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.     

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.     

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.     

Control of vehicular traffic through a sequence of traffic lights positioned with disordered interval

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights which are positioned with inhomogeneous interval on a roadway and turn on and off periodically with the synchronized strategy. The dynamics of vehicular traffic controlled by traffic lights is described in terms of the stochastic nonlinear map. When the interval between traffic lights fluctuates highly, vehicles cannot move together with the same tour time. While vehicles can move together with the other at less inhomogeneous interval between traffic lights for specific values of cycle time. If heterogeneity of traffic-light's interval is higher, it becomes more difficult to control vehicles moving together. The phase diagram (region map) is presented for controlling the vehicular traffic.     

Vehicular motion in counter traffic flow through a series of signals controlled by a phase shift

We study the dynamical behavior of counter traffic flow through a sequence of signals (traffic lights) controlled by a phase shift. There are two lanes for the counter traffic flow: the first lane is for east-bound vehicles and the second lane is for west-bound vehicles. The green-wave strategy is studied in the counter traffic flow where the phase shift of signals in the second lane has opposite sign to that in the first lane. A nonlinear dynamic model of the vehicular motion is presented by nonlinear maps at a low density. There is a distinct difference between the traffic flow in the first lane and that in the second lane. The counter traffic flow exhibits very complex behavior on varying the cycle time, the phase difference, and the split. Also, the fundamental diagram is derived by the use of the cellular automaton (CA) model. The dependence of east-bound and west-bound vehicles on cycle time, phase difference, and density is clarified.     

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 irregularity on vehicular traffic through a sequence of traffic lights

We present the stochastic nonlinear-map model of vehicular traffic controlled by irregular signals. The signal’s interval, the split of signal, and the offset time changes irregularly from signal to signal on a roadway. We study the effect of irregularity on dynamical behavior of vehicular traffic through a sequence of traffic lights. The vehicle exhibits the very complex behavior with varying cycle time. When the strength of irregularity is small, the arrival time does not change with irregularity for some values of cycle time, while it changes for other values of cycle time. The region in which the arrival time changes is expanding with increasing irregularity’s strength. The region map (phase diagram) is shown in the cycle time-irregularity’s strength space.     

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.     

交通灯控制下主干道的交通流研究

用元胞自动机模型模拟二维交通流.通过交叉口设置的红绿灯，研究交通激波的形成和传播 ；对于一定的红绿灯周期，交通流量出现多个极值现象；在交叉口间隔相同的情况下，对于 一定的红绿灯周期，在一定的车辆密度范围内，交通流量是一个与密度无关的常量；在车辆 密度较高的情况下，交叉口间距大于某一值后，交通流量保持恒定值. 关键词： 元胞自动机模型 交通流 交通激波     

Vehicular traffic through a self-similar sequence of traffic lights

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time T_s. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x)-x)∝x^d_f, where d_f is the fractal dimension of Cantor set. The landscape in the plot of T(x)−x against cycle time T_s shows a self-affine fractal with roughness exponent α=1−d_f.     

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.     

Optimization of green-times at an isolated urban crossroads

We propose a model for the intersection of two urban streets. The traffic status of the crossroads is controlled by a set of traffic lights which periodically switch to red and green with a total period of T. Two different types of crossroads are discussed. The first one describes the intersection of two one-way streets, while the second type models the intersection of a two-way street with an one-way street. We assume that the vehicles approach the crossroads with constant rates in time which are taken as the model parameters. We optimize the traffic flow at the crossroads by minimizing the total waiting time of the vehicles per cycle of the traffic light. This leads to the determination of the optimum green-time allocated to each phase. Received 19 October 2000 and Received in final form 25 May 2001     

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.     

Computer simulation model for the prediction of traffic noise levels

This paper describes a computer simulation model capable of predicting the noise levels generated by traffic passing through road intersections controlled by roundabouts where departures from free-flow traffic conditions occur. The model depends for its operation on the acoustical and flow characteristics of single vehicles travelling on a road from which the overall noise generated by traffic streams can be deduced using a sampling/integration technique. Distance effects, ground cover, vehicle type, velocity and headway characteristics, etc. are taken into account in the model and the simplest possible input parameters are used deliberately to facilitate the eventual use of the model by highway and planning authorities. Good agreement has been achieved between measured and predicted L₁₀ values for freely flowing traffic negotiating roundabouts. Further applications of the model involving road intersections controlled by traffic lights and the effect of traffic queues are nearing completion.     

Berechnung der häufigkeitsverteilung für vom strassenverkehr emittierte geräusche

A method of calculating the level distribution of noise emitted by road traffic is described which considers the different maximum levels of passing vehicles as well as the mutual temporal distances between vehicles (time intervals) using arbitrary distributions of maximum values and time intervals. In this way disturbances of the traffic flow, e.g. such as those caused by traffic lights, can be taken into account. Concerning the velocity of vehicles, the only limitation is that a characteristic performance has to be determined during the observation time but not a constant velocity of the vehicle group under consideration. There are no restrictions with respect to road conditions (length, surface, gradient) or to the type of buildings along the road. Comparisons between measured and calculated level distributions have so far revealed differences of less than ± 1·5 dB(A) of the percentage levels.     

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.     

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.     

Aspects of highway design and traffic management

This paper is concerned with the part that the design of the highway and the management of the traffic on it can play in noise problems. The noise characteristics of individual vehicles and of traffic are summarized in the Appendixes. Attention is confined to vehicles with conventional petrol and diesel engines and to noise outside the vehicles. Alternative methods of reducing traffic noise are compared and their effects on other aspects of the highway and the traffic are considered. The conclusion is drawn that there are two alternative approaches to noise reduction. One is to reduce traffic flow and the other is to make use of noise barriers and environmental design. The relative importance of these two approaches depends on the type of road under consideration.     

Traffic dispersion induced by noise in off-lattice model

We study the dispersion of vehicles induced by speed fluctuation on a single-lane highway under open boundary. We extend the cellular automaton model on one-dimensional lattice to the real-variable model on off-lattice (continuous-in space model) in order to take into account the fluctuation of vehicular speed. Vehicles extend over the highway when moving forward. The characteristics of traffic dispersion are derived. It is shown that vehicular traffic exhibits scaling property. When a vehicle accelerates for following the vehicle ahead, vehicles move forming a cluster without dispersion. The relationship between the width of vehicular cluster and acceleration rate is clarified.     

Traffic flow on a toll highway with electronic and traditional tollgates

We study the traffic states and jams occurring in traffic flow on a two-lane toll highway with electronic and manual (traditional) tollgates. The electronic and manual collection vehicles sort themselves into their respective lanes at low density, while they mix at each tollgate at high density. We derive the fundamental diagrams (flow-density diagrams) for the electronic and manual collection vehicles. The traffic states change with increasing density and varying the ratio. Dynamical phase transitions occur. It is shown that the fundamental diagrams for the two tollgates depend greatly on the density and fraction of both vehicles.