Density waves in traffic flow

An improved microscopic traffic model for heterogeneous vehicles using the vehicle's mass effect

This study aims to develop a traffic model for heterogeneous vehicle movement, which introduces the vehicle's heterogeneity by considering the internal mass effect. We explore the behavioral characteristics of the flow field generated by the proposed model and provide a comparative analysis of the conventional model. A linear stability condition is deduced to showcase the model's capacity to neutralize flow. Nonlinear analysis is employed to derive the modified Korteweg-de Vries (mKdV) equation and its corresponding analytical solution, enabling the observation of traffic flow behavior in proximity to the neutral stability condition. A numerical simulation is then conducted, considering cyclic boundary conditions. The results indicate that the mass effect tends to absorb traffic jams provided no time delay is imposed.

Effect of individual differences on the jamming transition in traffic flow

The individual difference, particularly in drivers' distance perception, is introduced in the microscopic one-dimensional optimal velocity model to investigate its effect on the onset of the jamming instability seen in traffic systems. We show analytically and numerically that the individual difference helps to inhibit the traffic jam at high vehicle densities while it promotes jamming transition at low vehicle densities. In addition, the jamming mechanism is further investigated by tracking how the spatial disturbance travels through traffics. We find that the jamming instability is uniquely determined by the overall distribution of drivers' distance perception rather than the spatial ordering of vehicles. Finally, a generalized form of the optimal velocity function is considered to show the universality of the effect of the individual difference.

Street map analysis with excitable chemical medium

Belousov-Zhabotinsky (BZ) thin layer solution is a fruitful substrate for designing unconventional computing devices. A range of logical circuits, wet electronic devices, and neuromorphic prototypes have been constructed. Information processing in BZ computing devices is based on interaction of oxidation (excitation) wave fronts. Dynamics of the wave fronts propagation is programed by geometrical constraints and interaction of colliding wave fronts is tuned by illumination. We apply the principles of BZ computing to explore a geometry of street networks. We use two-variable Oregonator equations, the most widely accepted and verified in laboratory experiments BZ models, to study propagation of excitation wave fronts for a range of excitability parameters, with gradual transition from excitable to subexcitable to nonexcitable. We demonstrate a pruning strategy adopted by the medium with decreasing excitability when wider and ballistically appropriate streets are selected. We explain mechanics of streets selection and pruning. The results of the paper will be used in future studies of studying dynamics of cities and characterizing geometry of street networks.

Cluster statistics and quasisoliton dynamics in microscopic optimal-velocity models

Using the non-linear optimal velocity models as an example, we show that there exists an emergent intrinsic scale that characterizes the interaction strength between multiple clusters appearing in the solutions of such models. The interaction characterizes the dynamics of the localized quasisoliton structures given by the time derivative of the headways, and the intrinsic scale is analogous to the "charge" of the quasisolitons, leading to non-trivial cluster statistics from the random perturbations to the initial steady states of uniform headways. The cluster statistics depend both on the quasisoliton charge and the density of the traffic. The intrinsic scale is also related to an emergent quantity that gives the extremum headways in the cluster formation, as well as the coexistence curve separating the absolute stable phase from the metastable phase. The relationship is qualitatively universal for general optimal velocity models.

Classification and unification of the microscopic deterministic traffic models

We identify a universal mathematical structure in microscopic deterministic traffic models (with identical drivers), and thus we show that all such existing models in the literature, including both the two-phase and three-phase models, can be understood as special cases of a master model by expansion around a set of well-defined ground states. This allows any two traffic models to be properly compared and identified. The three-phase models are characterized by the vanishing of leading orders of expansion within a certain density range, and as an example the popular intelligent driver model is shown to be equivalent to a generalized optimal velocity (OV) model. We also explore the diverse solutions of the generalized OV model that can be important both for understanding human driving behaviors and algorithms for autonomous driverless vehicles.

Collision-free nonuniform dynamics within continuous optimal velocity models

Optimal velocity (OV) car-following models give with few parameters stable stop-and -go waves propagating like in empirical data. Unfortunately, classical OV models locally oscillate with vehicles colliding and moving backward. In order to solve this problem, the models have to be completed with additional parameters. This leads to an increase of the complexity. In this paper, a new OV model with no additional parameters is defined. For any value of the inputs, the model is intrinsically asymmetric and collision-free. This is achieved by using a first-order ordinary model with two predecessors in interaction, instead of the usual inertial delayed first-order or second-order models coupled with the predecessor. The model has stable uniform solutions as well as various stable stop-and -go patterns with bimodal distribution of the speed. As observable in real data, the modal speed values in congested states are not restricted to the free flow speed and zero. They depend on the form of the OV function. Properties of linear, concave, convex, or sigmoid speed functions are explored with no limitation due to collisions.

Solitons and kinks in a general car-following model

We study a general car-following model of traffic flow on an infinitely long single-lane road, which assumes that a car's acceleration depends on time-delayed values of its own speed, the headway between it and the car ahead, and the rate of change of headway, but makes minimal assumptions about the functional form of that dependence. We present a detailed characterization of the onset of linear instability; in particular we find a specific limit on the delay time below which the marginal wave number at the onset of instability is zero, and another specific limit on the delay time above which steady flow is always unstable. Crucially, the threshold of absolute stability generally does not coincide with an inflection point of the steady-state velocity function. When the marginal perturbation at onset has wave number 0, we show that Burgers and Korteweg-de Vries (KdV) equations can be derived under the usual assumptions, and that corrections to the KdV equation "select" a single member of the one-parameter set of its one-soliton solutions by driving a slow evolution of the soliton parameter. While in previous models this selected soliton has always marked the threshold of a finite-amplitude instability of linearly stable steady flow, we find that it can alternatively be a stable, small-amplitude jam that occurs when steady flow is linearly unstable. The model reduces to the usual modified Korteweg-de Vries (mKdV) equation only in the special situation that the threshold of absolute stability coincides with an inflection point of the steady-state velocity function; in general, near the threshold of absolute stability the model reduces instead to a KdV equation in the regime of small solitons, while near an inflection point it reduces to a Hayakawa-Nakanishi equation. Like the mKdV equation, the Hayakawa-Nakanishi equation admits a continuous family of kink solutions, and the selection criterion arising from the corrections to this equation can be written down explicitly.

Intron delays and transcriptional timing during development

The time taken to transcribe most metazoan genes is significant because of the substantial length of introns. Developmentally regulated gene networks, where timing and dynamic patterns of expression are critical, may be particularly sensitive to intron delays. We revisit and comment on a perspective last presented by Thummel 16 years ago: transcriptional delays may contribute to timing mechanisms during development. We discuss the presence of intron delays in genetic networks. We consider how delays can impact particular moments during development, which mechanistic attributes of transcription can influence them, how they can be modeled, and how they can be studied using recent technological advances as well as classical genetics.

Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application

An extended car following model is proposed by incorporating an intelligent transportation system in traffic. The stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by applying the reductive perturbation method. The traffic jam could be thus described by the kink-antikink soliton solution for the mKdV equation. From the simulation of space-time evolution of the vehicle headway, it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front, and the analytical result is consonant with the simulation one.

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.

Towards a variational principle for motivated vehicle motion

We deal with the problem of deriving the microscopic equations governing individual car motion based on assumptions about the strategy of driver behavior. We presume the driver behavior to be a result of a certain compromise between the will to move at a speed that is comfortable for him under the surrounding external conditions, comprising the physical state of the road, the weather conditions, etc., and the necessity to keep a safe headway distance between the cars in front of him. Such a strategy implies that a driver can compare the possible ways of further motion and so choose the best one. To describe the driver preferences, we introduce the priority functional whose extremals specify the driver choice. For simplicity we consider a single-lane road. In this case solving the corresponding equations for the extremals we find the relationship between the current acceleration, velocity, and position of the car. As a special case we get a certain generalization of the optimal velocity model similar to the "intelligent driver model" proposed by Treiber and Helbing.

Noise-assisted traffic of spikes through neuronal junctions

The presence of noise, i.e., random fluctuations, in the nervous system raises at least two different questions. First, is there a constructive role noise can play for signal transmission in a neuron channel? Second, what is the advantage of the power spectra observed for the neuron activity to be shaped like 1/f(k)? To address these questions a simple stochastic model for a junction in neural spike traffic channels is presented. Side channel traffic enters main channel traffic depending on the spike rate of the latter one. The main channel traffic itself is triggered by various noise processes such as Poissonian noise or the zero crossings of Gaussian 1/f(k) noise whereas the variation of the exponent k gives rise to a maximum of the overall traffic efficiency. It is shown that the colored noise is superior to the Poissonian and, in certain cases, to deterministic, periodically ordered traffic. Further, if this periodicity itself is modulated by Gaussian noise with different spectral exponents k, then such modulation can lead to noise-assisted traffic as well. The model presented can also be used to consider car traffic at a junction between a main and a side road and to show how randomness can enhance the traffic efficiency in a network. (c) 2001 American Institute of Physics.

Traveling waves in an optimal velocity model of freeway traffic

Car-following models provide both a tool to describe traffic flow and algorithms for autonomous cruise control systems. Recently developed optimal velocity models contain a relaxation term that assigns a desirable speed to each headway and a response time over which drivers adjust to optimal velocity conditions. These models predict traffic breakdown phenomena analogous to real traffic instabilities. In order to deepen our understanding of these models, in this paper, we examine the transition from a linear stable stream of cars of one headway into a linear stable stream of a second headway. Numerical results of the governing equations identify a range of transition phenomena, including monotonic and oscillating travelling waves and a time- dependent dispersive adjustment wave. However, for certain conditions, we find that the adjustment takes the form of a nonlinear traveling wave from the upstream headway to a third, intermediate headway, followed by either another traveling wave or a dispersive wave further downstream matching the downstream headway. This intermediate value of the headway is selected such that the nonlinear traveling wave is the fastest stable traveling wave which is observed to develop in the numerical calculations. The development of these nonlinear waves, connecting linear stable flows of two different headways, is somewhat reminiscent of stop-start waves in congested flow on freeways. The different types of adjustments are classified in a phase diagram depending on the upstream and downstream headway and the response time of the model. The results have profound consequences for autonomous cruise control systems. For an autocade of both identical and different vehicles, the control system itself may trigger formations of nonlinear, steep wave transitions. Further information is available [Y. Sugiyama, Traffic and Granular Flow (World Scientific, Singapore, 1995), p. 137].