Exclusive Queueing Process: The Dynamics of Waiting in Line

Chikashi Arita () and Andreas Schadschneider ()
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Chikashi Arita: Universität des Saarlandes, Theoretische Physik
Andreas Schadschneider: Universität zu Köln, Institut für Theoretische Physik

A chapter in Traffic and Granular Flow '13, 2015, pp 299-304 from Springer

Abstract: Abstract The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by a M/M/1 queue which neglects the internal structure (density profile) of the queue by focussing on the queue length as the only dynamical variable. This is different in the exclusive queueing process (EQP) in which we consider the queue on a microscopic level. It is equivalent to a totally asymmetric exclusion process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability α and the service probability β. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used.

Keywords: Totally Asymmetric Exclusion Process (TASEP); System Length; Arrival Probability; Pedestrian Queue; Exact Stationary State (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10629-8_36

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DOI: 10.1007/978-3-319-10629-8_36

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