Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage

Abstract

Effects of a bottleneck in a linear trafficway is investigated using a simple\ncellular automaton model. Introducing a blockage site which transmit cars at\nsome transmission probability into the rule-184 cellular automaton, we observe\nthree different phases with increasing car concentration: Besides the free\nphase and the jam phase, which exist already in the pure rule-184 model, the\nmixed phase of these two appears at intermediate concentration with\nwell-defined phase boundaries. This mixed phase, where cars pile up behind the\nblockage to form a jam region, is characterized by a constant flow. In the\nthermodynamic limit, we obtain the exact expressions for several characteristic\nquantities in terms of the car density and the transmission rate. These\nquantities depend strongly on the system size at the phase boundaries; We\nanalyse these finite size effects based on the finite-size scaling.\n