Formation Of Traffic Jams Research Articles

HMI: Pre-warning Index of Traffic Jam Formation on Urban Freeway

In this paper, referring to the concepts of qualitative reasoning, the concepts, such as homogeneous measure index (HMI), are utilized to calculate the cross-lane synchronized degree of the traffic flow. The actual data of Beijing Third Ring Road are collected to describe the procedure of formation of traffic jam, and the concepts proposed in this paper are used to clearly illustrate such procedure. From the empirical data of traffic flow, we find out that for a multi-lane road, before the formation of traffic jam, the HMI of the traffic flow will change abruptly and the state transition from homogeneous (H-S) to non-homogeneous state (N-S) is likely occur. Therefore, the HMI can be considered as a pre-warning index of the formation of traffic jam.

Modeling traffic jams in intracellular transport in axons

Irregularities in intracellular traffic in axons caused by mutations of molecular motors may lead to “traffic jams”, which often result in swelling of axons causing various neurodegenerative diseases. The purpose of this paper is to suggest a model of the formation of traffic jams in axons during molecular-motor-assisted transport of intracellular organelles utilizing transport equations developed in Smith and Simmons [D.A. Smith, R.M. Simmons, Models of motor-assisted transport of intracellular particles, Biophys. J. 80 (2001) 45–68], which describe the motion of intracellular particles under the combined action of diffusion and motor-driven transport. According to this model, large intracellular organelles are transported in the cytoplasm by a combined action of diffusion and motor-driven transport. In an axon, organelles are transported away from the neuron’s body toward the axon’s terminal by kinesin-family molecular motors running on tracks composed by microtubules; old and used components are carried back toward neuron’s body by dynein-family molecular motors. Binding/detachment kinetic processes between the organelles and microtubules are specified by first rate reaction constants; these lead to coupling between the three organelle concentrations.

Granular gas dynamics: how Maxwell's demon rules in a non-equilibrium system

The main characteristic of a granular gas, which makes it fundamentally different from ordinary molecular gases, is its tendency to form clusters, i.e. to spontaneously separate into dense and dilute regions. This can be interpreted as a separation in cold and hot regions, meaning that Maxwell's demon is at work: this demon – notoriously powerless in any system in thermodynamic equilibrium – makes clever use of the non-equilibrium state of affairs that reigns in a granular gas, with on the one hand an external energy source and on the other a continuous loss of energy due to the inelastic particle collisions. We focus on vibrated compartmentalised systems, because these give a particularly clear-cut view of the clustering process and also because they resemble the typical machinery used in industrial applications to sort and transport granular materials. We discuss how the clustering can be exploited to build a Brownian motor, a fountain, a granular clock, and how it gives insight into a related clustering problem of prime importance in modern society, namely the formation of traffic jams.

Modelling and simulation of vehicular traffic jam formation

This paper deals with the modelling and simulation of traffic flow phenomena at the macroscopic level, based on a suitable development of the Aw-Rascle model, [2], and its modification, [4], [5]. An acceleration term and a minimal velocity--dependent safety distance are introduced in the evolution equations. Then, an eulerian computational scheme is introduced to simulate the formation and evolution of jams. The results are compared with those obtained in [4], where a lagrangian computational method was used instead.

A Model for the Formation and Evolution of Traffic Jams

In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynamical behavior of clusters (or traffic jams), defined as intervals where the density limit is reached. An existence result for a generic class of initial data is proved by means of an approximation of the solution by a sequence of clusters. Finally, numerical simulations are produced.

A NEW CELLULAR AUTOMATON MODEL FOR TRAFFIC FLOW WITH DIFFERENT PROBABILITY FOR DRIVERS

Based on the Nagel–Schreckenberg (NaSch) model of traffic flow, a new cellular automaton (CA) traffic model is proposed to simulate microscopic traffic flow. The probability p is a variable which contains a randomly selected term for each individual driver and a density-dependent term which is the same for all drivers. When the rational probability p is obtained, the larger value of maximum flow which is close to the observed data can be reached compared with that obtained from the NaSch model. The fundamental diagram obtained by simulation shows the ability of this modified CA model to capture the essential features of traffic flow, e.g., the spontaneous formation of traffic jams and appearance of the metastable state. These indicate that the presented model is more reasonable and realistic.

Mixed Traffic Flow in Anisotropic Continuum Model

An extended speed gradient model is developed to study the mixed traffic flow of two types of vehicles with different velocities and different lengths. Two new terms, representing the reaction of one type of vehicle to the other, are proposed and built into the dynamic speed evolution equations for fast cars and slow vehicles. With the developed model, the relation between the steady-state behavior of the mixed traffic flow system and two system parameters is analyzed, including the number density ratio R of the fast cars to the total vehicles and the vehicle length ratio α of the slow vehicle to the fast car. The formation and propagation of traffic jams, the dissolution process of the jams, and the local cluster effect of the mixed traffic system are also studied. The simulation results are reasonable and consistent with daily experience.

Zero-range model of traffic flow

A multicluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is directly mapped to the mathematically well-studied zero-range process. Knowledge of the asymptotic behavior of the transition rates for large clusters allows us to apply an established criterion for phase separation in one-dimensional driven systems. The distribution over cluster sizes in our zero-range model is given by a one-step master equation in one dimension. It provides an approximate mean-field dynamics, which, however, leads to the exact stationary state. Based on this equation, we have calculated the critical density at which phase separation takes place. We have shown that within a certain range of densities above the critical value a metastable homogeneous state exists before coarsening sets in. Within this approach we have estimated the critical cluster size and the mean nucleation time for a condensate in a large system. The metastablity in the zero-range process is reflected in a metastable branch of the fundamental flux-density diagram of traffic flow. Our work thus provides a possible analytical description of traffic jam formation as well as important insight into condensation in the zero-range process.

Extended Speed Gradient Model for Mixed Traffic

The speed gradient (SG) model was extended to a mixture of different types of vehicles. The extended SG model was used to study the steady state of the mixed traffic flow system, the formation of traffic jams at a traffic light switching from green to red, the dissolution of jams at a traffic light switching from red to green, and the local cluster effect of the mixed traffic system. The simulation result are qualitatively consistent with everyday experience.

Microscopic modeling of multi-lane highway traffic flow

We discuss a microscopic model for the study of multi-lane highway traffic flow dynamics. Each car experiences a force resulting from a combination of the desire of the driver to attain a certain velocity, aerodynamic drag, and change of the force due to car–car interactions. The model also includes multi-lane simulation capability and the ability to add and remove obstructions. We implement the model via a Java applet, which is used to simulate traffic jam formation, the effect of bottlenecks on traffic flow, and the existence of light, medium, and heavy traffic flow. The simulations also provide insight into how the properties of individual cars result in macroscopic behavior. Because the investigation of emergent characteristics is so common in physics, the study of traffic in this manner sheds new light on how the micro-to-macro transition works in general.

Density waves in traffic flow of two kinds of vehicles.

Through the car-following model, the traffic flow of two types of vehicles (cars and trucks) on a single-lane flow is studied, in which drivers on different vehicles have different sensitivities and the safety distance is assumed to be the same for all vehicles. The linear analysis is carried out to determine the condition of critical stability. With the nonlinear analysis, it proves that the small fluctuation of the vehicle density near the critical stable state satisfies the Korteweg-deVries equation and different sensitivities affect only the soliton evolution. When the headway in the critical state is more than the safety distance, the density around the soliton peak exceeds the density of the critical stable state, which can be explained as the formation of traffic jam. Contrarily, when the headway state is less than the safety distance, drivers will increase the headway to avoid the jam. The direct approach of the soliton perturbation shows that drivers' sensitivity will increase the soliton's amplitude continuously. Moreover, the increase of the number of trucks in the traffic flow will slow down the evolution of the amplitude.

Effect of obstacles on formation of traffic jam in a two-dimensional traffic network

We investigate the effect of obstacles on formation of a traffic jam for a traffic flow in a network of city roads. We consider a square lattice of two bonds between two nearest crossings as a network of city roads; we assume that there are three lattice sites in a crossing. We put five decorated sites on each bond between two nearest crossings. A car or an obstacle is assumed to be located on one of these decorated sites or one of the lattice sites. We assume only two types of cars; namely one type of cars move mainly in the positive x direction and change their direction to the positive y direction with a probability and the other type of cars move mainly in the positive y direction and change their direction to the positive x direction with the same probability. One of two lanes is assumed to be used mainly for passing the obstacles or jamming other cars. We set rules for car moving in order to make our traffic-flow model by taking into account all the possible situations. By using numerical simulations, we find that a phase transition from a free-moving phase to a traffic-jam phase is formed more easily for obstacles placed very close to traffic signals in the traffic direction than for those in the other cases.

Peak-Load Pricing of a Bottleneck with Traffic Jam

This paper generalizes the model of bottleneck congestion such that formation and development of traffic jams is explicitly formulated. The model is applied to the peak-load problem for the morning rush hour: every morning, a fixed number of commuters travel across a roadway, and each of them chooses departure time to minimize commuting cost consisting of travel time cost, scheduling cost, and toll. Equilibrium and optimal patterns of departure are solved and optimal peak-load toll is derived. Incorporating traffic jams alters the earlier results in the literature. That is, road users may be better off from paying the optimal peak-load toll. Conditions under which such a result is obtained are identified by simulations.

Noise Induced Congested Traffic Flow in Coupled Map Optimal Velocity Model

The optimal velocity traffic flow model is one of the car-following models which describe the behavior of cars by differential equations. In that model, each car controls its speed toward an optimal (safety) velocity, which depends only on the headway. We constructed a new car-following type simulation model for traffic flow in a coupled map form based on the optimal velocity model. We can easily simulate open road systems with the model. The emergence of weakly congested flow induced by noise is investigated. We observe the enhancement of the car density induced by noise. The strong traffic jam hardly occurs in open road systems. We discuss the problems of unrealistic acceleration in the optimal velocity model and the possibility of spontaneous formation of strong traffic jams.

Dynamic states of a continuum traffic equation with on-ramp.

We study the phase diagram of the continuum traffic flow model of a highway with an on-ramp. Using an open boundary condition, traffic states and metastabilities are investigated numerically for several representative values of the upstream boundary flux f(up) and for the whole range of the on-ramp flux f(rmp). An inhomogeneous but time-independent traffic state (standing localized cluster state) is found and related to a recently measured traffic state. Due to the density gradient near the on-ramp, a traffic jam can occur even when the downstream density is below the critical density of the usual traffic jam formation in homogeneous highways, and its structure varies qualitatively with f(rmp). The free flow, the recurring hump (RH) state, and the traffic jam can all coexist in a certain metastable region where the free flow can undergo phase transitions either to the RH state or to the traffic jam state. We also find two nontrivial analytic solutions. These solutions correspond to the standing localized cluster state and the homogeneous congested traffic state (one form of the traffic jam), which are observed in numerical simulations.

Diagnosis and treatment of congestion in central urban areas

The development and dispersal of area-wide traffic jams is a matter of considerable social concern. Work at Middlesex University, supported by EPSRC, has enabled the construction of a simulation model with greater geographical scope than most conventional congestion simulation models. Our simulation concentrates on a holistic view of traffic jam formation in a setting of isotropic flow. In the model, traffic incidents can effectively be introduced anywhere in the network. The growth of traffic jams can be observed using a graphical display and options are included to disperse and control the formation of traffic queues. Simulation results have confirmed that the uncontrolled growth of the traffic jam is both rapid and potentially irreversible. Experiments with dispersing the traffic jam have given greater insight to the ‘gridlock’ phenomena. We suggest a number of possible, practical counter-measures, which would both inhibit the growth process and contribute to the controlled dispersion of queues in congested networks. The effectiveness of the proposed strategies is evaluated via the simulation model and as a result, we provide a coherent set of remedies which would assist in the diagnosis and treatment of central urban congestion problems.

Speed Limit Effects on the Multilane Traffic Flow Through a Bottleneck

The presented macroscopic simulation of the traffic flow on a multilane test stretch with a bottleneck displays the significant effects of a speed limit reduction inside the bottleneck region on the formation and propagation of traffic jams. By comparison of different scenarios it is demonstrated, that it is possible to avoid traffic jams for a given amount of traffic volume. If this amount is exceeded, the formation of a traffic jam can at least be delayed.

Traffic Jam and Shock Formation in Stochastic Traffic-Flow Model of a Two-Lane Roadway

We present a stochastic cellular automaton (CA) model to simulate the traffic jam induced by a car accident in the traffic flow of a two-lane roadway. The CA model is an extended version of the one-dimensional asymmetric exclusion model to take into account the stochastic exchange of cars between the first and second lanes. We study the traffic flow of the system when the translation invariance is broken by the insertion of a blockage which is induced by a car accident on the first lane. Using the computer simulation, it is found that the dynamical jamming transions occur successively from the phase 1, through the phase 2, to the phase 3 with increasing the density of cars. The phase 1 is characterized by the property such that no cars exist in the first lane and the cars on the second lane move with the maximal velocity. The phase 2 is characterized by the shock formation (a discontinuity of density) and the maximal current. In the phase 3, the discontinuity disappears and the traffic flow is not affecte...