First Order Phase Transition in a New Cellular Automaton Model within the Framework of Kerner's Three-Phase Traffic Theory

Abstract

The cellular automata model proposed by Tian and Jia, was established in the framework of Kerner’s three-phase traffic theory and able to reproduce the three-phase traffic flow. But the first order transition from free flow to synchronized flow, which has been observed in the real traffic, could not be reproduced in the Tian and Jia model. One can see that the synchronized flow begin to emerge in Tian and Jia model, when the density is very low, which is obviously not consistent with the real traffic. Therefore, the authors improved their model by the following main aspects. (i) The randomisation probability function and the deceleration extent in the new model have considered more situations according to the real traffic than that of Tian and Jia model. (ii) The slow-to-start rule in the new model is different with that of Tian and Jia model, since the slow-to-start rule in Tian and Jia model is not insistent with the real traffic. (iii) According to the new model, all vehicles will go through the randomisation step first according to its updated rules. Through these improvements, the new model can successfully reproduce the first order transition from free flow to synchronized flow, which is clearly shown on the fundamental diagram. Moreover, one can see the coexistence of the free flow and synchronized flow on the space-time plots, which is strong evidence of this transition. Then the 1-min average flux density diagram, the correlation functions are presented to identify the synchronized flow state. All results have shown that the new model is well consistent with the empirical findings.