BML model on non-orientable surfaces

Abstract

a b s t r a c tTwo-dimensional Biham-Middleton-Levine traffic model on a N × N square lattice embedded on a Klein bottle and a projective plane is investigated by computer simulations. The behavior of the model with these boundary conditions is compared with the model under toroidal boundary conditions. Our numerical results show that the phase diagram depends strongly on the underlying topology. We also investigate the influence of the ratio between the number of red and blue particles has over the speed of the system and conclude that the projective plane case differs considerably from the other cases reviewed here.

Generalization of elementary cellular automata to a higher dimension family including the BML traffic model

“…Even then, it took a whole month for the simulations to run. Later researchers have implemented the BML traffic model on a graphics processing unit (GPU) [10], which is suitable for the task due to the embarrassingly parallel nature of the model.…”

“…Our implementation also uses the GPU to process several rows of the lattice in parallel. Like [10], our implementation uses the CUDA technology; the graphics card used in our experiments is a single NVIDIA GeForce GTX 970, which has 1664 CUDA cores [22].…”

“…The BML model's simplicity and interesting behavior has inspired research that tweak every aspect of the model [8], such as dimensionality [8,7], lattice geometry [9], boundary conditions [8,10,11], the update rule [8,7,11,12,14,15,18], initialization [8,13,16], and so on. Many other cellular automaton models were proposed for modelling traffic [8].…”

Parallel Implementations of Cellular Automata for Traffic Models

“…The original BML model has been extended in several directions. Cámpora et al [2] studied the behavior of the automaton on a square lattice embedded in a Klein bottle. Ding et al [5] analyzed a different update rule where a randomly chosen vehicle is allowed to move at each step.…”