Hideaki Ujino, Tetsu Yajima, “A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation”, SIGMA, 2015, Volume 11,065, 10 pp.

A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation

Hideaki Ujino^a, Tetsu Yajima^b

^a National Institute of Technology, Gunma College, Maebashi, Gunma 371–8530, Japan
^b Department of Information Systems Science, Graduate School of Engineering, Utsunomiya University, Utsunomiya 321–8585, Japan

Abstract: The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slow-to-start (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as well as the time continuous limit, which lead the s2s-OVCA to an integral-differential equation, are presented. Several traffic phases such as a free flow as well as slow flows corresponding to multiple metastable states are observed in the flow-density relations of the s2s-OVCA. Based on the properties of the stationary flow of the s2s-OVCA, the formulas for the flow-density relations are derived.

Keywords: optimal velocity (OV) model; slow-to-start (s2s) effect; cellular automaton (CA); ultradiscretization, flow-density relation.

MSC: 39A10; 39A06

Received: March 31, 2015; in final form July 27, 2015; Published online July 31, 2015

Language: English

DOI: 10.3842/SIGMA.2015.065