Biham-Middleton-Levine Model Research Articles

A LANE-CHANGING BML MODEL CONSIDERING THE INFLUENCE OF BOTH LANE INFORMATION AND TURN SIGNALS

The lane-changing behaviors of vehicles are frequently adopted by drivers in order to get better driving conditions and turn signal plays an essential role in guiding vehicles' lane-changing behaviors. In this paper, based on the BML (Biham-Middleton-Levine model ) model, we proposed a lane- changing cellular automata model which takes the influence of both lane information and turn signals into account. When a vehicle cannot move forward, the driver will judge whether the vehicle meets the lane-changing conditions or not. If the driver can change his/her lane, then the lane-changing probability is calculated according to the lane information (such as average velocities and densities of those vehicles in his own and target lanes) and the state of turn signals. Finally, the driver can determine whether he/she changes lane or not by the corresponding probability. Numerical simulations were carried out to investigate the effect of lane-changing behaviors on the phase transition between the free flow phase and the global jamming phase. Two kinds of BML models were studied, one with traffic lights and the other without traffic lights. Numerical results show that the critical density of the BML model without traffic lights increases considerably due to the introduction of lane-changing rules. At a smaller scale, the critical density approximates that of the BML model with traffic light control. The effect of lane change is significant on traffic dynamics. Furthermore, a new coexisting phase of both the free flow phase and the local jamming phase was found. The underlying generation and evolution mechanism of the coexisting phase is discussed in detail. It is shown that the local congestions will result in the global congestion under higher densities. However, the lane-changing rules does not have distinct effect on the critical density of the BML model with traffic lights. But the region of phase transition becomes narrower. It indicates that lane-changing behaviors can lead to variations of local traffic features and take less effect on the global features of traffic system.

Traffic gridlock on a honeycomb city.

Inspired by an old and almost in oblivion urban plan, we report the behavior of the Biham-Middleton-Levine (BML) model-a paradigm for studying phase transitions of traffic flow-on a hypothetical city with a perfect honeycomb street network. In contrast with the original BML model on a square lattice, the same model on a honeycomb does not show any anisotropy or intermediate states, but a single continuous phase transition between free and totally congested flow, a transition that can be completely characterized by the tools of classical percolation. Although the transition occurs at a lower density than for the conventional BML, simple modifications, like randomly stopping the cars with a very small probability or increasing the traffic light periods, drives the model to perform better on honeycomb lattices. As traffic lights and disordered perturbations are inherent in real traffic, these results question the actual role of the square gridlike designs and suggest the honeycomb topology as an interesting alternative for urban planning in real cities.

Phase Diagram of Symmetric Two-Dimensional Traffic Model

On the basis of the critical car density line in the phase diagram of the Biham–Middleton–Levine model for symmetric two-dimensional traffic systems, the formula of the flow in the intermediate jam flow phase is hypothesized. The formula is utilized to obtain the phase boundary between the free flow and jam flow phases, where the flow becomes maximum. The validity of this phase boundary has been confirmed by simulations.

Unraveling the puzzling intermediate states in the Biham-Middleton-Levine traffic model.

The Biham-Middleton-Levine (BML) traffic model, a cellular automaton with eastbound and northbound cars moving by turns on a square lattice, has been an underpinning model in the study of collective behavior by cars, pedestrians, and even internet packages. Contrary to initial beliefs that the model exhibits a sharp phase transition from freely flowing to fully jammed, it has been reported that it shows intermediate stable phases, where jams and freely flowing traffic coexist, but there is no clear understanding of their origin. Here, we analyze the model as an anisotropic system with a preferred fluid direction (northeast) and find that it exhibits two differentiated phase transitions: the system is either longer in the flow direction (longitudinal) or perpendicular to it (transversal). The critical densities where these transitions occur enclose the density interval of intermediate states and can be approximated by mean-field analysis, all derived from the anisotropic exponent relating the longitudinal and transversal correlation lengths. Thus, we arrive at the interesting result that the puzzling intermediate states in the original model are just a superposition of these two different behaviors of the phase transition, solving by the way most mysteries behind the BML model, which turns out to be a paradigmatic example of such anisotropic critical systems.

Effect of slow-to-start in the extended BML model with four-directional traffic

Abstract In this paper, an extended Biham–Middleton–Levine (BML) model is proposed to simulate complex characteristics of four-directional traffic flow by considering the effect of slow-to-start. The simulation results show that the system does not exhibit a sharp transition from moving phase to jamming phase, which is consistent with the results of the latest studies about the original BML model. Differently from the structure geometric patterns in previous studies, a new phase separation phenomenon, i.e., the coexistence of multiple free flow stripes and multi-local jams, can be observed. The formation mechanisms of typical dynamic patterns are also explored. Furthermore, a mean field analysis for the maximum velocity in the moving phase is obtained, which is in good accordance with simulation results. In addition, an interesting feature is found that this new coexistence phenomenon of two phases is determined only by the effect of slow-to-start and is completely independent of traffic light (only considering red light and green light) period.

Biham—Middleton—Levine model in consideration of cooperative willingness

In this paper, the Biham—Middleton—Levine (BML) model with consideration of cooperative willingness has been proposed to study the traffic flow in urban networks. An evolutionary game with a cooperative willingness profile is introduced to deal with conflicts between disturbing neighbors. Simulation results suggest that imitating cooperative willingness can ease the effect of premature seizure on traffic flow due to the introduction of evolutionary games. Phase diagrams with a strategy profile and cooperative willingness profile have been investigated in detail. Our findings also prove that by imitating the more successful, cooperative willingness instead of simply the more successful strategies, the evolution of cooperation is significantly promoted, hence improving the order of cooperation and relieving the pressure of traffic networks.

Asymmetric Effect on Jamming Transition in Biham-Middleton-Levine Traffic Model

Asymmetric effect on the dynamical jamming transition in Biham-Middleton-Levine (BML) model with random sequential update rule is studied. The numerical simulations show that under periodic boundary condition, the system exhibits a sharp transition from freely moving phase to completely jamming phase, and the critical density is smaller than that of original BML model with synchronous update rule. For the asymmetry of system size, it can be found that the critical density is independent of the system size only when the width W and the length L are larger than some critical values respectively. Furthermore, the phase diagram shows that the asymmetric effect of the number of vehicles in two different directions plays a key role in reducing the occurrence of jam, and the underlying mechanism is analyzed.

A Two-Dimensional BML Model of Traffic Flow Considering Overpass Configuration

Considering the widely existed grade separations in the two-dimensional urban road network, this paper incorporates some overpass configurations into the classic Biham-Middleton-Levine (BML) model, which has not yet been fully investigated. With the change of the overpass's quantity and its configuration, the effect of overpass on the network performance is discussed based on the extended BML model. Using the numerical simulation, it is found that overpass newly built but without deliberate and reasonable plan, could only aggravate the existing congestion conditions, if the overpass ratio is low. Furthermore, the configurations of grouped overpass, which could reflect the realistic characteristics of overpass distribution in the road network, such as squared and loop-shaped configurations, are incorporated into the network. It is found that the squared configuration would bring positive effects on the network flow, while loop-shaped configuration bring negative effects on the network flow under certain conditions. The simulation results overthrow the conventional perception and have the extensive applicability and practical significance.

Premature seizure of traffic flow due to the introduction of evolutionary games

We study the impact of evolutionary games on the flow of traffic. Since traffic participants do not always conform to the imposed rules, the introduction of games, i.e. set of strategies defining the behavioural pattern of agents on the road, appears justified. With this motivation, and the fact that individuals can change their strategy in the course of time, the evolutionary prisoner's dilemma game is introduced between neighbouring agents, enabling them to choose between cooperation and defection. Mutual cooperation enables forwarding to both agents for one step, while the defector is able to advance two steps when facing a cooperator, whereby the latter is forced to go one step backwards. Two defectors end up in a halt until the next iteration. Irrespective of their strategy, however, agents can move only if the road ahead is free. Jumps are never allowed. We show that this simple and plausible supplementation of the discrete cellular automaton Biham–Middleton–Levine (BML) model induces a traffic flow seizure by a substantially lower initial density of cars as in the absence of evolutionary games. The phenomenon is explained by studying the one-dimensional variant of the BML model with different advancement steps on the circular ring. In view of the proposed explanation, findings are generalized also to other types of games, such is the snowdrift game, and some statistical properties of gridlock formation in the presence of evolutionary rules are outlined. Our findings suggest that ‘bending the law’ results in a premature occurrence of traffic jams and thus unnecessarily burdens the transportation system.

Biham–Middleton–Levine model with four-directional traffic

We study the four-directional traffic flow on a two-dimensional lattice. In the case of discrete densities, we assume equal number of vehicles in each lane. Except for the minimum density, the gridlock emerges swiftly. Two kinds of gridlock have been observed. The global gridlock dominates the system when the density is twice the minimum value. At higher densities, the system is pervaded by local gridlocks. We also analyze the time evolution of average speed. In the case of continuous densities, the vehicle numbers vary from lane to lane. The global gridlock is then destroyed by the fluctuations; while the local gridlock can still be observed.

Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods

We propose a cellular automata model for vehicular traffic in cities by combining (and appropriately modifying) ideas borrowed from the Biham-Middleton-Levine (BML) model of city traffic and the Nagel-Schreckenberg (NS) model of highway traffic. We demonstrate a phase transition from the "free-flowing" dynamical phase to the completely "jammed" phase at a vehicle density which depends on the time periods of the synchronized signals and the separation between them. The intrinsic stochasticity of the dynamics, which triggers the onset of jamming, is similar to that in the NS model, while the phenomenon of complete jamming through self-organization as well as the final jammed configurations are similar to those in the BML model. Using our new model, we have made an investigation of the time-dependence of the average speeds of the cars in the "free-flowing" phase as well as the dependence of flux and jamming on the time period of the signals.