2014/09/15 by Chikashi Arita, C. Arita, Andreas Schadschneider +1 · 1 citation
Business, Management and Accounting · Mathematics · Physics and Astronomy · #Advanced Queuing Theory Analysis #Bulk queue #Fork–join queue #Layered queueing network #Process (computing) #Queue #Queueing system #Queueing theory #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #nlin.CG #physics.soc-ph
paper · pdf · doi:10.1142/s0218202515400011
published as Math. Models Methods Appl. Sci. 25, 401 (2015) · 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
arxiv created 2014/09/15 · openalex publication_date 2014/09/26 · arxiv updated 2015/02/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Pedestrian queues like those observed at ticket counters or supermarket checkouts are usually described by classical queueing theory. However, models like the M/M/1 queue neglect 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 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. In this paper, we review the main properties of the EQP and its applications to pedestrian dynamics, vehicular traffic and biological systems. We also mention extensions of the EQP and some related models.