Some Further Results in the Theory of Pedestrians and Road Traffic

Mayne, Alan J.

doi:10.2307/2332718

Cited by 12 publications

(10 citation statements)

References 2 publications

(3 reference statements)

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“…Therefore, a number of simulation models have been proposed, e.g. queueing models (Yuhaski and Macgregor Smith, 1989;Roy, 1992;Løvås, 1994), transition matrix models (Garbrecht, 1973), and stochastic models (Mayne, 1954;Ashford et al, 1976), which are partly related to each other. In addition, there are models for the route choice behavior of pedestrians Timmermans, 1986a, 1986b;Timmermans et al, 1992;Helbing, 1992a).…”

Section: Pedestrian Trafficmentioning

confidence: 99%

Traffic and related self-driven many-particle systems

2001

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46 1. Gas-kinetic and macroscopic models 46 2. Microscopic models and cellular automata 47 E. Bi-directional and city traffic 47 F. Effects beyond physics 48 G. Traffic control and optimization 48 V. Pedestrian traffic 49 A. Observations 49 B. Behavioral force model of pedestrian dynamics 50 C. Self-organization phenomena and noise-induced ordering 51 1. Segregation 51 2. Oscillations 52 3. Rotation 52 D. Collective phenomena in panic situations 53 1. "Freezing by heating" 53 2. "Faster-is-slower effect" 53 3. "Phantom panics" 54 4. Herding behavior 54 VI. Flocking and spin systems 54 A.

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Section: Pedestrian Trafficmentioning

confidence: 99%

Traffic and related self-driven many-particle systems

2001

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“…In Section (6) moments of the inter-evsnt distributions are obtained in terms of the vehicle flow rate when vehicles appear in bunches but each vehicle is separated by a minimum headway. Section (7) compares some of the results obtained in this paper with results of earlier authors.…”

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confidence: 55%

Distribution of Gaps and Blocks in a Traffic Stream

OLIVER¹

1961

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This paper studies some of the theoretical questions of large openings or gaps in a single stream of traffic. A gap in the traffic stream is defined as a headway between vehicles greater than or equal to some minimum size --say x. Several authors have studied the probability distribution of the wait which a randomly located observer must endure before he finds a gap. This paper, while briefly reviewing the solutions of this well known problem, is primarily concerned with expressions for: (i) the distribution of gap sizes; (ii) the distribution of spacings between vehicles and gaps; (iii) the mean and variance of inter-vehicle and intergap spacings; (iv) the stationary flow rates of gaps; and (v) the distribution of blocked and unblocked periods. It is assumed that the origin of measurements may be located (i) with the passing of a vehicle, (ii) at the beginning of a gap. or (iii) at random. It is also assumed that the distribution of inter-vehicle spacings are independently, but identically, distributed random variables.

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“…Many authors, e.g. Mayne (1951Mayne ( , 1954, Tanner (1951Tanner ( , 1953, Garwood (1940), Greenshields (1946) and others, have used the random vehicles model to study specific traffic problems. Much of this work could easily be revised for a random queues model and so made more realistic and presumably more accurate.…”

Section: The Application Of the Random Queues Model To The Study Of Wmentioning

confidence: 99%

A Queueing Model for Road Traffic Flow

Miller

1961

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary It is proposed that on roads which are uninterrupted by traffic signals, intersections, etc., vehicles should be considered as travelling in random queues. Criteria for determining the queues in actual traffic are found. A crude model is then used to study the formation of these queues in an attempt to derive the Borel–Tanner distribution of queue lengths. The random queues model is then used to study waiting times for pedestrians (or vehicles) wishing to cross one lane of traffic.

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Some Further Results in the Theory of Pedestrians and Road Traffic

Cited by 12 publications

References 2 publications

Traffic and related self-driven many-particle systems

Traffic and related self-driven many-particle systems

Distribution of Gaps and Blocks in a Traffic Stream

A Queueing Model for Road Traffic Flow

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