Vehicular motion in 2D city traffic network with signals controlled by phase shift

We study the dynamic behavior of vehicular traffic through the series of traffic lights controlled by phase shift in two-dimensional (2D) city traffic network. The nonlinear-map model is presented for the vehicular traffic. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. There are two traffic lights for the movement to north or that to east at each crossing. The traffic lights are controlled by the cycle time, split, and phase shift. The vehicle moves through the series of signals on a path selected by the driver. The city traffic with a heterogeneous density distribution is also studied. The dependence of the arrival time on cycle time, split, phase shift, selected path, and density is clarified for 2D city traffic. It is shown that the vehicular traffic is efficiently controlled by the phase shift.     

Vehicular traffic flow through a series of signals with cycle time generated by a logistic map

We study the dynamical behavior of vehicular traffic through a series of traffic signals. The vehicular traffic is controlled with the use of the cycle time generated by a logistic map. Each signal changes periodically with a cycle time, and the cycle time varies from signal to signal. The nonlinear dynamic model of the vehicular motion is presented by a nonlinear map including the logistic map. The vehicular traffic exhibits very complex behavior on varying both the cycle time and the logistic-map parameter a$a$. For a>3$a>3$, the arrival time shows a linear dependence on the cycle time. Also, the dependence of vehicular motion on parameter a$a$ is clarified.     

Randomness control of vehicular motion through a sequence of traffic signals at irregular intervals

We study the regularization of irregular motion of a vehicle moving through the sequence of traffic signals with a disordered configuration. Each traffic signal is controlled by both cycle time and phase shift. The cycle time is the same for all signals, while the phase shift varies from signal to signal by synchronizing with intervals between a signal and the next signal. The nonlinear dynamic model of the vehicular motion is presented by the stochastic nonlinear map. The vehicle exhibits the very complex behavior with varying both cycle time and strength of irregular intervals. The irregular motion induced by the disordered configuration is regularized by adjusting the phase shift within the regularization regions.     

Effect of restart at signals on traffic flow through a series of signals

We study the effect of restart at signals on the vehicular traffic controlled by a series of signals. The Nagel–Schreckenberg model (NS model) and Fukui–Ishibashi model (FI model) are applied to the vehicular motion. In the FI model, the step-by-step acceleration is not taken into account but the acceleration effect is included in the NS model. It is shown that the difference between both models results in the restart effect at signals. The extended version of the NS model with signals is formulated by the difference equation. The restart at signals has an effective effect on the traffic flow. The fundamental diagram changes highly by the restart effect. The dependences of mean speed on the cycle time are shown.     

Regularization and control of irregular vehicular motion through a series of signals at disordered intervals

We study the control and regularization of irregular motion of a vehicle moving through the series of traffic signals positioned at disordered intervals. All signals are controlled by both cycle time and phase shift. The nonlinear dynamic model of the vehicular motion controlled by signals is described in terms of the stochastic nonlinear map. The vehicle exhibits a very complex behavior with varying both cycle time and strength of disordered intervals. The delay or advance of tour time is compensated by synchronizing the phase shift with disordered intervals. The irregular motion induced by the disordered configuration of signals is regularized for various values of cycle time.     

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.     

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.     

Effect of speed fluctuations on a green-light path in a 2d traffic network controlled by signals

When a vehicle moves through a series of green lights, avoiding red signals in a two-dimensional (2d) city traffic network, the vehicle describes a characteristic trajectory (green-light path) and the travel time has a minimal value. The green-light path depends on the cycle time, split, signal-control strategy, and fluctuations of vehicular speed. We clarify the effect of speed fluctuations on a green-light path in a 2d traffic network controlled by signals. Even if an extremely small quantity of speed fluctuation is added, the green-light path changes greatly. It is shown that the root-mean square (RMS) of the deviation from the mean path depends highly on the cycle time. Also, the dependence of the green-light path on the speed-fluctuation strength is shown under a constant value of cycle time.     

Effect of signals on two-route traffic system with real-time information

We study the effect of signals on the vehicular traffic in the two-route system at the tour-time feedback strategy where the vehicles move ahead through a series of signals. The Nagel–Schreckenberg model is applied to the vehicular motion. The traffic signals are controlled by both cycle time and split. The tour times on two routes fluctuate periodically and alternately. The period increases with decreasing the split. Also, the tour time on each route varies with time by synchronizing with the density. The dependences of tour times and densities on both split and cycle time are clarified.     

Green-wave control of an unbalanced two-route traffic system with signals

We introduce the preference parameter into the two-route dynamic model proposed by Wahle et al. The parameter represents the driver’s preference for the route choice. When the driver prefers a route, the traffic flow on route A does not balance with that on route B. We study the signal control for the unbalanced two-route traffic flow at the tour-time feedback strategy where the vehicles move ahead through a series of signals. The traffic signals are controlled by both cycle time and phase shift (offset time). We find that the mean tour time can be balanced by selecting the offset time successfully. We derive the relationship between the mean tour time and offset time (phase shift). Also, the dependences of the mean density and mean current on the offset time are derived.     

Dynamics in two-elevator traffic system with real-time information

We study the dynamics of traffic system with two elevators using a elevator choice scenario. The two-elevator traffic system with real-time information is similar to the two-route vehicular traffic system. The dynamics of two-elevator traffic system is described by the two-dimensional nonlinear map. An elevator runs a neck-and-neck race with another elevator. The motion of two elevators displays such a complex behavior as quasi-periodic one. The return map of two-dimensional map shows a piecewise map.     

Influences of overtaking on two-lane traffic with signals

Based on the cellular automata method (CA method), two-lane traffic flow with the consideration of overtaking is investigated. Discrete equations are proposed to describe the traffic dynamics by using the rules of CA model. Influences of signal cycle time (t_s) and vehicular density (ρ) on the mean velocity 〈v〉 and mean overtaking times 〈c〉 of the traffic flow are discussed. The effects of slow vehicles and road barricades on the traffic flow are also studied. Simulation results shows that the vehicular density and the signal cycle time have significant influences on the traffic flow. The mean velocity of the traffic flow could keep a comparatively large value when ρ≤0.45. For a certain value of ρ, 〈v〉 displays a serrated fluctuation with t_s. Therefore, there may exist a certain combination of ρ and t_s which optimizes the traffic flow efficiency. As compared with the results in Nagatani (2009) [7], the model proposed here and the simulation results which took into account the effects of signal cycle time, slow vehicles, and road barricades on the traffic flow with overtaking allowed, can reflect the situation of traffic flow in a more realistic way.     

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.     

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.     

Vehicular motion through a sequence of traffic lights controlled by logistic map

We study the dynamical behavior of a single vehicle through the sequence of traffic lights controlled by the logistic map. The phase shift of traffic lights is determined by the logistic map and varies from signal to signal. The nonlinear dynamic model of the vehicular motion is presented by the nonlinear map including the logistic map. The vehicle exhibits the very complex behavior with varying both cycle time and logistic-map parameter a. For a>3, the dependence of arrival time on the cycle time becomes smoother and smoother with increasing a. The dependence of vehicular motion on parameter a is clarified.     

Vehicular motion on a selected path in a 2d traffic network controlled by signals

We study the dynamic behavior of vehicular traffic through a series of traffic lights on selected paths in a two-dimensional (2d) traffic network. The city traffic network is made of one-way perpendicular streets arranged in a square lattice with traffic signals where vertical streets are oriented upwards and horizontal streets are oriented rightwards. A vehicle moves through the series of signals on a path selected by the driver. The selected path is one of the straight, zigzag, and random paths in a 2d traffic network. The vehicular motion on a selected path is presented by the nonlinear-map model. Vehicular traffic exhibits very complex behavior with varying selected paths, cycle times, and vehicular density. The dependence of the arrival time on cycle time, selected path, and density is clarified for 2d city traffic.     

Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp

Mixed traffic flow consisting of vehicles equipped with adaptive cruise control (ACC) and manually driven vehicles is analyzed using car-following simulations. Simulations of merging from an on-ramp onto a freeway reported in the literature have not thus far demonstrated a substantial positive impact of ACC. In this paper cooperative merging for ACC vehicles is proposed to improve throughput and increase distance traveled in a fixed time. In such a system an ACC vehicle senses not only the preceding vehicle in the same lane but also the vehicle immediately in front in the other lane. Prior to reaching the merge region, the ACC vehicle adjusts its velocity to ensure that a safe gap for merging is obtained. If on-ramp demand is moderate, cooperative merging produces significant improvement in throughput (20%) and increases up to 3.6 km in distance traveled in 600 s for 50% ACC mixed flow relative to the flow of all-manual vehicles. For large demand, it is shown that autonomous merging with cooperation in the flow of all ACC vehicles leads to throughput limited only by the downstream capacity, which is determined by speed limit and headway time.     

Synchronized flow and phase separations in single-lane mixed traffic flow

In this paper, we have studied synchronized flow and phase separations in mixed (heterogeneous) single-lane highway traffic. It is found that the flux–density (occupancy) curve of heterogeneous flow, as expected, lies in between two flux–density (occupancy) curves of homogeneous flow R=0$R=0$ (all vehicles are slow vehicles) and R=1$R=1$ (all vehicles are fast vehicles). However, unexpectedly, the velocity–density (occupancy) curve of heterogeneous flow does not. We also found that cross-correlation function (CCF) analysis shows that heterogeneous flow has almost the same strong coupling as homogeneous flow. In other words, when traffic is in free flow or jams, the value of CCF is approximate to be 1.0, while the value is about 0.1 in synchronized flow.     

Driver choice compared to controlled diversion for a freeway double on-ramp in the framework of three-phase traffic theory

Two diversion schemes that apportion demand between two on-ramps to reduce congestion and improve throughput on a freeway are analyzed. In the first scheme, drivers choose to merge or to divert to a downstream on-ramp based on information about average travel times for the two routes: (1) merge and travel on the freeway or (2) divert and travel on a surface street with merging downstream. The flow, rate of merging at the ramps, and the travel times oscillate strongly, but irregularly, due to delayed feedback. In the second scheme, diversion is controlled by the average mainline velocities just upstream of the on-ramps. Driver choice is not involved. If the average upstream velocity on the mainline drops below a predetermined value (20 m/s) vehicles are diverted to the downstream ramp. When the average mainline velocity downstream becomes too low, diversion is no longer permitted. The resultant oscillations in this scheme are nearly periodic. The period is dominated by the response time of the mainline to interruption of merging rather than delayed feedback, which contributes only a minor component linear in the distance separating the on-ramps. In general the second scheme produces more effective congestion reduction and greater throughput. Also the travel times for on-ramp drivers are less than that obtained by drivers who attempt to minimize their own travel times (first scheme). The simulations are done using the Kerner-Klenov stochastic three-phase theory of traffic [B.S. Kerner, S.L. Klenov, Phys. Rev. E 68 (2003) 036130].     

Traffic states and jamming transitions induced by a bus in two-lane traffic flow

We study the traffic states and jamming transitions induced by a bus (slow car) in a two-lane traffic of cars. We use the dynamic model which is an extended one of the optimal velocity model to take into account the lane changing. The fundamental (flow-density) diagram is presented. The fundamental diagram changes highly by introducing a bus on a two-lane roadway. It is found that there are the six distinct states for the two-lane traffic flow including a bus. The spatio-temporal patterns are presented for the distinct traffic states. The dynamical state of traffic changes with density of cars. It is shown that the dynamical transitions among the distinct traffic states occur at some values of density. The phase diagram (region map) is shown for the two-lane traffic flow including a bus.