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 cellular automaton model. Introducing a blockage site which transmit cars at some transmission probability into the rule-184 cellular automaton, we observe three different phases with increasing car concentration: Besides the free phase and the jam phase, which exist already in the pure rule-184 model, the mixed phase of these two appears at intermediate concentration with well-defined phase boundaries. This mixed phase, where cars pile up behind the blockage to form a jam region, is characterized by a constant flow. In the thermodynamic limit, we obtain the exact expressions for several characteristic quantities in terms of the car density and the transmission rate. These quantities depend strongly on the system size at the phase boundaries; We analyse these finite size effects based on the finite-size scaling.

Asymmetric simple exclusion process describing conflicting traffic flows

“…It is a well-known fact that a local defect can affect the system on a global scale [20,21]. This has been con- firmed not only for simple exclusion process but also for cellular automata models, such as Nagel-Schreckenberg [29], describing vehicular traffic flow [4,30,31]. Analogous to static defects, in our case of dynamical impurity we observe that the effect of the dynamic defect is to form a plateau region ρ ∈ [ρ − , ρ + ] in which ρ ± = 0.5 ± ∆ and 2∆ is the extension of the plateau region in the fundamental diagram.…”

Vehicular Traffic Flow at a Non-Signalised Intersection

“…It is a well-known fact that a local defect can affect the low dimensional non-equilibrium systems on a global scale [30,31,32,33,34,35,36,37,38]. This has been confirmed not only for simple exclusion process but also for cellular automata models describing vehicular traffic flow [39,40]. Analogous to static defects, in our case of dynamical impurity, we observe that the effect of the site-wise dynamic defect is to form a plateau region ρ ∈ [ρ − , ρ + ] in which ∆ = ρ + − ρ − is the extension of the plateau region in the fundamental diagram.…”

Cellular Automaton Modeling of Passenger Transport Systems

“…9, showing a trapezoidal shape. This trapezoidal shape is similar to the fundamental diagram in [25] and [26] , where a blockage effect is artificially introduced into the rule-184 cellular automaton to take a flow bottleneck into account. Thus, in the absence of waiting Fig.…”