scholarly journals Exclusive queueing processes and their application to traffic systems

2014 ◽  
Vol 25 (03) ◽  
pp. 401-422 ◽  
Author(s):  
Chikashi Arita ◽  
Andreas Schadschneider
Keyword(s):  
Exclusion Process ◽  
Dynamical Variable ◽  
Asymmetric Exclusion Process ◽  
Transition Line ◽  
Pedestrian Dynamics ◽  
Queueing Process ◽  
Traffic Systems ◽  
Structure Density ◽  
System Length ◽  
Queueing Processes

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.

scholarly journals Totally asymmetric exclusion process with site-wise dynamic disorder

2019 ◽  
Vol 52 (6) ◽  
pp. 065002 ◽  
Author(s):  
Bartlomiej Waclaw ◽  
Justyna Cholewa-Waclaw ◽  
Philip Greulich
Keyword(s):  
Exclusion Process ◽  
Asymmetric Exclusion Process ◽  
Dynamic Disorder ◽  
Asymmetric Exclusion

scholarly journals A Combinatorial Derivation of the PASEP Stationary State

10.37236/1134 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Richard Brak ◽  
Sylvie Corteel ◽  
John Essam ◽  
Robert Parviainen ◽  
Andrew Rechnitzer
Keyword(s):  
Markov Chain ◽  
Stationary State ◽  
Stationary Distribution ◽  
Exclusion Process ◽  
Direct Proof ◽  
Asymmetric Exclusion Process ◽  
Original Process ◽  
Combinatorial Derivation ◽  
Path Models ◽  
Asymmetric Exclusion

We give a combinatorial derivation and interpretation of the weights associated with the stationary distribution of the partially asymmetric exclusion process. We define a set of weight equations, which the stationary distribution satisfies. These allow us to find explicit expressions for the stationary distribution and normalisation using both recurrences and path models. To show that the stationary distribution satisfies the weight equations, we construct a Markov chain on a larger set of generalised configurations. A bijection on this new set of configurations allows us to find the stationary distribution of the new chain. We then show that a subset of the generalised configurations is equivalent to the original process and that the stationary distribution on this subset is simply related to that of the original chain. We also provide a direct proof of the validity of the weight equations.

scholarly journals Multivariate Eulerian Polynomials and Exclusion Processes

2016 ◽  
Vol 25 (4) ◽  
pp. 486-499 ◽  
Author(s):  
P. BRÄNDÉN ◽  
M. LEANDER ◽  
M. VISONTAI
Keyword(s):  
Finite Number ◽  
Exclusion Process ◽  
Partition Functions ◽  
Asymmetric Exclusion Process ◽  
Negative Dependence ◽  
Combinatorial Interpretation ◽  
Exclusion Processes ◽  
Eulerian Polynomials ◽  
The Third ◽  
Dependence Properties

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and coloured permutations. The corresponding expressions of the multivariate partition functions are then related to multivariate generalisations of Eulerian polynomials for coloured permutations considered recently by N. Williams and the third author, and others. We also discuss stability and negative dependence properties satisfied by the partition functions.

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