1/f noise in a cellular automaton model for traffic flow with open boundaries and additional connection sites

The effect of additional input and output sites (as a connection to other roads) on the traffic flow in a cellular automaton model on a road with open boundaries is investigated. For a very low value of probability p of the velocity fluctuation of the vehicles, the 1/fα fluctuations are computed from the power spectrum of the traffic flow. As a result, α 1 in the free-flow and maximal current phases, and α is reduced in the jammed phase. Due to the vehicles movement through different chain boundaries, α can never reach the value zero in the jammed phase. It is to note that α can reach the value zero in periodic roads at very high densities [K. Nassab, R. Barlovic, M. Schreckenberg, S. Ouaskit, to submit]. The inflow (pin) and outflow (pout) of the vehicles through the connection sites to other roads lead to the formation of the region corresponding to the maximal flow phase in the phase diagram of the traffic flow. This result is found in the case of the low probabilities p of the fluctuations of the vehicles velocities in the road with open boundaries. This region grows in length if the rates of pin and pout increase. In the case of the chain without connection sites, the region of the maximal flow becomes large if the probability p is high, and vanishes if p=0 and pin=pout=0.