Phase diagram of congested traffic flow: An empirical study

Characteristics of vehicular traffic flow at a roundabout

We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated and the delay experienced by the traffic at each individual street is evaluated. We discuss the impact of the geometrical properties of the roundabout on the total delay. We compare our results with traffic-light signalization schemes, and obtain the critical traffic volume over which the intersection is optimally controlled through traffic-light signalization schemes.

Generalized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process

We consider the discrete-time evolution of a finite number of particles obeying the totally asymmetric exclusion process with backward-ordered update on an infinite chain. Our first result is a determinant expression for the conditional probability of finding the particles at given initial and final positions, provided that they start and finish simultaneously. The expression has the same form as the one obtained by J. Stat. Phys. 88, 427 (1997)] for the continuous-time process. Next we prove that under some sufficient conditions the determinant expression can be generalized to the case when the particles start and finish at their own times. The latter result is used to solve a nonstationary zero-range process on a finite chain with open boundaries.

Steady-state solutions of hydrodynamic traffic models

We investigate steady-state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady-state solutions. The seven solutions include those that have been reported previously only for microscopic models. The characteristic properties of wide jam such as moving velocity of its spatiotemporal pattern and/or out-flux from wide jam are shown to be uniquely determined and thus independent of initial conditions of dynamic evolution. Topological considerations suggest that all of the solutions should be common to a wide class of traffic models. The results are discussed in connection with the universality conjecture for traffic models. Also the prevalence of the limit-cycle solution in a recent study of a microscopic model is explained in this approach.

Microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks

A microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks due to on-ramps, merge bottlenecks (a reduction of highway lanes), and off-ramps is presented. The basic postulate of three-phase traffic theory is used, which claims that homogeneous (in space and time) model solutions (steady states) of synchronized flow cover a two dimensional region in the flow-density plane [B. S. Kerner, Phys. Rev. Lett. 81, 3797 (1998); Trans. Res. Rec. 1678, 160 (1999)]. Phase transitions leading to diverse congested patterns, pattern evolution, and pattern nonlinear features have been found. Diagrams of congested patterns, i.e., regions of the pattern emergence dependent on traffic demand, have been derived. Diverse effects of metastability with respect to the pattern formation have been found. The microscopic theory allows us to explain the main empirical pattern features at on-ramps and off-ramps which have recently been found [B. S. Kerner, Phys. Rev. E 65, 046138 (2002)]. (i) Rather than moving jams, synchronized flow first occurs at bottlenecks if the flow rate is slowly increasing. Wide moving jams can spontaneously occur only in synchronized flow. (ii) General patterns (GP) and synchronized flow patterns (SP) can spontaneously emerge at the bottlenecks. There can be the widening SP (WSP), the moving SP (MSP), and the localized SP. (iii) At on-ramps cases of "weak" and "strong" congestion should be distinguished. In contrast to weak congestion, under strong congestion the flow rate in synchronized flow in GP reaches a limit flow rate, the frequency of the moving jam emergence reaches a maximum, i.e., the GP characteristics under strong congestion do not depend on traffic demand. (iv) At the off-ramp GP with weak congestion occur. (v) A study of the pattern formation on a highway with two bottlenecks shows that diverse expanded patterns can occur, which cover both bottlenecks. SP first emerged at the downstream bottleneck can be caught at the upstream bottleneck (the catch effect). MSP, WSP, or wide moving jams first emerged at the downstream bottleneck induce diverse patterns at the upstream bottleneck. The onset of congestion at the upstream bottleneck can lead to an intensification of congestion at the downstream bottleneck. This causes a change in the pattern type and/or the pattern features.

Cellular automata model simulating traffic interactions between on-ramp and main road

In this paper, we study the on-ramp system using the cellular automata traffic flow model. Different from previous works, we consider not only the influence of the on-ramp flow on the main road but also the opposite influence. The update rules are given in detail and the concept of priority is introduced. The numerical simulations are carried out and the phase diagram is presented. Two different types of phase diagram are distinguished and the currents of the on-ramp system are discussed.

Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model

The present paper proposes an interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypothesis about the existence of a multitude of metastable states in the fundamental diagram. Using single-vehicle data collected at the German highway A1, temporal velocity patterns have been analyzed to show a collection of certain fragments with approximately constant velocities and sharp jumps between them. The particular velocity values in these fragments vary in a wide range. In contrast, the flow rate is more or less constant because its fluctuations are mainly due to the discreteness of traffic flow. Subsequently, we develop a model for synchronized traffic that can explain these characteristics. Following previous work [I. A. Lubashevsky and R. Mahnke, Phys. Rev. E 62, 6082 (2000)] the vehicle flow is specified by car density, mean velocity, and additional order parameters h and a that are due to the many-particle effects of the vehicle interaction. The parameter h describes the multilane correlations in the vehicle motion. Together with the car density it determines directly the mean velocity. The parameter a, in contrast, controls the evolution of h only. The model assumes that a fluctuates randomly around the value corresponding to the car configuration optimal for lane changing. When it deviates from this value the lane change is depressed for all cars forming a local cluster. Since exactly the overtaking maneuvers of these cars cause the order parameter a to vary, the evolution of the car arrangement becomes frozen for a certain time. In other words, the evolution equations form certain dynamical traps responsible for the long-time correlations in the synchronized mode.

Single-vehicle data of highway traffic: microscopic description of traffic phases

We present a detailed analysis of single-vehicle data, which sheds some light on the microscopic interaction of the vehicles. Besides the analysis of free flow and synchronized traffic the data sets especially provide information about wide jams that persist for a long time. The data have been collected at a location far away from ramps and in the absence of speed limits, which allows a comparison with idealized traffic simulations. We also resolve some open questions concerning the time-headway distribution.

Empirical macroscopic features of spatial-temporal traffic patterns at highway bottlenecks

Results of an empirical study of congested patterns measured during 1995-2001 at German highways are presented. Based on this study, various types of congested patterns at on and off ramps have been identified, their macroscopic spatial-temporal features have been derived, and an evolution of those patterns and transformations between different types of the patterns over time has been found out. It has been found that at an isolated bottleneck (a bottleneck that is far enough from other effective bottlenecks) either the general pattern (GP) or the synchronized flow pattern (SP) can be formed. In GP, synchronized flow occurs and wide moving jams spontaneously emerge in that synchronized flow. In SP, no wide moving jams emerge, i.e., SP consists of synchronized flow only. An evolution of GP into SP when the flow rate to the on ramp decreases has been found and investigated. Spatial-temporal features of complex patterns that occur if two or more effective bottlenecks exist on a highway have been found out. In particular, the expanded pattern where synchronized flow covers two or more effective bottlenecks can be formed. It has been found that the spatial-temporal structure of congested patterns possesses predictable, i.e., characteristic, unique, and reproducible features, for example, the most probable types of patterns that are formed at a given bottleneck. According to the empirical investigations the cases of the weak and the strong congestion should be distinguished. In contrast to the weak congestion, the strong congestion possesses the following characteristic features: (i) the flow rate in synchronized flow is self-maintaining near a limit flow rate; (ii) the mean width of the region of synchronized flow in GP does not depend on traffic demand; (iii) there is a correlation between the parameters of synchronized flow and wide moving jams: the higher the flow rate out from a wide moving jam is, the higher is the limit flow rate in the synchronized flow. The strong congestion often occurs in GP whereas the weak congestion is usual for SP. The weak congestion is often observed at off ramps whereas the strong congestion much more often occurs at on ramps. Under the weak congestion diverse transformations between different congested patterns can occur.

Highway on-ramp control

We study the phase transition on a highway induced by the fluctuations of on-ramp flow. The highway traffic is provided by a hydrodynamical model. We analyze the characteristics of perturbations to induce congestion near on ramp. The phase boundary is obtained. A scaling relation is revealed. We also analyze the time evolution of the local density profile. Conventional control mechanisms to regulate the on-ramp flow are examined. A control scheme is proposed to suppress the congestion.

Capacity drop due to the traverse of pedestrians

In this paper, we have proposed a simplified model to describe the traffic flow when there are pedestrians traversing the road. The numerical simulation shows that the capacity of the road decreases in the presence of pedestrians. If the traffic flow rate is small, the traffic flow is basically unaffected even if some pedestrians traverse the road. However, if the flow rate exceeds a critical value, the vehicles cannot pass without delay, and a traffic jam appears. We also discuss simplified conditions of the model and accordingly present a modified model, which predicts qualitatively the same results except with a different capacity.

Macroscopic traffic models from microscopic car-following models

We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a momentum equation, and the latter contains a relaxation term, an anticipation term, and a diffusion term. Properties of the resulting macroscopic model are compared with those of the optimal velocity model through numerical simulations, and reasonable agreement is found although there are deviations in the quantitative level. The derivation is also extended to general car-following models.

Standing localized cluster in a continuum traffic model

We study the emergence of standing localized cluster in a continuum traffic model. The local-density profile, local velocity profile, and the phase boundary are obtained. The effect of the on ramp is discussed. The indication of the boundary induced phase transition is also discussed.