Phase transitions in a cellular automaton model of a highway on-ramp

Abstract

We introduce a lattice gas model for the merging of two single-lane automobile highways. The merging rules for traffic on the two lanes are deterministic, but the inflow on both lanes is stochastic. Analysing the stationary distribution of this stochastic cellular automaton, we find a discontinuous phase transition from a free-flow phase which depends on the initial state of the road to a jammed phase where all memory of the initial state is lost. Inside the jammed phase we identify dynamical phase transitions in the approach to stationarity. Each dynamical phase is characterized by a fixed number of relaxation cycles which is decreasing as one moves deeper into the jammed phase. In each cycle step, the number of 'desperate' drivers who force their way onto the main road when they reach the end of the on-ramp increases until stationarity.

Microscopic position and structure of a shock in CA 184

“…In the last two decades this model has been widely used as starting point to develop more realistic models of vehicular highway traffic, for a comprehensive review see [6]. Not long ago, a two-lane extension of this model was used by the authors to study the effect of an on-ramp on the flow along a main highway [17]. We found an intriguing family of dynamic phase transitions pertaining to relaxation cycles in a non-stationary state of the on-ramp.…”

When are cellular automata random?

“…Cellular automata have been studied by physicists as they can be used to model physical phenomena including traffic flow [2][3][4][5], disease epidemics [6,7], stochastic growth [8], predator-prey dynamics [9,10], invasion of populations [11], earthquakes [12] and dynamics of stock markets [13].…”

Human-Oriented Autonomous Traffic Simulation

“…Microscopic models describe traffic at a high level of detail (agent level) and attempt to model the actions and reactions of vehicles as accurately as possible. These include optimal velocity models [24,25], intelligent driver models [26], and the cellular automaton models [27].…”