Abstract
We study the statistical properties of a cellular automata model of traffic flow with the look-ahead potential. The model defines stochastic rules for the movement of cars on a lattice. We analyze the underlying statistical assumptions needed for the derivation of the coarse-grained model and demonstrate that it is possible to relax some of them to obtain an improved coarse-grained ODE model. We also demonstrate that spatial correlations play a crucial role in the presence of the look-ahead potential and propose a simple empirical correction to account for the spatial dependence between neighboring cells.
| Original language | English |
|---|---|
| Article number | 1350022 |
| Journal | Stochastics and Dynamics |
| Volume | 14 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2014 |
Funding
The work presented in this paper emerged as a result of discussions in a working group at the NSF funded Statistical and Applied Mathematical Sciences Institute. I.T. also acknowledges support from SAMSI as a long-term visitor in the Fall of 2010 and the Fall of 2011. C.H. was sponsored by the Office of Advanced Scientific Computing Research and performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725. I.T. was supported in part by the NSF Grant DMS-1109582. Y.S. was partially supported by a USC startup fund and a SC EPSCoR GEAR Award.
| Funders | Funder number |
|---|---|
| USC startup fund | |
| National Science Foundation | DMS-1109582 |
| Directorate for Mathematical and Physical Sciences | 1109582 |
| Advanced Scientific Computing Research | DE-AC05-00OR22725 |
Keywords
- Cellular automata model
- Coarse-grained PDE model
- Look-ahead potential
- Traffic flow