
SIGMA 11 (2015), 065, 10 pages arXiv:1503.08669
https://doi.org/10.3842/SIGMA.2015.065
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet
A CA Hybrid of the SlowtoStart and the Optimal Velocity Models and its FlowDensity Relation
Hideaki Ujino ^{a} and Tetsu Yajima ^{b}
^{a)} National Institute of Technology, Gunma College, Maebashi, Gunma 3718530, Japan
^{b)} Department of Information Systems Science, Graduate School of Engineering, Utsunomiya University, Utsunomiya 3218585, Japan
Received March 31, 2015, in final form July 27, 2015; Published online July 31, 2015
Abstract
The s2sOVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slowtostart (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as well as the time continuous limit, which lead the s2sOVCA to an integraldifferential 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 flowdensity relations of the s2sOVCA. Based on the properties of the stationary flow of the s2sOVCA, the formulas for the flowdensity relations are derived.
Key words:
optimal velocity (OV) model; slowtostart (s2s) effect; cellular automaton (CA); ultradiscretization, flowdensity relation.
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