Order Parameter as an Additional State Variable of Unstable Traffic Flow

Abstract

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that could explain in a simple way such observed self-organizing phenomena as the sequence of the phase transitions "free flow -> synchronized motion -> jam" and the hysteresis in them. We introduce a new variable called order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to "many-body" effects in the car interaction in contrast to such variables as the mean car density and velocity being actually the zeroth and first moments of the "one-particle" distribution function. Therefore, we regard the order parameter as an additional independent state variable of traffic flow and formulate the corresponding evolution equation governing the lane changing rate. In this context we analyze the instability of homogeneous traffic flow manifesting itself in both of the mentioned above phase transitions where and endowing them with the hysteresis. Besides, the jam state is characterized by the vehicle flows at different lanes being independent of one another.