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.
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Acknowledgements
AS is supported by Deutsche Forschungsgemeinschaft (DFG) under grant “Scha 636/8-1”.
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Arita, C., Schadschneider, A. (2015). Exclusive Queueing Process: The Dynamics of Waiting in Line. In: Chraibi, M., Boltes, M., Schadschneider, A., Seyfried, A. (eds) Traffic and Granular Flow '13. Springer, Cham. https://doi.org/10.1007/978-3-319-10629-8_36
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DOI: https://doi.org/10.1007/978-3-319-10629-8_36
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