Exclusive Queueing Processes and their Application to Traffic Systems
arXiv:1409.4731 · doi:10.1142/S0218202515400011
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 the M/M/1 queue that neglects the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered 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 alpha and the service probability beta. 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. In this article, we review the main properties of the EQP. We also mention extensions and applications of the EQP and some related models.
20 pages, 11 figures, to appear in Mathematical Models and Methods in Applied Sciences, Special Issue "Traffic, Crowds and Swarms 2015"; contains a review of results from arXiv:1012.4525, arXiv:1109.0425, arXiv:1210.1482, arXiv:1308.2417, arXiv:1409.0329 and some new results
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Cited by in corpus (8)
- Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics
- Effect of self-deflection on a totally asymmetric simple exclusion process with functions of site-assignments
- Exclusive queueing model including the choice of service windows
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