EconPapers    
Economics at your fingertips  
 

Simple stochastic model with safe speed using Exchange approach to recognizing synchronized flow as speed-synchronized phase

Masayuki Fukuichi ()
Additional contact information
Masayuki Fukuichi: Faculty of Liberal Arts, The Open University of Japan, 2-11 Wakaba, Mihama-Ku, Chiba 261-8586, Japan

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 06, 1-25

Abstract: In order to unravel the physical and mathematical mystery of synchronized-flow mechanism and to reveal the fundamental mechanism and origin of synchronized flow produced by nonlinear stochastic processes, we have produced simple stochastic traffic flow models (the gradual-NaSch, Phoenix and mPhoenix models) with nonlinear safe speeds. In the mNaSch model and our gradual-NaSch model, the ith vehicle’s speed is the same as or different from the jth vehicle’s speed because they are discrete values. In the mNaSch and gradual-NaSch models, the same discrete values of the ith and jth states make it easy to identify synchronized flow with speed-synchronized phase of the ith and jth states. On the other hand, when we deal with synchronized flow in continuous traffic flow models, we face a problem. Continuous values cause the difficulty in identification of synchronization. In order to definitely clarify whether or not synchronized flow occurs in continuous models, we have established a novel idea of Exchange approach to recognizing synchronized flow as speed-synchronized phase. Our idea is generated from the analogical image that the whole system of synchronized metronomes does not change even if the ith and jth synchronized metronomes are exchanged. The Exchange approach (exchanging the ith vehicle’s state for any jth vehicle’s state in the whole system of traffic flow), which causes distortion such as a collision if non-synchronized vehicle’s states are exchanged and makes it possible to definitely clarify whether or not synchronized flow occurs in continuous models, is applied to our simple stochastic continuous model (the mPhoenix model). On the basis of the Exchange approach, we can recognize that the mPhoenix model surely reproduces synchronized flow. In addition, we have proposed mathematical approach to deriving nonlinear safe speeds which guarantee collision free driving and reproduce synchronized flow.

Keywords: Synchronized flow; cellular automaton model; Exchange approach; traffic flow; stochastic model; speed-synchronized phase; phase transition (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183124500761
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:35:y:2024:i:06:n:s0129183124500761

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183124500761

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().

 
Page updated 2025-03-20
Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:06:n:s0129183124500761