Volk und Reich, Berlin, Germany. In German) Google Scholar
• Whitham G. B.Linear and Nonlinear Waves (1974) (Wiley, New York) Google Scholar
• Wiedemann R. Simulation des Straßenverkehrsflußes. (1974) . Technical report, Institut für Verkehrswesen, Universität Karlsruhe, Karlsruhe, GermanyGoogle Scholar
• Wiedemann R., Schwerdtfeger T. Makroskopisches simulations-modell für schnellstrassennetze mit berücksichtigung von einzelfahrzeugen. (1987) . Technical report, Bundesministerium für Verkehr, Abt. Strassenbau, Bonn, Germany. In GermanGoogle Scholar
• Wilson R. E. An analysis of Gipps' model of highway traffic. IMA J. Appl. Math. (2001) 66(5):509–537Crossref, Google Scholar
• Windover J. R., Cassidy M. J. Some observed details for freeway traffic evolution. Transportation Res. A (2001) A35:881–894Google Scholar
• Wolf D. Cellular automata for traffic simulations. Physica A (1999) 263:438–451Crossref, Google Scholar
• Wolfram S.Theory and Applications of Cellular Automata (1986) (World Scientific, Singapore) Google Scholar
• Wu N. Verkehr auf schnellstraßen im fundamentaldiagramm—ein neues modell und seine anwendungen. Straßenverkehrstechnik (2000) 44:7–12Google Scholar
• Yukawa S., Kikuchi M., Helbing D., Hermann H. J., Schreckenberg M., Wolf D. E. Coupled-map modeling of one-dimensional traffic flow. Traffic and Granular Flow '99 (1999) (Springer, Berlin, Germany) 319–334Google Scholar
• Zhang X., Jarrett D. F. Stability analysis of the classical car-following model. Transportation Res. B. (1997) 31:443–462Crossref, Google Scholar