Universität zu Köln

Arita, Chikashi and Schadschneider, Andreas ORCID: 0000-0002-2054-7973 (2015). Exclusive queueing processes and their application to traffic systems. Math. Models Meth. Appl. Sci., 25 (3). S. 401 - 423. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. ISSN 1793-6314

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Abstract

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 a 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 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Arita, Chikashi UNSPECIFIED UNSPECIFIED UNSPECIFIED Schadschneider, Andreas UNSPECIFIED orcid.org/0000-0002-2054-7973 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-406161
DOI:	10.1142/S0218202515400011
Journal or Publication Title:	Math. Models Meth. Appl. Sci.
Volume:	25
Number:	3
Page Range:	S. 401 - 423
Date:	2015
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
Place of Publication:	SINGAPORE
ISSN:	1793-6314
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language STEADY-STATES; MODEL; PARALLEL Multiple languages Mathematics, Applied Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/40616