Effect of headway and velocity on safety-collision transition induced by lane changing in traffic flow

We study the traffic behavior when a vehicle changes from the first lane to the second lane on a two-lane highway. The incoming vehicle decelerates or accelerates by interacting with the vehicle ahead or behind on the second lane. We apply the extended optimal velocity model to the vehicular motion to take into account the velocity difference. We investigate whether or not the incoming vehicle collides with the vehicles ahead or behind. We derive such conditions that the incoming vehicle comes into collision with the vehicles ahead or behind. The safety-collision transition occurs by changing the lane. The dynamic transition depends highly on the headway, the vehicular speed, the sensitivity, and the velocity difference. We present the phase diagram (or region map) for the safety-collision transition.     

Dispersion and scaling of fluctuating vehicles through a sequence of traffic lights

We study the dynamical behavior of vehicles moving with fluctuating speed through a sequence of traffic lights which are controlled by the synchronized strategy. The dynamics of fluctuating vehicular traffic controlled by traffic lights is described in terms of the stochastic nonlinear map. We study two kinds of traffic: case (A) in which vehicles are allowed to pass other vehicles freely and case (B) in which vehicles are inhibited to pass other vehicles. Vehicles move together (without dispersion) for specific values of cycle time, while vehicles extend over the road for other values of cycle time. Then, vehicular traffic exhibits the dispersion. When the dispersion of vehicles occurs, the variance of arrival time shows the scaling behavior. The scaling properties are derived. The scaling form and exponents are discussed by comparing with those of dynamic scaling of rough surface.     

Bunching and transition of vehicles controlled by a sequence of traffic lights

We study the dynamical behavior of many vehicles with different desired velocities, moving through a sequence of traffic lights on a single-lane highway, where the traffic lights turn on and off periodically with the synchronized strategy. The dynamics of vehicular traffic controlled by traffic lights is described in terms of the nonlinear maps. For specific values of cycle time, the group (cluster) of vehicles exhibits the bunching without extending over the highway. It is found that two types of traffic states appear: the one is the bunching traffic and the other is the extended traffic. In the bunching traffic, all vehicles move together with the same tour time, while vehicles spread over the highway in the extended traffic. The dynamical transition between two traffic states occurs at specific values of cycle time. The phase diagram (region map) is presented.     

Clustering and maximal flow in vehicular traffic through a sequence of traffic lights

We study the maximal current (maximum traffic capacity) of vehicular traffic through a sequence of traffic lights on a highway, where all signals turn on and off synchronously. The dynamical model of vehicular traffic controlled by signals is expressed in terms of a nonlinear map, where the excluded-volume effect is taken into account. The dynamical behaviors of vehicles are clarified by analyzing traffic patterns. The clustering of vehicles varies with the cycle time of signals. The maximum current is closely connected to vehicular clustering. Clustering of vehicles is controlled by varying both split and cycle time of signals. The dependence of the maximal current on both split and cycle time is derived.     

Safety-collision transition induced by lane changing in traffic flow

We study the traffic behavior when a vehicle changes from the first lane to the second lane on a two-lane highway. We apply the optimal velocity model to the vehicular motion. If the incoming vehicle does not decelerate successfully, it crashes into the vehicle ahead. On the other hand, if the headway between the incoming vehicle and the vehicle behind on the second lane is not long sufficiently, the rear vehicle may come into collision with the incoming vehicle. The safety-collision transition occurs by changing the lane. The dynamical transition depends highly on the vehicular speed, the sensitivity, and the headway. We derive the phase diagram (or region map) for the safety-collision transition.     

Fluctuation and transition of vehicular traffic through a sequence of traffic lights

We study the dynamical behavior of N vehicles with no passing, but are moving through a sequence of traffic lights on a single-lane highway, where the traffic lights turn on and off periodically with the synchronized strategy. The dynamical model of N vehicles controlled by traffic lights is described in terms of coupled maps with three parameters. The motions of vehicles display a complex behavior, interacting with other vehicles through the sequence of traffic lights. Fluctuation of the leading vehicle is amplified to the following vehicles. The amplification of fluctuation changes with cycle time. The dynamical behavior of vehicles depends highly on their position of grouping vehicles. Signal traffic at a low density changes at specific values of cycle time. The complex dynamical transitions occur by varying three parameters.     

Stochastic Description of Traffic Flow

We propose a traffic model based on microscopic stochastic dynamics. We built a Markov chain equipped with an Arrhenius interaction law. The resulting stochastic process is comprised of both spin-flip and spin-exchange dynamics which models vehicles exiting, entering and interacting in a two-dimensional lattice environment corresponding to a multi-lane highway. The process is further equipped with a novel look-ahead type, anisotropic interaction potential which allows drivers/vehicles to ascertain local fluctuations and advance to new cells forward or sideways. The resulting vehicular traffic model is simulated via kinetic Monte Carlo and examined under both, typical and extreme traffic flow scenarios. The model is shown to correctly predict both qualitative as well as quantitative traffic observables for any highway geometry. Furthermore it also captures interesting multi-scale phenomena in traffic flows after a simulated accident which lead to oscillatory, dissipating, traffic waves with different periods per lane.     

Traffic states and fundamental diagram in cellular automaton model of vehicular traffic controlled by signals

We present a cellular automaton (CA) model for vehicular traffic controlled by traffic lights. The CA model is not described by a set of rules, but is given by a simple difference equation. The vehicular motion varies highly with both signals’ characteristics and vehicular density. The dependence of tour time on both cycle time and vehicular density is clarified. In the dilute limit of vehicles, the vehicular motion is compared with that by the nonlinear-map model. The fundamental diagrams are derived numerically. It is shown that the fundamental diagram depends highly on the signals’ characteristics. The traffic states are shown for various values of cycle time in the fundamental diagram. We also study the effect of a slow vehicle on the traffic flow.     

Fundamental diagram in traffic flow of mixed vehicles on multi-lane highway

We study the fundamental diagram for traffic flow of vehicular mixture on a multi-lane highway. We present the car-following model of multi-lane traffic in which slow and fast vehicles flow with changing lanes. We investigate the traffic states of the vehicular mixture under the periodic boundary. Two values of the current appear at a density and two current curves are obtained. Vehicles move with changing lanes in the traffic state of high current, while vehicles move without changing lanes in the traffic state of low current. They depend on the density, the fraction of slow vehicles, and the initial condition. In the high-current curve, the jamming transition between the free flow and the jammed state occurs at a low density. The fundamental diagrams (current-density diagrams) are shown for the single-lane, two-lane, three-lane, and four-lane traffics.     

Multiple-vehicle collision in traffic flow by a sudden slowdown

We study the multiple-vehicle collision when a vehicle decelerates suddenly in a single-lane traffic flow. The extended optimal velocity model is used for the vehicular motion to take into account the relative velocity. If a vehicle slows down suddenly and the following vehicle does not decelerate successfully, it crashes into the vehicle ahead with a residual speed and the crash may induce more collisions. The number of crumpled vehicles depends on the initial headway, the sensitivity, the initial velocity, and the relative velocity. We derive the region map (phase diagram) for the multiple-vehicle collision. The dependence of the multiple-vehicle collision on the density, sensitivity, and relative velocity is shown.     

Cellular automaton model for traffic flow based on safe driving policies and human reactions

This paper proposes a new single-lane cellular automaton model for traffic flow. The model takes into account normal drivers’ spacing policies and transportation engineering practices to guarantee that microscopic vehicle behavior is more in line with vehicular movement in the real world. As a result, drivers’ reactions are based on a safety analysis that determines the most appropriate action for a vehicle to take. Hence, the model introduces a new set of simple rules to change the speed of vehicles that incorporates three important thresholds required by the follower vehicle to accelerate, slow down or maintain its speed. Thus, the space gap, relative speed and limited acceleration/deceleration capabilities are introduced into simulations. Simulation results obtained from a system with periodic conditions show that the model can smooth the speed drop when vehicles approach the upstream front of the traffic jam. Therefore, the model avoids unrealistic deceleration behavior found in most previous cellular automata models. Besides, the model is also capable of reproducing most empirical findings including the three states of traffic flow, the backward speed of the downstream front of the traffic jam, and different congested traffic patterns induced by a system with open boundary conditions with an on-ramp. Moreover, the new model preserves the computational simplicity of the cellular automata models.     

Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances

In the Nagel-Schreckenberg model of vehicular traffic on single-lane highways vehicles are modelled as particles which hop forward from one site to another on a one dimensional lattice and the inter-particle interactions mimic the manner in which the real vehicles influence each other's motion. In this model the number of empty lattice sites in front of a particle is taken to be a measure of the corresponding distance-headway (DH). The time-headway (TH) is defined as the time interval between the departures (or arrivals) of two successive particles recorded by a detector placed at a fixed position on the model highway. We investigate the effects of spatial inhomogeneities of the highway (static hindrances) on the DH and TH distributions in the steady-state of this model. Received: 2 March 1988 / Revised: 13 April 1998 / Accepted: 17 April 1998     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

Nonlinear-map model for split effect on vehicular traffic through periodic signals

We study the effects of both split and cycle time on dynamical behavior of vehicles moving through a sequence of traffic lights on a highway, where the traffic lights turn on and off periodically. The dynamical model of vehicular traffic controlled by signals is expressed in terms of a nonlinear map. The vehicle exhibits complex behavior with varying split and cycle time. The tour time between signals shows a self-similar behavior. When split s_p is lower than 0.5, vehicular traffic shows a similar behavior as that of s_p=0.5, while vehicular traffic of s_p  >0.5 is definitely different from that of _sp?0.5$s_p?0.5$. The algebraic expression among the tour time, cycle time, and split is derived.     

Traffic flow through multi-lane tollbooths on a toll highway

We study the traffic states and queuing occurring in traffic flow on a toll highway with multi-lane tollgates. The traffic states change with increasing density and varying number of tollgates. When the manual-collection vehicles sort themselves into the tollgates, the queues occur just in front of the tollgates if the vehicular density is higher than a critical value. The queuing in front of tollgates is induced by the competition between the lane expansion and slowdown effects. When the lane expansion effect is superior to the slowdown effect, no queuing occurs. We derive the fundamental diagrams (current-density diagrams) for the traffic flow on the toll highway. The current saturates at the nearest tollgate at a low density and the saturation extends to the next-nearest tollgate with increasing density.     

Effect of the lane reduction in the cellular automata models applied to the two-lane traffic

More investigated situations in the field of traffic modelling are those of traffic bottlenecks caused by slow vehicles or road defects. The new aspect of this paper is the simulation of vehicular dynamics near a partial reduction in a road from two lanes to one lane. In order to reduce the bad impact of waiting vehicles behind the defect region, a strategy regulating the vehicle movement in the vicinity of the reduced lane is taken into account. The simulation model is based on the cellular automata model of Nagel–Schreckenberg with additional rules of lane change. The partial lane reduction strongly reduces the road capacity, and the added regulation strategy leads to a more interesting shape of the fundamental diagram, which depends on different constraints on the model parameters, e.g., the length of the reduced lane, the maximal speed, and the length of the connection sites near the entry of the reduced lane.     

A refined cellular automaton model to rectify impractical vehicular movement behavior

When implementing cellular automata (CA) into a traffic simulation, one common defect yet to be rectified is the abrupt deceleration when vehicles encounter stationary obstacles or traffic jams. To be more in line with real world vehicular movement, this paper proposes a piecewise-linear movement to replace the conventional particle-hopping movement adopted in most previous CA models. Upon this adjustment and coupled with refined cell system, a new CA model is developed using the rationale of Forbes’ et al. car-following concept. The proposed CA model is validated on a two-lane freeway mainline context. It shows that this model can fix the unrealistic deceleration behaviors, and thus can reflect genuine driver behavior in the real world. The model is also capable of revealing Kerner’s three-phase traffic patterns and phase transitions among them. Furthermore, the proposed CA model is applied to simulate a highway work zone wherein traffic efficiency (maximum flow rates) and safety (speed deviations) impacted by various control schemes are tested.     

Cellular automata model for traffic flow with safe driving conditions

In this paper, a recently introduced cellular automata （CA） model is used for a statistical analysis of the inner micro-scopic structure of synchronized traffic flow. The analysis focuses on the formation and dissolution of clusters or platoons of vehicles, as the mechanism that causes the presence of this synchronized traffic state with a high flow. This platoon formation is one of the most interesting phenomena observed in traffic flows and plays an important role both in manual and automated highway systems （AHS）. Simulation results, obtained from a single-lane system under periodic boundary conditions indicate that in the density region where the synchronized state is observed, most vehicles travel together in pla- toons with approximately the same speed and small spatial distances. The examination of velocity variations and individual vehicle gaps shows that the flow corresponding to the synchronized state is stable, safe and highly correlated. Moreover, results indicate that the observed platoon formation in real traffic is reproduced in simulations by the relation between vehicle headway and velocity that is embedded in the dynamics definition of the CA model.     

Two-lane traffic simulations with a blockage induced by an accident car

Based on the two-lane traffic model proposed by Chowdhury et al., a highway traffic model with a blockage induced by an accident car is proposed, in which both symmetric lane changing rules and asymmetric lane changing rules are adopted. The fundamental diagrams and spatial-temporal profiles are presented after the numerical simulation and the jam transition is studied. It is shown that the accident car not only causes a local jam behind the accident car, but also causes vehicles to cluster in the bypass lane. The asymmetric lane changing rules are more advantageous in reducing the local jam than the symmetric lane changing rules when the accident car is in the right lane, and the symmetric lane changing rules are superior when the accident car is in the left lane. Furthermore the curves of lane-changing frequency against the total density are given. It is found that the vehicles will change lane more frequently when traffic is inhomogeneous with different types of vehicle or with an accident car.