Loading conditions for self‐organization in the BML model with stochastic direction choice

Author:

Yashina Marina V.123ORCID,Tatashev Alexander G.12

Affiliation:

1. Moscow Automobile and Road Construction State Technical University (MADI) Moscow Russian Federation

2. Moscow Technical University of Communications and Informatics Moscow Russian Federation

3. Moscow Aviation Institute (National Research University) Moscow Russian Federation

Abstract

A dynamical system is considered such that, in this system, particles move on a toroidal lattice of the dimension according to a version of the rule of particle movement in Biham–Middleton–Levine traffic model. We introduce a stochastic case with direction choice for particles. Particles of the first type move along rows, and the particles of the second type move along columns. The goal is to find conditions of self‐organization system for any lattice dimension. We have proved that the BML model as a dynamical system is a special case of Buslaev nets. This equivalence allows us to use of Buslaev net analysis techniques to investigate the BML model. In Buslaev nets conception, the self‐organization property of the system corresponds to the existence of velocity single point spectrum equal to 1. In the paper, we consider the model version when one notable aspect is that a particle may change its type. Exactly, we assume a constant probability that a particle changes type at each step. In the case where , the system corresponds to the classical version of the BML model. We define a state of the system where all particles continue to move indefinitely, in both the present and the future, as a state of free movement. A sufficient condition for the system to result in a state of free movement from any initial state (condition for self‐organization) has been found. This condition is that the number of particles be not greater than half the greatest common divisor of the numbers . It has been proved that, if , and whether or and there are both at least one particle of the first type and at least particle of the second type, then a necessary condition for a state of free movement to exist is the greatest common divisor of and be not less than 3. The theorems are formulated in terms of the algebraic structures and terms of the dynamical system. The spectrum of particle velocities has been found for the net . This approach allows us to hope that the spectrum of dynamical system can be studied for an arbitrary dimension of the net.

Publisher

Wiley

Reference18 articles.

1. O.Biham A. A.Middleton andD.Levine Self organization and dynamic transition in traffic models 1992. arXiv preprint cond‐mat/9206001.

2. Statistical mechanics of cellular automata

3. N. J.LineshandR. M.D'Souza Periodic states local effects and coexistence in the BML traffic jam model 2008. arXiv:0709.3604v3 [cond‐math.stat‐mech].

4. T.AustinandI.Benjamini For what number must self organization occur in the Biham–Middleton–Levine traffic model from any possible starting configuration?2006. arXiv preprint math/0607759.

5. The number of collisions in Biham–Middleton–Levine model on a square lattice with limited number of cars;Moradi H. R.;Appl. Math. E‐Notes,2019

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3