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## Traffic and related self-driven many-particle systems (2000)

Citations: | 345 - 40 self |

### Citations

2964 |
The Fractal Geometry of Nature
- Mandelbrot
- 1977
(Show Context)
Citation Context ...3; Domb and Lebowitz, 1983–2000; Voss, 1985; Schuster, 1988). In nonequilibrium systems, one can frequently find self-organized criticality (Bak et al., 1987, 1988; Bak, 1996) and fractal properties (=-=Mandelbrot, 1983-=-; Family and Vicsek, 1991; Vicsek, 1992; Barabási and Stanley, 1995). Self-organized criticality means that the respective system drives itself to the critical point, which is normally characterized b... |

1589 |
The genetical theory of natural selection
- Fisher
- 1930
(Show Context)
Citation Context ...andom locations, the clusters eventually merge with each other, resulting in one big cluster. The growth and competition of these clusters can be described by an Eigen-Fisher-like selection equation (=-=Fisher, 1930-=-; Eigen, 1971; Eigen and Schuster, 1979; Schweitzer and Schimansky-Geier, 1994). 4. Pattern formation of bacterial colonies In 1994, Eshel Ben-Jacob et al. proposed a communicating walker model for th... |

1251 | Interacting particle systems - Liggett - 2005 |

734 |
How Nature Works: The Science of Self-organized Criticality,
- Bak
- 1996
(Show Context)
Citation Context ...aterials (Pöschel and Herrmann, 1995; Santra et al., 1996; Makse et al., 1997), or self-organized criticality with power-law distributed avalanche sizes in growing sand heaps (Bak et al., 1987, 1988; =-=Bak, 1996-=-) or in the outflow from hoppers (Schick and Verveen, 1974; Peng and Herrmann, 1995). In spite of the many differences between flows of fluids, granular media, and vehicles or pedestrians, due to diff... |

641 |
The Mathematical Theory of Nonuniform Gases
- Chapman, Cowling
- 1970
(Show Context)
Citation Context ...utomata (Frisch et al., 1986; Chen et al., 1991; Peng and Herrmann, 1994; Tan et al., 1995) or cellular automata (see Sec. III.B); (iii) gas-kinetic (Boltzmann- and Enskog-like) models (Enskog, 1917; =-=Chapman and Cowling, 1939-=-; Boltzmann, 1964; Cohen, 1968, 1969; Lun et al., 1984; Jenkins and Richman, 1985; Cercignani and Lampis, 1988; McNamara and Young, 1993; Dufty Rev. Mod. Phys., Vol. 73, No. 4, October 20011070 Dirk ... |

354 | Field Theory - Lewin - 1964 |

296 |
Modern theory of critical phenomena
- Ma
- 1976
(Show Context)
Citation Context ...ng arguments. These give universal power-law scaling exponents for the (critical) behavior of the system close to the phase-transition point (critical point; Stanley, 1971; Domb and Green, 1972–1976; =-=Ma, 1976-=-; Hohenberg and Halperin, 1977; Stinchcombe, 1983; Domb and Lebowitz, 1983–2000; Voss, 1985; Schuster, 1988). In nonequilibrium systems, one can frequently find self-organized criticality (Bak et al.,... |

281 |
An introduction to probability theory and its applications, 3rd edition
- Feller
- 1968
(Show Context)
Citation Context ...lim�t→0q/�t��. 1. Solution methods, mapping to spin chains, and the matrix product ansatz Since the master equation is linear, many solution methods are available for it (cf. the books and reviews by =-=Feller, 1967-=-; Haken, 1977; van Kampen, 1981; Gardiner, 1985; Haus and Kehr, 1987; Weiss, 1994; Helbing, 1995a; Schütz, 2000a; see also Helbing and Molini, 1995). For example, one can map the TASEP to a spin syste... |

165 |
Stochastic Interacting Systems,
- Liggett
- 1999
(Show Context)
Citation Context ...culations are difficult due to correlations, this relation becomes exact for the stationary state of periodic systems (Spohn, 1991; Schadschneider and Schreckenberg, 1993; Schreckenberg et al., 1995; =-=Liggett, 1999-=-). A spatially continuous approximation of Eq. (41) results in the Burgers equation (53) or, in lowest-order approximation, in the LighthillWhitham equation (49). �n j�1�t�n j�t�n j�1�t�n j�2�t�� � �n... |

156 |
Dissipative Structures and Weak Turbulence
- Manneville
- 1990
(Show Context)
Citation Context ...y different kinds of systems like equilibrium and nonequilibrium ones, or microscopic and macroscopic ones, whose equivalence cannot simply be shown by transformation to normal forms (Kuramoto, 1989; =-=Manneville, 1990-=-; Eckmann et al., 1993). Defining universality classes by mathematically equivalent phase diagrams, one can even compare systems as different as physical, chemical, biological, and social ones, which ... |

138 |
Numerical Methods for Conservation Laws, Birkhauser
- LEVEQUE
- 1990
(Show Context)
Citation Context ...f shock waves results in serious difficulties for solving the Lighthill-Whitham model numerically. A suitable integration method is the Godunov scheme (Godunov, 1959; Ansorge, 1990; Bui et al., 1992; =-=LeVeque, 1992-=-; Lebaque, 1995). As an alternative, Newell (1993), Daganzo (1994, 1995a, 1995b), and Lebacque (1997) have recently developed variants of the Lighthill-Whitham model. To avoid the development of shock... |

123 |
Statistical Thermodynamics of Nonequilibrium 87
- Keizer
- 1987
(Show Context)
Citation Context ... loosely related to traffic. E. Particle hopping models, power-law scaling, and selforganized criticality Many-particle systems in equilibrium can be well understood with methods from thermodynamics (=-=Keizer, 1987-=-) and statistical physics (Uhlenbeck and Ford, 1963; Landau and Lifshits, 1980; Ma, 1985; Klimontovich, 1986; Huang, 1987). Two examples are phase transitions between different aggregate states of mat... |

121 |
Lectures on Gas Theory.
- Boltzmann
- 1964
(Show Context)
Citation Context ...6; Chen et al., 1991; Peng and Herrmann, 1994; Tan et al., 1995) or cellular automata (see Sec. III.B); (iii) gas-kinetic (Boltzmann- and Enskog-like) models (Enskog, 1917; Chapman and Cowling, 1939; =-=Boltzmann, 1964-=-; Cohen, 1968, 1969; Lun et al., 1984; Jenkins and Richman, 1985; Cercignani and Lampis, 1988; McNamara and Young, 1993; Dufty Rev. Mod. Phys., Vol. 73, No. 4, October 20011070 Dirk Helbing: Traffic ... |

119 |
The Hypercycle.
- Eigen, Schuster
- 1979
(Show Context)
Citation Context ...rs eventually merge with each other, resulting in one big cluster. The growth and competition of these clusters can be described by an Eigen-Fisher-like selection equation (Fisher, 1930; Eigen, 1971; =-=Eigen and Schuster, 1979-=-; Schweitzer and Schimansky-Geier, 1994). 4. Pattern formation of bacterial colonies In 1994, Eshel Ben-Jacob et al. proposed a communicating walker model for the beautiful pattern formation in certai... |

116 |
Introduction to mathematical sociology.
- Coleman
- 1964
(Show Context)
Citation Context ... see Helbing, 1992b, 1997a). Individuals who know each other may form groups which are entities behaving similarly to single pedestrians. Group sizes are Poisson distributed (Coleman and James, 1961; =-=Coleman, 1964-=-; Goodman, 1964). In situations of escape panic (Helbing, Farkas, and Vicsek, 2000b), individuals are often nervous, and sometimes they move irrationally. Moreover, people move or try to move consider... |

97 | The Godunov scheme and what it means for first order traffic flow models, - Lebacque - 1996 |

81 |
An Introduction to the Theory of Traffic Flow,
- Leutzbach
- 1988
(Show Context)
Citation Context ...atial one (the density). This can be compensated for by the harmonic average velocity V(x,t) defined by 1 1 �� , (10) V�x,t� v�� giving a greater weight to small velocities (Gerlough and Huber, 1975; =-=Leutzbach, 1988-=-). Using Eq. (10) instead of the commonly applied equation (8) together with the relation ��Q/V results in similarly shaped velocitydensity relations, but the density range is much higher (see Fig. 2)... |

60 |
Evolutionary Algorithms in Theory and Practice.
- Baeck
- 1996
(Show Context)
Citation Context ... of a learning process based on trial and error (Helbing, Molnar, et al., 2001), which can be simulated with evolutionary algorithms (Klockgether and Schwefel, 1970; Rechenberg, 1973; Schwefel, 1977; =-=Baeck, 1996-=-). For example, pedestrians have a preferred side for walking (Oeding, 1963; Older, 1968; Weidmann, 1993), since an asymmetrical avoidance behavior turns out to be profitable (Bolay, 1998). The relate... |

57 |
Microscopic modeling of traffic flow: Investigation of collision free vehicle dynamics,”
- Krauß
- 1998
(Show Context)
Citation Context ...a�t…, while the safe velocity is calculated via v� (t) �v ��1(t)�b�s ��v ��1(t)�t�/�v �(t)�b�t�. This model was developed and investigated in detail by Krauß and co-workers (Krauß et al., 1996, 1997; =-=Krauß, 1998-=-a, 1998b). A model developed by Ianigro (1994) is based on Petri nets. Yukawa and Kikuchi (1995, 1996) have studied traffic models based on coupled maps (see also Tadaki et al., 1998). Although there ... |

54 | Information and Self-Organization - Haken - 1988 |

54 |
Quantitative Sociodynamics: Stochastic Methods and Models of Social Interaction Processes (Springer,
- Helbing
- 2010
(Show Context)
Citation Context ...gogine, 1977; Pasteels and Deneubourg, 1987; Feistel and Ebeling, 1989; Weidlich, 1991; DeAngelis and Gross, 1992; Kai, 1992; Vicsek, 1992; Vallacher and Nowak, 1994; Cladis and Palffy-Muhoray, 1995; =-=Helbing, 1995-=-a. From this ‘‘microscopic,’’ molecular-dynamics type of equation, one can systematically derive ‘‘macroscopic,’’ fluid-dynamic equations for the spatio-temporal evolution of the particle density, the... |

46 | A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections. Transportation Research Part B: Methodological,
- Daganzo
- 2002
(Show Context)
Citation Context ...st the direction of the vehicle flow (Edie and Foote, 1958; Mika et al., 1969). Some disturbances have been found to propagate without spreading (Cassidy and Windover, 1995; Windower, 1998; Muñoz and =-=Daganzo, 1999-=-; see also Kerner and Rehborn, 1996a, and the flow and speed data reported by Foster, 1962; Cassidy and Bertini, 1999). The propagation velocity C in congested traffic seems to be roughly comparable w... |

43 |
Nonequilibrium Molecular Dynamics,
- Hoover
- 1986
(Show Context)
Citation Context ...hicles or pedestrians, due to different conservation laws and driving terms, one can apply similar methodological approaches. For example: (i) microscopic, molecular dynamic models (see, for example, =-=Hoover, 1986-=-; Buchholtz and Pöschel, 1993; Goldhirsch et al., 1993; Hirshfeld et al., 1997; Sec. III.A); (ii) lattice gas automata (Frisch et al., 1986; Chen et al., 1991; Peng and Herrmann, 1994; Tan et al., 199... |

31 |
Mathematical Theories of Traffic Flow”,
- Haight
- 1963
(Show Context)
Citation Context ...tz (2000a). Related studies have been also carried out by Nagatani (1995c). 2. The Burgers equation The Lighthill-Whitham model is very instructive and is the basis of an elaborate shock-wave theory (=-=Haight, 1963-=-; Gazis, 1974; Whitham, 1974; Hida, 1979; Newell, 1993; Daganzo, 1999b), but the development of shock waves results in serious difficulties for solving the Lighthill-Whitham model numerically. A suita... |

27 |
Fundamentals of Transportation and Traffic Operations, Pergamon-Elsevier,
- Daganzo
- 1997
(Show Context)
Citation Context ...ronization 1. Gas-kinetic and macroscopic models Traffic models have also been developed for multilane traffic (Gazis et al., 1962; Munjal et al., 1971; Munjal and Pipes, 1971; Makigami et al., 1983; =-=Daganzo, 1997-=-b; Daganzo et al., 1997; Holland and Woods, 1997). In gaskinetic and macroscopic traffic models, this is reflected by additional lane-changing terms (Rørbech, 1976; Michalopoulos et al., 1984; Helbing... |

25 |
Traffic Flow Theory,
- Gerlough, Huber
- 1975
(Show Context)
Citation Context ...erage (the flow) with a spatial one (the density). This can be compensated for by the harmonic average velocity V(x,t) defined by 1 1 �� , (10) V�x,t� v�� giving a greater weight to small velocities (=-=Gerlough and Huber, 1975-=-; Leutzbach, 1988). Using Eq. (10) instead of the commonly applied equation (8) together with the relation ��Q/V results in similarly shaped velocitydensity relations, but the density range is much hi... |

21 |
Multiclass continuum modelling of multilane traffic flow.
- Hoogendoorn, P
- 2000
(Show Context)
Citation Context ... the treatment of vehicle platoons (Andrews, 1970a, 1970b, 1973a, 1973b; Beylich, 1979, 1981). One possibility, related to an approach by Lampis (1978) and others (Poethke, 1982; see Leutzbach, 1988; =-=Hoogendoorn, 1999-=-; Hoogendoorn and Bovy, 1999a, 1999b), is to distinguish a fraction ĉ(�) of free vehicles and a fraction �1�ĉ(�)� of bound (i.e., obstructed) vehicles, for which separate but coupled equations can be ... |

19 |
Traffic Science
- Gazis
- 1974
(Show Context)
Citation Context ...lated studies have been also carried out by Nagatani (1995c). 2. The Burgers equation The Lighthill-Whitham model is very instructive and is the basis of an elaborate shock-wave theory (Haight, 1963; =-=Gazis, 1974-=-; Whitham, 1974; Hida, 1979; Newell, 1993; Daganzo, 1999b), but the development of shock waves results in serious difficulties for solving the Lighthill-Whitham model numerically. A suitable integrati... |

15 |
Autosolutions, a New Approach to Problems of Self-Organization and Turbulence Kluwer,
- Kerner, Osipov
- 1994
(Show Context)
Citation Context ...lier application of thermodynamic ideas to traffic. Approximate equations for nonlinear solutions at large amplitudes have been developed by Kerner et al. (1997), based on the theory of autosolitons (=-=Kerner and Osipov, 1994-=-). Moreover, the features of wide moving jams have been compared with autosolitons in physical systems (Kerner, 1995). They are reminiscent of properties found in some reaction-diffusion systems (Mikh... |

11 |
Stochastische Methoden, nichtlineare Dynamik und quantitative Modelle sozialer Prozesse
- Helbing
- 1992
(Show Context)
Citation Context ...ions can we apply the above force equations? First of all, we need to consider a phenomenon of motion in some (quasi)continuous space, which may also be an abstract behavioral space or opinion scale (=-=Helbing, 1992-=-a, 1993b, 1994, 1995a). It is favorable to have a system in which the fluctuations due to unknown influences are not large compared to the systematic, deterministic part of the motion. This is usually... |

10 |
An extended traffic model for freeway control
- Cremer, May
- 1985
(Show Context)
Citation Context ...nd eventually entering the realm of driver psychology (Daganzo, 1999a). G. Traffic control and optimization Traffic control and optimization is an old and large field (see, for example, Cremer, 1978; =-=Cremer and May, 1985-=-; Smulders, 1989; Kühne, 1993; Dougherty, 1995; Kühne et al., 1995, 1997; Taale and Middelham, 1995; Schweitzer, Ebeling, et al., 1998), too extensive to be discussed in detail here. Overviews of opti... |

8 |
Sociology and Modern Systems Theory, Prentice-Hall Inc, Englewood Cliffs,
- Buckley
- 1967
(Show Context)
Citation Context ...niversality classes by mathematically equivalent phase diagrams, one can even compare systems as different as physical, chemical, biological, and social ones, which is done in general systems theory (=-=Buckley, 1967-=-; von Bertalanffy, 1968; Rapoport, 1986). The phase diagram for the different traffic states on a homogeneous, circular one-lane road as a function of the density ϱ is usually called the instability d... |

8 |
Kinetic Theory (Prentice-Hall
- Liboff
- 1990
(Show Context)
Citation Context ..., 1999a, 1999b). For ordinary gases, the Navier-Stokes terms (transport terms) are calculated from the kinetic equation by means of the Chapman-Enskog method (Enskog, 1917; Chapman and Cowling, 1939; =-=Liboff, 1990-=-). Here I shall sketch the more intuitive relaxation-time approximation (Huang, 1987; for details see Helbing and Treiber, 1998c). This assumes that (i) (ii) the deviation ��˜ (x,v,t)���˜ (x,v,t)��˜ 0... |

7 |
Verfahren für die Berechnung der Leistungsfähigkeit und Qualität des Verkehrsablaufs auf Straßen (Methods for calculation of capacity and quality of traffic operation). Schriftenreihe "Forschung Straßenbau und Straßenverkehrstechnik", Heft 669
- Brilon, Großmann, et al.
- 1996
(Show Context)
Citation Context ...; Whyte, 1988; Helbing, 1997a; Helbing, Molnár, et al., 2001), or planning guidelines (Kirsch, 1964; Predtetschenski and Milinski, 1971; Transportation Research Board, 1985; Davis and Braaksma, 1988; =-=Brilon et al., 1993-=-). The guidelines usually have the form of regression relations which are, however, not very well suited for the prediction of pedestrian flows in pedestrian zones and buildings with an unusual archit... |

6 |
Verkehrsfluß auf Schnellstraßen
- Cremer, Der
- 1979
(Show Context)
Citation Context ... example, Papageorgiou (1983). Cremer and co-workers multiplied the anticipation term by a factor of �/(��� 0) with some constant �0�0 to get a more realistic behavior at small vehicle densities ��0 (=-=Cremer, 1979-=-; Cremer and Papageorgiou, 1981; Cremer and May, 1986; Cremer and Meißner, 1993). A discrete version of this model is used in the simulation package SIMONE (Meißner and Böker, 1996). Smulders (1986, 1... |

6 | Transportation and Traffic Theory - Lesort - 1996 |

5 | Handbook of Transportation Science - Hall - 1999 |

3 |
Motorway Traffic Flow Analysis
- Hoogendoorn, Bovy, et al.
- 1998
(Show Context)
Citation Context ...adway distributions have an interesting property. It turns out that the distribution becomes sharply peaked around approximately 1 s for densities close to congestion (Smulders, 1990; Hoogendoorn and =-=Bovy, 1998-=-; Neubert, Santen et al., 1999). For lower and higher densities, the distribution is considerably broader; see Fig. 6 (Tilch and Helbing, 2000). This indicates that congestion is an overcritical pheno... |

3 |
Motorway traffic flow analysis: new methodologies and recent empirical findings
- Bovy, Thijs
- 1998
(Show Context)
Citation Context ...y, driver behavior is influenced not only by the clearance to the next car, but also by the relative velocity and the driver velocity (Koshi et al., 1983; Bleile, 1997; 1999; Manstetten et al., 1997; =-=Dijker et al., 1998-=-; Neubert, Santen, et al., 1999). Note that the relative velocity in congested traffic is oscillating because of the instability of traffic flow; see Fig. 11 (Hoefs, 1972; Helbing and Tilch, 1998). As... |

3 | Rathi (Eds.), Traffic Flow Theory, Federal Highway Administration - Gartner, Messer, et al. - 1997 |

3 |
in Traffic and Granular Flow, edited by
- Helbing
- 1996
(Show Context)
Citation Context ...tability of traffic flow. After Helbing, 1997a, 1997c, 1997e, 1998a. variance are positively correlated, since both quantities are related via a positive but density-dependent prefactor; see Fig. 17 (=-=Helbing, 1996-=-b, 1997a, 1997c; Shvetsov and Helbing, 1999; Treiber et al., 1999; Helbing et al., 2001a, 2001b). Finally, it is interesting to look at the velocity correlations among successive cars. Neubert, Santen... |

3 |
Self-organization of Complex Structures: From Individual to Collective Dynamics, Chapter Self-organization phenomena in pedestrian crowds, 569–577
- Helbing, Molnar
- 1997
(Show Context)
Citation Context ...more efficient than one single door with double width. By self-organization, each door is then used by one walking direction for a long time; see Fig. 46 (Molnár, 1996a, 1996b; Helbing, 1997a, 1998b; =-=Helbing and Molnár, 1997-=-; Helbing, Molnár, et al., 2001). The reason is that pedestrians who pass a door clear the way for their successors, in a manner similar to lane formation. 3. Rotation At intersections one is confront... |

2 |
in Traffic and Granular Flow, edited by
- Brackstone, McDonald
- 1996
(Show Context)
Citation Context ...escribes analogous changes to lane (i�1). Empirical measurements of lane-specific data and lane-changing rates are rare (Sparman, 1978; Hall and Lam, 1988; Chang and Kao, 1991; McDonald et al., 1994; =-=Brackstone and McDonald, 1996-=-; Brackstone et al., 1998). Based on his data, Sparman (1978) proposed the relation 1/� i � �ci � �i(� max�� i�1) with suitable lane-dependent constants c i � . The additional terms in the velocity eq... |

2 | In: Transport phenomena in fluids, edited by - Cohen - 1969 |

2 |
An Extended Traffic Flow Model for Inner Urban Freeways
- Cremer, May
- 1986
(Show Context)
Citation Context ...workers multiplied the anticipation term by a factor of �/(��� 0) with some constant �0�0 to get a more realistic behavior at small vehicle densities ��0 (Cremer, 1979; Cremer and Papageorgiou, 1981; =-=Cremer and May, 1986-=-; Cremer and Meißner, 1993). A discrete version of this model is used in the simulation package SIMONE (Meißner and Böker, 1996). Smulders (1986, 1987, 1989) introduced additional fluctuation terms in... |

2 | in Special Report 194, edited by - Gibson - 1981 |

2 |
Ein phänomenologisches Modell des dynamischen Verkehrsflusses
- Hilliges
- 1995
(Show Context)
Citation Context ...(iii) the wide scattering of flow-density data. In other simulations with inhomogeneities, researchers have recognized wavelike forms of congested traffic behind bottlenecks (Csahók and Vicsek, 1994; =-=Hilliges, 1995-=-; Klar et al., 1996; Nagatani, 1997c; Lee et al., 1998). One can even find period-doubling scenarios upstream of stationary bottlenecks (Nagatani, 1997c) or due to time-dependent local perturbations (... |

2 |
in Modelling and Simulation 1993, edited by A. Pave (Society for Computer Simulation International
- Hilliges, Reiner, et al.
- 1993
(Show Context)
Citation Context ...tive velocity between cars. The probably best parameter set was specified by Lee et al. (1998). 6. The Weidlich-Hilliges model The basic version of the model by Weidlich and Hilliges (Weidlich, 1992; =-=Hilliges, Reiner, and Weidlich, 1993-=-; Hilliges and Weidlich, 1995) is discrete and related to Daganzo’s cell transmission model (Daganzo, 1994, 1995a): The freeway is divided into cells j of equal length �x, reminiscent of cellular auto... |

2 | in Pedestrian and Evacuation Dynamics, edited by M. Schreckenberg and - Keßel, Klüpfel, et al. - 2001 |

2 |
in Traffic and Granular Flow ’97, edited by M. Schreckenberg and
- Krauß
- 1998
(Show Context)
Citation Context ...a�t…, while the safe velocity is calculated via v� (t) �v ��1(t)�b�s ��v ��1(t)�t�/�v �(t)�b�t�. This model was developed and investigated in detail by Krauß and co-workers (Krauß et al., 1996, 1997; =-=Krauß, 1998-=-a, 1998b). A model developed by Ianigro (1994) is based on Petri nets. Yukawa and Kikuchi (1995, 1996) have studied traffic models based on coupled maps (see also Tadaki et al., 1998). Although there ... |

1 |
in Highway Capacity and Level of Service, edited by U. Brannolte (Balkema
- Agyemang-Duah, Hall
- 1991
(Show Context)
Citation Context ... 1996b, 1998b; Persaud et al., 1998; Westland, 1998; Cassidy and Bertini, 1999; see also May, 1964, for an idea on how to exploit this phenomenon with ramp metering; Persaud, 1986; Banks, 1989, 1990; =-=Agyemang-Duah and Hall, 1991-=-; Daganzo, 1996. bottleneck defines the discharge flow Q˜ out�Q bot , which appears to be larger than (or equal to) the characteristic outflow Qout from wide jams: Q˜ out�Q out . In extended congested... |

1 |
in Transportation and Traffic Theory
- Ahmed, Ben-Akiva, et al.
- 1996
(Show Context)
Citation Context ...s on the lane-specific variance �. 2. Microscopic models and cellular automata A microscopic modeling of lane changes (Fox and Lehmann, 1967; Levin, 1976; Daganzo, 1981; Mahamassani and Sheffi, 1981; =-=Ahmed et al., 1996-=-) turns out to be an intricate problem for several reasons: (i) Because of legal regulations, lane changing is not symmetric, at least in Europe. (ii) Drivers accept smaller gaps than usual in respons... |

1 |
Transp
- Ansorge
- 1990
(Show Context)
Citation Context ...zo, 1999b), but the development of shock waves results in serious difficulties for solving the Lighthill-Whitham model numerically. A suitable integration method is the Godunov scheme (Godunov, 1959; =-=Ansorge, 1990-=-; Bui et al., 1992; LeVeque, 1992; Lebaque, 1995). As an alternative, Newell (1993), Daganzo (1994, 1995a, 1995b), and Lebacque (1997) have recently developed variants of the Lighthill-Whitham model. ... |

1 |
Video films of pedestrian crowds (available from
- Arns
- 1993
(Show Context)
Citation Context ...d Ostrowsky, 1986). The emergence of pedestrian streams through standing crowds Rev. Mod. Phys., Vol. 73, No. 4, October 2001Dirk Helbing: Traffic and related self-driven many-particle systems 1121 (=-=Arns, 1993-=-; Helbing, 1997a, Fig. 2.6; 1998b, Fig. 1; Helbing, Molnár, et al., 2001, Fig. 1) appears analogous to the formation of river beds (Stølum, 1996; Rodríguez-Iturbe and Rinaldo, 1997; Caldarelli, 2001).... |

1 | 2001 Helbing: Traffic and related self-driven many-particle systems - Phys, Vol |

1 |
Transp. Theory Stat
- Barone
- 1981
(Show Context)
Citation Context ... the velocity variance, the covariance, the average desired velocity, and so on are different. The construction and properties of solutions to the Paveri-Fontana equation have been carefully studied (=-=Barone, 1981-=-; Semenzato, 1981a, 1981b). In addition, it should be noted that there are further alternatives to the specification (75) of the acceleration term. For example, Alberti and Belli (1978) assume a densi... |

1 | in Modelling and Simulation 1993, edited by A. Pave (Society for Computer Simulation Intenational - Benz - 1993 |

1 |
in Rarefied Gas Dynamics, edited by R. Campargue (Commissariat a l’Energie Atomique
- Beylich
- 1979
(Show Context)
Citation Context ..., in which the variation of vehicle velocities is considerably reduced (see Sec. II.D). There have been several suggestions for the treatment of vehicle platoons (Andrews, 1970a, 1970b, 1973a, 1973b; =-=Beylich, 1979-=-, 1981). One possibility, related to an approach by Lampis (1978) and others (Poethke, 1982; see Leutzbach, 1988; Hoogendoorn, 1999; Hoogendoorn and Bovy, 1999a, 1999b), is to distinguish a fraction ĉ... |

1 | in Neue Wege in der Mechanik, edited by G. Adomeit and H.-J. Frieske (VDI-Verlag - Beylich - 1981 |

1 | 2001b, in Pedestrian and Evacuation Dynamics, edited by M. Schreckenberg and - Blue, Adler |

1 |
Fußgängerbereiche�Gestaltungselemente/Pedestrian Areas and Design Elements/Zones pour Piétons�Elements de Conception (Krämer
- Boeminghaus
- 1982
(Show Context)
Citation Context ...1997), the main goal of these studies was to develop a level-of-service concept (Fruin, 1971; Polus et al., 1983; Mōri and Tsukaguchi, 1987), design elements of pedestrian facilities (Schubert, 1967; =-=Boeminghaus, 1982-=-; Pauls, 1984; Whyte, 1988; Helbing, 1997a; Helbing, Molnár, et al., 2001), or planning guidelines (Kirsch, 1964; Predtetschenski and Milinski, 1971; Transportation Research Board, 1985; Davis and Bra... |

1 | Ed., Highway Capacity and Level of Service (Balkema - Brannolte - 1991 |

1 |
in Traffic and Granular Flow, edited by
- Brilon, Ponzlet
- 1996
(Show Context)
Citation Context ...ream of a bottleneck. Headways of less than 5 m are due to measurement errors. The dependence of the v(d) relation on the vehicle density and traffic regime is called the frustration effect (see also =-=Brilon and Ponzlet, 1996-=-). From Tilch and Helbing, 2000; note the related study by Neubert, Santen, et al., 1999. amount of �(V i�V) 2 � than the velocity variance evaluated over all lanes, which is particularly important at... |

1 |
in Traffic and Mobility: Simulation—Economics—Environment, edited by
- Brilon, Wu
- 1999
(Show Context)
Citation Context ...mata have been developed, as well (Nagatani, 1993, 1994a, 1994b, 1996a; Zhang and Hu, 1995; Rickert et al., 1996; Chowdhury, Ghosh, et al., 1997; Wagner et al., 1997; Awazu, 1998; Nagel et al., 1998; =-=Brilon and Wu, 1999-=-). In modern lane-changing models, the lane is changed if both an incentive criterion and a safety criterion are fulfilled (Nagel et al., 1998). The incentive criterion checks whether the considered d... |

1 |
in Modelling and Simulation 1993, edited by A. Pave (Society for Computer Simulation International
- Cremer, Meißner
- 1993
(Show Context)
Citation Context ... anticipation term by a factor of �/(��� 0) with some constant �0�0 to get a more realistic behavior at small vehicle densities ��0 (Cremer, 1979; Cremer and Papageorgiou, 1981; Cremer and May, 1986; =-=Cremer and Meißner, 1993-=-). A discrete version of this model is used in the simulation package SIMONE (Meißner and Böker, 1996). Smulders (1986, 1987, 1989) introduced additional fluctuation terms in the continuity and veloci... |

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Working Paper UCB-ITS-WP-97-4 (Institute of Transportation Studies
- Daganzo
- 1997
(Show Context)
Citation Context ...ronization 1. Gas-kinetic and macroscopic models Traffic models have also been developed for multilane traffic (Gazis et al., 1962; Munjal et al., 1971; Munjal and Pipes, 1971; Makigami et al., 1983; =-=Daganzo, 1997-=-b; Daganzo et al., 1997; Holland and Woods, 1997). In gaskinetic and macroscopic traffic models, this is reflected by additional lane-changing terms (Rørbech, 1976; Michalopoulos et al., 1984; Helbing... |

1 | in Traffic and Granular Flow ’97, edited by M. Schreckenberg and - Castillo, M - 1996 |

1 | in Transportation and Traffic Theory - Castillo, M - 1996 |

1 | 2001, in Pedestrian and Evacuation Dynamics, edited by M. Schreckenberg and - Dijkstra, Jessurun, et al. |

1 |
Transp
- Dougherty
- 1995
(Show Context)
Citation Context ...gy (Daganzo, 1999a). G. Traffic control and optimization Traffic control and optimization is an old and large field (see, for example, Cremer, 1978; Cremer and May, 1985; Smulders, 1989; Kühne, 1993; =-=Dougherty, 1995-=-; Kühne et al., 1995, 1997; Taale and Middelham, 1995; Schweitzer, Ebeling, et al., 1998), too extensive to be discussed in detail here. Overviews of optimization approaches by physicists can be found... |

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in Modelling and Simulation ESM 1995, edited by
- Dutkiewicz, Suda, et al.
- 1995
(Show Context)
Citation Context ...nberg, 1997; Belitsky et al., 2001; see also Goldbach et al., 2000; Lubashevsky and Mahnke, 2000). E. Bidirectional and city traffic Traffic models have also been developed for bidirectional traffic (=-=Dutkiewicz et al., 1995-=-; Lee et al., 1997; Simon and Gutowitz, 1998; Fouladvand and Lee, 1999) and city traffic. 9 Interested readers should consult the reviews by Papageorgiou (1999), Chowdhury, Santen, and Schadschneider ... |

1 | 2001 Dirk Helbing: Traffic and related self-driven many-particle systems Stinchcombe - Phys, Vol |

1 | in Probability and Phase Transition, edited by - Ferrari - 1993 |

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in Spatial Choices and Processes, edited by
- Gopal, Smith
- 1990
(Show Context)
Citation Context ...l et al., 1993; Okazaki and Matsushita, 1993; Still, 1993, 2000; Thomson and Marchant, 1993; Løva˚s, 1998; Klüpfel et al., 2000; Hamacher and Tjandra, 2001), and artificial-intelligence-based models (=-=Gopal and Smith, 1990-=-; Reynolds, 1994, 1999; Schelhorn et al., 1999; Dijkstra et al., 2001). A. Observations (iii) (iv) (v) Together with my collaborators I have investigated pedestrian motion for several years and have e... |

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in Nonlinear Physics of Complex Systems—Current Status and Future Trends, edited by
- Hänggi, Bartussek
- 1996
(Show Context)
Citation Context ...mfortable with such systems may instead imagine special kinds of granular, colloidal, or spin systems driven by gravitational or electrical forces, or imagine particular systems with Brownian motors (=-=Hänggi and Bartussek, 1996-=-; Astumian, 1997; Jülicher, Ajdari, and Prost, 1997; Reimann, 2000). Moreover, I would like to encourage everyone to perform analogous experiments in these related physical systems. Despite the comple... |

1 | 2001b, in Pedestrian and Evacuation Dynamics, edited by M. Schreckenberg and - Hamacher, Tjandra |

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in Economic Evolution and Demographic Change. Formal Models in Social Sciences, edited by
- Helbing
- 1992
(Show Context)
Citation Context ...ions can we apply the above force equations? First of all, we need to consider a phenomenon of motion in some (quasi)continuous space, which may also be an abstract behavioral space or opinion scale (=-=Helbing, 1992-=-a, 1993b, 1994, 1995a). It is favorable to have a system in which the fluctuations due to unknown influences are not large compared to the systematic, deterministic part of the motion. This is usually... |

1 | in Transportation Systems, edited by M - Helbing - 1997 |

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in A Perspective Look at Nonlinear Media. From Physics to Biology and Social Sciences, edited by
- Helbing
- 1998
(Show Context)
Citation Context ...hose along the edges, supplying maximum walking comfort at a minimal detour of 22% for everyone, which is a fair solution. After Helbing, Keltsch, and Molnar, 1997; Helbing, Schweitzer, et al., 1997; =-=Helbing, 1998-=-b; Helbing and Vicsek, 1999; Helbing, Molnar, et al., 2001. 1997; Helbing, 1998c). Interestingly enough, the model yields fair solutions and optimal compromises between short and comfortable ways; see... |

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in Traffic and Granular Flow ’97, edited by M. Schreckenberg and
- Helbing
- 1998
(Show Context)
Citation Context ...hose along the edges, supplying maximum walking comfort at a minimal detour of 22% for everyone, which is a fair solution. After Helbing, Keltsch, and Molnar, 1997; Helbing, Schweitzer, et al., 1997; =-=Helbing, 1998-=-b; Helbing and Vicsek, 1999; Helbing, Molnar, et al., 2001. 1997; Helbing, 1998c). Interestingly enough, the model yields fair solutions and optimal compromises between short and comfortable ways; see... |

1 | 2000, in Traffic and Granular Flow ’99: Social, Traffic, and Granular Dynamics, edited by - Hennecke, Treiber, et al. |

1 |
in Theoretical and
- Hida
- 1979
(Show Context)
Citation Context ... carried out by Nagatani (1995c). 2. The Burgers equation The Lighthill-Whitham model is very instructive and is the basis of an elaborate shock-wave theory (Haight, 1963; Gazis, 1974; Whitham, 1974; =-=Hida, 1979-=-; Newell, 1993; Daganzo, 1999b), but the development of shock waves results in serious difficulties for solving the Lighthill-Whitham model numerically. A suitable integration method is the Godunov sc... |

1 |
Untersuchung des Fahrverhaltens
- Hoefs
- 1972
(Show Context)
Citation Context ...stetten et al., 1997; Dijker et al., 1998; Neubert, Santen, et al., 1999). Note that the relative velocity in congested traffic is oscillating because of the instability of traffic flow; see Fig. 11 (=-=Hoefs, 1972-=-; Helbing and Tilch, 1998). As a consequence, the relative velocity variance �, as compared to the average velocity V, is considerably higher in congested than in free traffic (see Figs. 12 and 17). I... |

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in Modelling and Simulation ESM 1995, edited by
- Hoque, McDonald
- 1995
(Show Context)
Citation Context ...969b; SchmidtSchmiedebach, 1973; Herman and Prigogine, 1979; SCOOT by Hunt et al., 1982; Cremer and Ludwig, 1986; Williams et al., 1987; Mahmassani et al., 1990; MAKSIMOS by Putensen, 1994; MIXSIM by =-=Hoque and McDonald, 1995-=-; PADSIM by Peytchev and Bargiela, 1995. due to a gridlock of northbound and eastbound traffic along diagonal lines (see also Fukui and Ishibashi, 1996b). This first-order transition is also character... |

1 | in Traffic and Granular Flow ’97, edited by M. Schreckenberg and - Kates, Bogenberger, et al. - 1998 |

1 | 2000, in Traffic and Granular Flow ’99: Social, Traffic, and Granular Dynamics, edited by - Kaumann, Froese, et al. |

1 | in The Handbook of Social Psychology, edited by - Kelley, Thibaut - 1969 |

1 | in Transportation Systems 1997, edited by M - Kerner - 1997 |

1 |
in Traffic and Granular Flow ’97, edited by M. Schreckenberg and
- Kerner
- 1998
(Show Context)
Citation Context ...991; Persaud et al., 1998; Westland, 1998). I shall call these homogeneous congested traffic. States in which only the average vehicle speed is stationary, named homogeneous-in-speed states (see also =-=Kerner, 1998-=-b; Lee et al., 2000). I interpret this state as ‘‘recovering traffic,’’ since it bears several signatures of free traffic (see Secs. II.B and IV.C.2). Nonstationary and nonhomogeneous states (see also... |

1 | 2000a, in Traffic and Granular Flow ’99: Social, Traffic, and Granular Dynamics, edited by - Kerner |

1 | in Engineering for Crowd Safety, edited by - Stephens, Fraser, et al. - 1993 |

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Leistungsfähigkeit und Dimensionierung von Fußgängerwegen (Bundesministerium für Verkehr
- Kirsch
- 1964
(Show Context)
Citation Context ...i and Tsukaguchi, 1987), design elements of pedestrian facilities (Schubert, 1967; Boeminghaus, 1982; Pauls, 1984; Whyte, 1988; Helbing, 1997a; Helbing, Molnár, et al., 2001), or planning guidelines (=-=Kirsch, 1964-=-; Predtetschenski and Milinski, 1971; Transportation Research Board, 1985; Davis and Braaksma, 1988; Brilon et al., 1993). The guidelines usually have the form of regression relations which are, howev... |

1 | 2000, in Theoretical and Practical Issues on Cellular Automata - Klüpfel, Meyer-König, et al. |

1 | 2000a, in Traffic and Granular Flow ’99: Social, Traffic, and Granular Dynamics, edited by - Knospe, Santen, et al. |

1 | in Theory of Traffic Flow, edited by R - Kometani, Sasaki - 1961 |

1 |
in Highway Capacity and Level of Service
- Kühne
- 1991
(Show Context)
Citation Context ...er, 1998b, 1999a, 1999b, 1999c, 2000a, 2000b). The flow-density data in the congested part are widely scattered within a two-dimensional area (see, for example, Koshi et al., 1983; Hall et al., 1986; =-=Kühne, 1991-=-b). This complexity in traffic flow is usually interpreted as an effect of fluctuations, of jam formation, or of an instability of vehicle dynamics. The scattering is reduced by increasing the samplin... |

1 |
in 21st Summer Annual Meeting on Traffic Management and Road Safety (Inst
- Kühne
- 1993
(Show Context)
Citation Context ...iver psychology (Daganzo, 1999a). G. Traffic control and optimization Traffic control and optimization is an old and large field (see, for example, Cremer, 1978; Cremer and May, 1985; Smulders, 1989; =-=Kühne, 1993-=-; Dougherty, 1995; Kühne et al., 1995, 1997; Taale and Middelham, 1995; Schweitzer, Ebeling, et al., 1998), too extensive to be discussed in detail here. Overviews of optimization approaches by physic... |

1 |
Validation of the Incremental Transfer Model. PATH Working Paper (Institute of Transportation Studies
- Lawson, Lin, et al.
- 1999
(Show Context)
Citation Context ...vergences [due to ‘‘negative’’ perturbations (see Sec. IV.B), weaving flows by vehicles trying to switch to the slow exit lane, or congestion on the offramp; see Daganzo, 1999a; Daganzo et al., 1999; =-=Lawson et al., 1999-=-; Muñoz and Daganzo, 1999]. Moving bottlenecks due to slow vehicles are possible as well (Gazis and Herman, 1992), leading to a forward movement of Rev. Mod. Phys., Vol. 73, No. 4, October 2001Dirk H... |

1 | in Transportation Systems, edited by M - Lebacque - 1997 |

1 | in Modelling and Simulation 1993, edited by A. Pave (Society for Computer Simulation - Løva˚s - 1993 |