Discrete stochastic models for traffic flow

Schreckenberg, Michael; Schadschneider, Andreas; Nagel, Kai; Ito, Nobuyasu

doi:10.1103/physreve.51.2939

Cited by 473 publications

(445 citation statements)

References 29 publications

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“…Increasing the density further, more jams develop and the plateau ceases. Note that this behaviour is completely different from the prediction of mean-field theory in that limit [140] (see Sec. 8.3.1) showing the importance of correlations.…”

Section: Nasch Model In the Limit V Max = ∞mentioning

confidence: 72%

“…It turns out [140] that the naive SOMF underestimates the flux for all v max . Curiously, if instead of parallel updating one uses the random sequential updating, the NaSch model with v max = 1 reduces to the TASEP for which the equation (66) is known to be the exact expression for the corresponding flux (see, e.g., [20])!…”

Section: Site-oriented Naive Mean-field Theory For the Nasch Modelmentioning

confidence: 99%

“…In the simplest case of v max = 1 and periodic boundary conditions one gets [140] c 0 (i; t + 1) = c(i; t)c(i + 1; t) + pc(i; t)d(i + 1; t),…”

Section: Site-oriented Naive Mean-field Theory For the Nasch Modelmentioning

confidence: 99%

“…In some of the analytical calculations of steady-state properties of the NaSch model one follows, for convenience, the sequence 2 − 3 − 4 − 1, instead of 1−2−3−4 of the stages of updating [140] as this merely shifts the starting step and, therefore, does not influence the steady-state properties of the model. The advantage of this new sequence is that, in a site-oriented theory, the variable σ j can now take v max + 1 values as none of the vehicles can have a speed v = 0 at the end of the acceleration stage of the updating.…”

Section: Site-oriented Naive Mean-field Theory For the Nasch Modelmentioning

confidence: 99%

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Statistical physics of vehicular traffic and some related systems

2000

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In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the way the vehicles influence each others' movement. Therefore, vehicular traffic, modeled as a system of interacting "particles" driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called "particle-hopping" models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

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Section: Nasch Model In the Limit V Max = ∞mentioning

confidence: 72%

Section: Site-oriented Naive Mean-field Theory For the Nasch Modelmentioning

confidence: 99%

“…In the simplest case of v max = 1 and periodic boundary conditions one gets [140] c 0 (i; t + 1) = c(i; t)c(i + 1; t) + pc(i; t)d(i + 1; t),…”

Section: Site-oriented Naive Mean-field Theory For the Nasch Modelmentioning

confidence: 99%

Section: Site-oriented Naive Mean-field Theory For the Nasch Modelmentioning

confidence: 99%

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Statistical physics of vehicular traffic and some related systems

2000

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“…In particular, the spontaneous formation of tra c jams provides a rich testbed for studying the emergence of complex activity from seemingly chaotic states 119,121]. Furthermore, the dynamics of tra c ow is particular amenable to the application and testing of many novel numerical methods in a controlled environment 16,30,237]. Many experimental studies have con rmed the usefulness of applying insights gleaned from such w ork to real world tra c scenarios 119,198,197].…”

Section: Tra C Theorymentioning

confidence: 99%

Theory of Collective Intelligence

Wolpert

2004

Collectives and the Design of Complex Systems

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This paper surveys the emerging science of how to design a \COllective INtelligence" (COIN). A COIN is a large multi-agent system where: i) There is little to no centralized, personalized communication and/or control. ii) There is a provided world utility function that rates the possible histories of the full system.In particular, we a r e i n terested in COINs in which e a c h a g e n t runs a reinforcement learning (RL) algorithm. The conventional approach to designing large distributed systems to optimize a world utility does not use agents running RL algorithms. Rather, that approach begins with explicit modeling of the dynamics of the overall system, followed by detailed hand-tuning of the interactions between the components to ensure that they \cooperate" as far as the world utility i s concerned. This approach is labor-intensive, often results in highly nonrobust systems, and usually results in design techniques that have limited applicability. In contrast, we w i s h t o s o l v e the COIN design problem implicitly, via the \adaptive" character of the RL algorithms of each of the agents. This approach i n troduces an entirely new, profound design problem: Assuming the RL algorithms are able to achieve high rewards, what reward functions for the individual agents will, when pursued by those agents, result in high world utility? In other words, what reward functions will best ensure that we d o n o t have phenomena like t h e tragedy of the commons, Braess's paradox, or the liquidity trap? Although still very young, research speci cally concentrating on the COIN design problem has already resulted in successes in arti cial domains, in particular in packet-routing, the leader-follower problem, and in variants of Arthur's El Farol bar problem. It is expected that as it matures and draws upon other disciplines related to COINs, this research will greatly expand the range of tasks addressable by human engineers. Moreover, in addition to drawing on them, such a fully developed science of COIN design may provide much insight into other already established scienti c elds, such as economics, game theory, and population biology.

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