Biham-Middleton-Levine Research Articles

The Impact of Traffic Crashes on Urban Network Traffic Flow

This paper aims to investigate the impact of occasional traffic crashes on the urban traffic network flow. Toward this purpose, an extended model of coupled Nagel–Schreckenberg (NaSch) and Biham–Middleton–Levine (BML) models is presented. This extended model not only improves the initial conditions of the coupled models, but also gives the definition of traffic crashes and their spatial/time distribution. Further, we simulated the impact of the number of traffic crashes, their time distribution, and their spatial distribution on urban network traffic flow. This research contributes to the comprehensive understanding of the operational state of urban network traffic flow after traffic crashes, towards mastering the causes and propagation rules of traffic congestion. This work also a theoretical guidance value for the optimization of urban traffic network flow and the prevention and release of traffic crashes.

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.

Effect of violating the traffic light rule in the Biham-Middleton-Levine traffic flow model

This paper studies the effect of violating the traffic light rule in the Biham-Middleton-Levine (BML) traffic flow model. It is assumed that there are two kinds of drivers: normal drivers obey the traffic light rule and violators disobey it. Simulation results show that although the existence of violators increases the average velocity in the free-flowing phase, it decreases the threshold from free-flowing phase to jam. With the presence of violators, a new kind of configuration with stripe slopes −2 and −1/2 has been found in the free-flowing phase. We have developed an analytical investigation which successfully predicts the average velocity in the free-flowing phase. A phase separation phenomenon, where jams and freely flowing traffic coexist, has been found in the intermediate car density range. The mechanism of the phase separation has been illustrated.

Violating traffic light behavior in the Biham-Middleton-Levine traffic flow model

Effects of violating traffic light behavior are studied in this paper based on the cellular automata (CA) model proposed by Biham-Middleton-Levine (BML). We define two kinds of drivers: one obeys the traffic light rule, the other ignores it. Simulation results show that the violator increases the average velocity of free flowing phase while decreases the critical car density. We predicted the average velocity in the free flowing phase by ignoring the correlation among cars. A phase separation phenomenon, where jams and freely flowing traffic coexist, has been found in intermediate car density range. The occurrence reason of phase separation has been explained.

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.

Slow-to-start effect in two-dimensional traffic flow

This paper studies slow-to-start effect in two-dimensional Biham–Middleton–Levine (BML) traffic flow model with traffic light periods T = 2 τ . In most cases, the model exhibits free flow, jam, and phase separation phenomenon. Nevertheless, when the slow-to-start parameter p = 0 , and traffic light parameter τ = 3 or 5, it is found that phase separation phenomenon does not occur. We have explained this via the evolution process from a designed regular initial configuration. Moreover, it is also found that the free flow self-organizes into grid-like structure when τ is large and the slow-to-start parameter 0 < p < 1 .

Effect of randomization in the Biham–Middleton–Levine traffic flow model

This paper studies the effect of randomization in the Biham–Middleton–Levine(BML) traffic flow model. It is found that the average velocity exhibits a first-orderphase transition from moving phase to jamming phase under periodic boundaryconditions. The intermediate stable phase identified in the original deterministic BMLmodel disappears with the introduction of randomization. The average velocityin the moving phase and the critical car density decrease as the randomizationprobability increases. We have developed a mean-field theory which successfullypredicts the average velocity in the moving phase. Under open boundary conditions,there are only two phases and the maximum current phase does not occur. Thedependence of the average velocity, the density and the flow rate on the injectionprobability in the moving phase have also been obtained through the mean-fieldtheory.

Timing of traffic lights and phase separation in two-dimensional traffic flow

Abstract In this paper, we study the effects of traffic light period in two-dimensional Biham–Middleton–Levine (BML) traffic flow model. It is found that a phase separation phenomenon, in which the system separates into coexistence of free flow and jam, could be observed in intermediate vehicle density range when traffic light period T ⩾ 4 . We have explained the reason of occurrence of phase separation and investigated its behavior in different traffic light period.

Periodic states, local effects and coexistence in the BML traffic jam model

The Biham–Middleton–Levine (BML) model is simple lattice model of traffic flow, self-organization and jamming. Rather than a sharp phase transition between free-flow and jammed, it was recently shown that there is a region where stable intermediate states exist, with details dependent on the aspect ratio of the underlying lattice. Here we investigate square aspect ratios, focusing on the region where random, disordered intermediate (DI) states and conventional global jam (GJ) states coexist, and show that DI states dominate for some densities and timescales. Moreover, we show that periodic intermediate (PI) states can also coexist. PI states converge to periodic limit cycles with short recurrence times and were previously conjectured to arise from idiosyncrasies of relatively prime aspect ratios. The observed coexistence of DI, PI and GJ states shows that global parameters, density together with aspect ratio, are not sufficient to determine the full jamming outcome. We investigate additional features that lead towards jamming and show that a strategic perturbation of a few selected bits can change the nature of the flow, nucleating a global jam.

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.

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.

Temporal Variations of Traffic Flow in the Biham-Middleton-Levine Model

The temporal variation of the average velocity of cars in the Biham-Middleton-Levine (BML) model is studied. The equations which govern the temporal variation of the car velocities for various densities of cars are derived. By utilizing these equations, the final average velocity is approximately obtained for most self-organized states.