Exact stationary state for a deterministic high-speed traffic model with open boundaries

Jan De Gier

doi:10.1088/0305-4470/34/18/301

Exact stationary state for a deterministic high-speed traffic model with open boundaries

Jan De Gier^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

An exact solution for a high-speed deterministic traffic model with open boundaries and synchronous update rule is presented. Due to the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. It is shown in the case of υ_max = 2 that a detailed analysis of this structure leads to an exact solution. Explicit expressions for the stationary state probabilities are given in terms of products of 24 × 24 matrices. From this solution an exact expression for the correlation length is derived.

Original language	English
Pages (from-to)	3707-3720
Number of pages	14
Journal	Journal of Physics A: Mathematical and General
Volume	34
Issue number	18
DOIs	https://doi.org/10.1088/0305-4470/34/18/301
Publication status	Published - 11 May 2001

Access to Document

10.1088/0305-4470/34/18/301

Cite this

@article{321dab0c598b4ffa8092d8c685ee4504,

title = "Exact stationary state for a deterministic high-speed traffic model with open boundaries",

abstract = "An exact solution for a high-speed deterministic traffic model with open boundaries and synchronous update rule is presented. Due to the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. It is shown in the case of υmax = 2 that a detailed analysis of this structure leads to an exact solution. Explicit expressions for the stationary state probabilities are given in terms of products of 24 × 24 matrices. From this solution an exact expression for the correlation length is derived.",

author = "\{De Gier\}, Jan",

year = "2001",

month = may,

day = "11",

doi = "10.1088/0305-4470/34/18/301",

language = "English",

volume = "34",

pages = "3707--3720",

journal = "Journal of Physics A: Mathematical and General",

issn = "0305-4470",

publisher = "IOP Publishing Ltd.",

number = "18",

}

TY - JOUR

T1 - Exact stationary state for a deterministic high-speed traffic model with open boundaries

AU - De Gier, Jan

PY - 2001/5/11

Y1 - 2001/5/11

N2 - An exact solution for a high-speed deterministic traffic model with open boundaries and synchronous update rule is presented. Due to the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. It is shown in the case of υmax = 2 that a detailed analysis of this structure leads to an exact solution. Explicit expressions for the stationary state probabilities are given in terms of products of 24 × 24 matrices. From this solution an exact expression for the correlation length is derived.

AB - An exact solution for a high-speed deterministic traffic model with open boundaries and synchronous update rule is presented. Due to the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. It is shown in the case of υmax = 2 that a detailed analysis of this structure leads to an exact solution. Explicit expressions for the stationary state probabilities are given in terms of products of 24 × 24 matrices. From this solution an exact expression for the correlation length is derived.

UR - https://www.scopus.com/pages/publications/0035844115

U2 - 10.1088/0305-4470/34/18/301

DO - 10.1088/0305-4470/34/18/301

M3 - Article

SN - 0305-4470

VL - 34

SP - 3707

EP - 3720

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 18

ER -

Exact stationary state for a deterministic high-speed traffic model with open boundaries

Abstract

Access to Document

Other files and links

Fingerprint

Cite this