Spatio-temporal organization of a cellular automaton model for computer network Original Research Article

It was unveiled by Ren et al. [Comput. Phys. Comm. (2001)] that congestion transition emerges in cellular automaton models for computer network and this NaSch network model with Q=1 has similar behaviours as the NaSch traffic model with maximum velocity vmax=1. For these two NaSch models, the main difference lies in a node cell contained in the NaSch network model. In this paper, we will focus on our further investigation on spatio-temporal organization of the NaSch network model. More interesting phenomena of phase transition are discovered. Firstly, fundamental diagram illustrates that when Q>1 for the NaSch network model it is significantly different from its counterpart, i.e. the NaSch traffic model in a road traffic system. The addition of a node cell, which is allowed to have more than one packets, will lead to generating a new phase. Secondly, in order to characterize phase transition occurred in the NaSch network model, an order parameter is presented with the use of the time average density of nearest-neighbor pairs m. The computational results obtained show that criticality will disappear in a strict sense if noise exists. Finally, two other numerical features, i.e. spatial correlation functions G(r) and relaxation times τ, are analyzed so as to deeply describe behaviours near critical points.