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Ihor Lubashevsky

Publications and source records attributed to Ihor Lubashevsky.

48 records · Page 3Linked to original sources
arXiv2005

States of Traffic Flow in Deep Lefortovo Tunnel (Moscow): Empirical Data

The paper presents a preliminary analysis of traffic flow data collected in the Lefortovo tunnel located on the 3-rd circular highway of Moscow. It is shown that the observed tunnel congested traffic in fact exhibits cooperative phenomena in vehicle motion, namely, there is a region of widely scatted states on the fundamental diagrams which is related typically to the appearance of synchronized traffic. Besides, the spatial autocorrelations in the occupancy, vehicle velocity, and flow rate measured by different detectors are found to be essential. Especially it concerns the correlations in the velocity and occupancy, their correlation length gets values about 1 km. The phase portrait of the vehicle ensemble dynamics on the occupancy-velocity plane is also studied. It is demonstrated that there are two substantially different region on it. One matches actually the cooperative vehicle motion and contains some kernel where the dynamics is pure chaotic. The other part of the phase plane corresponds to the irreversible stage of jam formation.

physics.soc-ph↗
arXiv2004

Long-lived states of oscillator chain with dynamical traps

A simple model of oscillator chain with dynamical traps and additive white noise is considered. Its dynamics was studied numerically. As demonstrated, when the trap effect is pronounced nonequilibrium phase transitions of a new type arise. Locally they manifest themselves via distortion of the particle arrangement symmetry. Depending on the system parameters the particle arrangement is characterized by the corresponding distributions taking either a bimodal form, or twoscale one, or unimodal onescale form which, however, deviates substantially from the Gaussian distribution. The individual particle velocities exhibit also a number of anomalies, in particular, their distribution can be extremely wide or take a quasi-cusp form. A large number of different cooperative structures and superstructures made of these formations are found in the visualized time patterns. Their evolution is, in some sense, independent of the individual particle dynamics, enabling us to regard them as dynamical phases.

cond-mat.stat-mech↗
arXiv2004

Probabilistic Description of Traffic Breakdowns Caused by On-ramp Flow

The characteristic features of traffic breakdown near on-ramp are analyzed. To describe this phenomenon the probabilistic description regarding the jam emergence as the formation of a large car cluster on highway inside the synchronized traffic is constructed. In these terms the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which is located near the on-ramp. The strong cooperative car interaction in the synchronized traffic enables us to treat the size of critical jam nuclei as a large value and to apply to an effective one-lane model. This model assumes the following. First, the growth of a car cluster is governed by the attachment of cars to the cluster whose rate is mainly specified by the total traffic flow. Second, the cluster dissolution is determined by the car escape from the cluster whose rate depends on the cluster size directly. Third, the generation of one-car clusters (preclusters) is caused by cars entering the main road from the on-ramp. The appropriate master equation for the car cluster evolution is written and the generation rate of critical jam nuclei is found. The obtained results are in agreement with the empirical facts that the characteristic time scale of the breakdown phenomenon is about or greater than one minute and the traffic flow rate interval inside which traffic breakdowns are observed is sufficiently wide. Besides, as a new results, it is shown that the traffic breakdown probability can be analyzed, at least approximately, based solely on the data of the total vehicle flow without separating it into the vehicle streams on the main road and on-ramp when the relative on-ramp flow volume exceeds 10%--20%.

cond-mat.soft↗
arXiv2003

Empirical basis for car-following theory development

By analyzing data from a car-following experiment, it is shown that drivers control their car by a simple scheme. The acceleration $a(t)$ is held approximately constant for a certain time interval, followed by a jump to a new acceleration. These jumps seem to include a deterministic and a random component; the time $T$ between subsequent jumps is random, too. This leads to a dynamic, that never reaches a fixed-point ($a(t) \to 0$ and velocity difference to the car in front $Δv \to 0$) of the car-following dynamics. The existence of such a fixed-point is predicted by most of the existing car-following theories. Nevertheless, the phase-space distribution is clustered strongly at $Δv=0$. Here, the probability distribution in $Δv$ is (for small and medium distances $Δx$ between the cars) described by $p(Δv) \propto \exp(-|Δv|/Δv_0)$ indicating a dynamic that attracts cars to the region with small speed differences. The corresponding distances $Δx$ between the cars vary strongly. This variation might be a possible reason for the much-discussed widely scattered states found in highway traffic.

cond-mat.stat-mech↗
arXiv2003

Towards the fundamentals of car following theory

The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks the outcomes of different driving strategies is constructed, which applies to fairly general properties of the driver behavior. Assuming the driver behavior to be rational, the existence of the Nash equilibrium is proved. Rational driving is defined by supposing that a driver corrects continuously the car motion to follow the optimal path minimizing the cost functional. The corresponding car-following dynamics is described quite generally by a boundary value problem based on the obtained extremal equations. Linearization of these equations around the stationary state results in a generalization of the widely used optimal velocity model. Moreover, it is shown that there are conditions (the ``dense traffic'' limit) under which the rational car dynamics comprises two stages, fast and slow. During the fast stage a driver eliminates the velocity difference between the cars, the subsequent slow stage optimizes the headway. In the ``dense traffic'' limit an effective Hamiltonian description is constructed. This allows a more detailed nonlinear analysis. Finally, the differences between rational and bounded rational driver behavior are discussed. The latter, in particular, justifies some basic assumptions used recently by the authors to construct a car-following model lying beyond the frameworks of rationality.

cond-mat.soft↗
arXiv2003

Noised induced phase transition in an oscillatory system with dynamical traps

A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular forces are depressed substantially. By way of an example, a simple oscillatory system {x,v} with additive white noise is considered and its dynamics is analyzed numerically. The dynamical trap region is assumed to be located near the x-axis where the velocity v of the system becomes sufficiently low. The meaning of this assumption is discussed. The observed phase transition is caused by the asymmetry in the residence time distribution in the vicinity of zero value velocity. This asymmetry is due to a cooperative effect of the random Langevin force in the trap region and the regular force not changing the direction of action when crossing the trap region.

cond-mat.soft↗
arXiv2002

A Bounded Rational Driver Model

This paper introduces a car following model where the driving scheme takes into account the deficiencies of human decision making in a general way. Aditionally, it improves certain shortcomings of most of the models currently in use: it is stochastic but has a continuous acceleration. This is achieved at the cost of formulating the model in terms of the time derivative of the acceleration, making it non-Newtonian.

cond-mat.soft↗
arXiv2002

Long-lived states in synchronized traffic flow. Empirical prompt and dynamical trap model

The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses 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, R.Mahnke, Phys. Rev. E v. 62, p. 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 manoeuvres 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.

cond-mat.soft↗
arXiv2001

Probabilistic Description of Traffic Breakdowns

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply to the probabilistic model regarding the jam emergence as the formation of a large car cluster on highway. In these terms the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, may be, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car escape from the cluster whose rate depends on the cluster size directly. The latter is justified using the available experimental data for the correlation properties of the synchronized mode. We write the appropriate master equation converted then into the Fokker-Plank equation for the cluster distribution function and analyze the formation of the critical car cluster due to the climb over a certain potential barrier. The further cluster growth irreversibly gives rise to the jam formation. Numerical estimates of the obtained characteristics and the experimental data of the traffic breakdown are compared. In particular, we draw a conclusion that the characteristic intrinsic time scale of the breakdown phenomenon should be about one minute and explain the case why the traffic volume interval inside which traffic breakdown is observed is sufficiently wide.

cond-mat.soft↗
arXiv2001

Towards a variational principle for motivated vehicle motion

We deal with the problem of deriving the microscopic equations governing the individual car motion based on the assumptions about the strategy of driver behavior. We suppose 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 his 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.

cond-mat.soft↗
arXiv1998

Two boundary model for freezing front propagation in biological tissue

The response of the living tissue to the effects of strong heating or cooling can cause the blood flow rate to vary by an order of magnitude. A mathematical model for the freezing of living tissue is formulated which takes into account the nonlocal temperature dependence of the blood flow rate when the temperature distribution in the tissue is substantially nonuniform, as in cryosurgery.

patt-sol↗