Lattice Model Of Traffic Flow Research Articles

A NOVEL LATTICE TRAFFIC FLOW MODEL AND ITS SOLITARY DENSITY WAVES

A novel lattice traffic flow model with a slope effect is proposed. Neutral stability condition is obtained by the use of the linear stability theory. The standard KdV equation is derived in the meta-stable region and soliton solution is obtained near the neutral stability line. The solitary waves are reproduced through the numerical simulations. Results show that the solitary density wave appears in upward form when the average density is less than critical density, otherwise it exhibits downward form.

A new lattice model of traffic flow with the anticipation effect of potential lane changing

A new lattice model of traffic flow is presented by taking into account the anticipation of potential lane changing on front site on single lane. The stability condition of the extended model is obtained by using the linear stability theory. The modified KdV equation near the critical point is constructed and solved through nonlinear analysis. And the phase space of traffic flow in the density–sensitivity space could be divided into three regions: stable, metastable and unstable ones, respectively. Numerical simulation also shows that the consideration of lane changing probability in lattice model can stabilize traffic flow, which implies that the new consideration has an important effect on traffic flow in lattice models.

A new lattice model of traffic flow with the consideration of the traffic interruption probability

In this paper, we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways. The stability condition of the new model is obtained by the linear stability analysis and the modified Korteweg–de Vries (KdV) equation is derived through nonlinear analysis. Thus, the space will be divided into three regions: stable, metastable and unstable. The simulation results also show that the traffic interruption probability could stabilize traffic flow.

A NEW LATTICE MODEL OF TRAFFIC FLOW WITH THE CONSIDERATION OF THE HONK EFFECT

In this paper, a new lattice model is presented with the consideration of the honk effect. The stability condition is obtained by the linear stability analysis. The modified Korteweg–de Vries (KdV) equation is derived to describe the phase transition of traffic flow through nonlinear analysis. The space is divided into three regions: the stable region, the metastable region and the unstable region, respectively. And numerical simulation is carried out to validate the analytic results. The results implied that the honk effect could stabilize traffic flow and suppress the traffic jam in lattice model of traffic flow.

A driver’s memory lattice model of traffic flow and its numerical simulation

A new lattice model of traffic flow based on Nagatani’s model is proposed by taking the effect of driver’s memory into account. The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the stabile area of the new model is larger than that of the original lattice hydrodynamic model by adjusting the driver’s memory intensity parameter p of the past information in the system. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis, and the phase space could be divided into three regions: the stability region, the metastable region, and the unstable region, respectively. Numerical simulation also shows that our model can stabilize the traffic flow by considering the information of driver’s memory.

A new lattice model of traffic flow with the consideration of the driverʼs forecast effects

In this Letter, a new lattice model is presented with the consideration of the driverʼs forecast effects (DFE). The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the new model can improve the stability of traffic flow by considering DFE. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis. Numerical simulation also shows that the new model can improve the stability of traffic flow by adjusting the driverʼs forecast intensity parameter, which is consistent with the theoretical analysis.

A traffic flow lattice model with the consideration of driver anticipation effect and its numerical simulation

With the consideration of the effect of driver anticipation behavior on traffic flow, a new one-dimensional lattice model is proposed. The linear stability condition of the presented model is obtained by employing the linear stability theory. The density wave near the critical stable point is investigated analytically with the nonlinear analysis method. The results show that the occurrence of traffic jamming transitions can be described by the kink-antikink solution of the modified Korteweg-de Vries (mKdV) equation. The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the effect of driver anticipation behavior is considered.

A traffic flow lattice model considering relative current influence and its numerical simulation

Based on Xue's lattice model, an extended lattice model is proposed by considering the relative current information about next-nearest-neighbour sites ahead. The linear stability condition of the presented model is obtained by employing the linear stability theory. The density wave is investigated analytically with the perturbation method. The results show that the occurrence of traffic jamming transitions can be described by the kink–antikink solution of the modified Korteweg-de Vries (mKdV) equation. The simulation results are in good agreement with the analytical results, showing that the stability of traffic flow can be enhanced when the relative current of next-nearest-neighbour sites ahead is considered.

A coupling lattice model of traffic flow on two lanes and numerical simulation

An improved coupling lattice model of two-lane traffic flow is proposed by taking into account the effect of the two-lane coupling and lane changing. And the lane changing rate of traffic flow is modified. The analysis of the modified lane changing rate shows that it is in better accordance with the real traffic than the previous ones. The linear stability condition of the extended model is obtained by using the linear stability theory. Numerical simulation also shows that our model can better reproduce the lane changing of traffic flow than previous ones by considering the information of two-lane coupling interaction. And there is unavoidable effect on the two-lane traffic flow from the coupling effect between the two lanes.

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.

An improved two-lane traffic flow lattice model

An improved two-lane traffic flow lattice model is proposed. The model introduces a new function to govern the flow shift between two lanes, and then eliminates the flaws of vehicle backward movement which may appear in existing lattice models. The sufficient and necessary conditions for keeping the model’s linear stability are derived. Numerical simulations which correctly reproduce the lane changing behavior induced by small disturbances are presented.

Lattice models of the optimal traffic current

Based on the lattice model of traffic flow, the lattice models which consider the next-nearest-neighbour flow on traffic and pay attention to the following vehicle as well as the preceding vehicle are presented, respectively. The stability criterion is derived by the linear stability analysis. The evolution of density wave has been investigated analytically with the perturbation method. The results show that the occurrence of traffic jamming transitions is described by the kink solution of the modified KdV equation. The theoretical results are in good agreement with the simulation. Moreover, the simulation indicates that the lattice models considering the next-nearest-neighbour interaction can stabilize the traffic flow, but the other model is just in opposition to the former model.