Arvind Kumar Gupta

A new multi-class continuum model for traffic flow

In this paper, we propose a new continuum model and study some qualitative properties. The new model contains an additional speed gradient term (anisotropic term) in comparison to Bergs model (Berg et al., 2000, Physical Review E, 61, 1056–1066). This anisotropic term guarantees the property that the characteristic speeds can be made less than or equal to the macroscopic flow speed. We extend this model for multi-class traffic flow with heterogeneous drivers. Each user class is characterized by their choice of speeds in a traffic stream. The choice of the speed of a particular user class at any location on the highway is affected by the presence of all user class on that location. Numerical simulations show that the model is able to explain some of the observed traffic phenomena such as platoon dispersion that challenge old homogeneous models presented in the literature.

Analyses of Lattice Traffic Flow Model on a Gradient Highway

The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram. Using nonlinear stability analysis, the Burgers, Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.

Nonlinear analysis of traffic jams in an anisotropic continuum model

This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traffic flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.

Analysis of the wave properties of a new two-lane continuum model with the coupling effect

A multilane extension of the single-lane anisotropic continuum model (GK model) developed by Gupta and Katiyar for traffic flow is discussed with the consideration of the coupling effect between the vehicles of different lanes in the instantaneous traffic situation and the lane-changing effect. The conditions for securing the linear stability of the new model are presented. The shock and the rarefaction waves, the local cluster effect and the phase transition are investigated through simulation experiments with the new model and are found to be consistent with the diverse nonlinear dynamical phenomena observed in a real traffic flow. The analysis also focuses on empirically observed two-lane phenomena, such as lane usage inversion and the density dependence of the number of lane changes. It is shown that single-lane dynamics can be extended to multilane cases without changing the basic properties of the single-lane model. The results show that the new multilane model is capable of explaining some particular traffic phenomena and is in accordance with real traffic flow.

A SECTION APPROACH TO A TRAFFIC FLOW MODEL ON NETWORKS

The development of real time traffic flow models for urban road networks is of paramount importance for the purposes of optimizing and control of traffic flow. Motivated by the modeling of road networks in last decade, this paper proposes a different and simplified approach, known as section approach to model road networks in the framework of macroscopic traffic flow models. For evaluation of the traffic states on a single road, an anisotropic continuum GK-model developed by [Gupta and Katiyar, J. Phys. A 38, 4069 (2005)] is used as a single-section model. This model is applied to a two-section single lane road with points of entry and exits. In place of modeling the effect of off- and on-ramps in the continuity equation, a set of special boundary condition is taken into account to treat the points of entry and exit. A four-section road network comprised of two one-lane roads is also modeled using this methodology. The performances of the section approaches are investigated and obtained results are demonstrated over simulated data for different boundary conditions.

Asymmetric coupling in two-lane simple exclusion processes with Langmuir kinetics: phase diagrams and boundary layers.

We use boundary layer analysis for an open system consisting of two parallel totally asymmetric simple exclusion processes with Langmuir kinetics under a biased lane-changing rule. The two kinds of phase transitions--bulk transitions and surface transitions--have been examined. The dynamics of shock and their dependence on the system parameters have been investigated. We find a reduction in the number of steady-state phases with increase in lane-changing rate.

Stochasticity and bistability in insect outbreak dynamics

There is a long history in ecology of using mathematical models to identify deterministic processes that may lead to dramatic population dynamic patterns like boom-and-bust outbreaks. Stochasticity is also well-known to have a significant influence on the dynamics of many ecological systems, but this aspect has received far less attention. Here, we study a stochastic version of a classic bistable insect outbreak model to reveal the role of stochasticity in generating outbreak dynamics. We find that stochasticity has strong effects on the dynamics and that the stochastic system can behave in ways that are not easily anticipated by its deterministic counterpart. Both the intensity and autocorrelation of the stochastic environment are important. Stochasticity with higher intensity (variability) generally weakens bistability, causing the dynamics to spend more time at a single state rather than jumping between alternative stable states. Which state the population tends toward depends on the noise color. High-intensity white noise causes the insect population to spend more time at low density, potentially reducing the severity or frequency of outbreaks. However, red (positively autocorrelated) noise can make the population spend more time near the high density state, intensifying outbreaks. Under neither type of noise do early warning signals reliably predict impending outbreaks or population crashes.

Two-channel totally asymmetric simple exclusion process with Langmuir kinetics: The role of coupling constant

In this letter, we study the dynamics of a coupled two-channel totally asymmetric simple exclusion process with particle attachment and detachment in the bulk. The coupling constant C, which signifies the ratio of lane-changing rates, is introduced and the steady-state dynamics of the system are analyzed for different values of C. Singular perturbation technique is used on continuum mean-field equations to construct the phase diagrams, which have been characterized in terms of C for all possible orders of lane-changing rates. It is found that for lower orders of lane-changing rates, the effect of C is minor; while the effect is significant for higher orders. A critical value of is identified, above which the disappearance as well as the appearance of certain phases is observed. Moreover, synchronization of shocks also occurs for . We have also analyzed the effect of the system size on the Monte Carlo simulation results. Our theoretical arguments are in good agreement with Monte Carlo simulation results.

Phase diagrams of three-lane asymmetrically coupled exclusion process with Langmuir kinetics

This letter studies a fully asymmetrically coupled three-lane totally asymmetric simple exclusion process with Langmuir kinetics under open boundary conditions. Phase diagrams and density profiles for different kinetic rates are obtained using a mean-field analysis along with a singular perturbation technique and are found to be in good agreement with Monte Carlo simulation results. Some mixed phases are observed in the middle lane resulting into bulk-induced phase transitions. We have found that a number of steady-state phases firstly increases then decreases with respect to an increase in lane changing rate. Critical values of the lane changing rate are identified at which the appearance or disappearance of certain phases is observed. We have identified the jumping effect in the position of shock in the middle lane with respect to an increase in the lane changing rate.

Collective Dynamics on a Two-Lane Asymmetrically Coupled TASEP with Mutually Interactive Langmuir Kinetics

Motivated by the recent experimental observations on clustering of motor proteins on microtubule filament, we study an open system of two parallel totally asymmetric simple exclusion processes under asymmetric coupling conditions, which incorporates the mutual interaction with the surrounding environment through Langmuir Kinetics (LK) in both the lanes. In the modified LK, the attachment and detachment rates depends on the configuration of nearest neighboring sites. We analyse the model within the framework of continuum mean-field theory and the phase diagrams along with density profiles are obtained using boundary layer analysis. The effect of mutual interactions on the phase diagram for two different situations of attachment and detachment (LK) rates is discussed. Under the symmetric LK dynamics, the topological structure of the phase diagram remains similar to the one in without mutual interaction; while for the antisymmetric case, after a certain critical value of attractive/repulsive mutual attraction, significant changes are found in the qualitative nature of phase diagram. Moreover, it is shown that the type of mutual interaction affects the dynamic properties of motor proteins. The theoretical findings are examined by extensive Monte-Carlo simulations.