On the coupling of steady and adaptive velocity grids in vehicular traffic modelling

Abstract

This work deals with the derivation and the analysis of a new mathematical model for vehicular traffic along a one-way road obtained by the coupling of a uniform and an adaptive discretization of the velocity variable in the frameworks of the kinetic theory. Interactions are modelled by stochastic games where the output of interactions depends on the local density and is not linearly additive

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

“…The KTAP has been actively used for modeling phenomena not only in physics (see e.g., Reference [39,40]) but also in many other areas of applied and life sciences, for example in the political [41], economic and social [42][43][44][45][46][47] systems, psychological interactions [48], the dynamics of crowds [49][50][51][52][53][54] and swarms [55][56][57][58][59][60][61], traffic flow [62][63][64][65][66][67][68] and so forth.…”

Study on the influence of one-way street optimization design on traffic operation system

“…Therefore, game theory is also used in the study of one-way street. Bianca and Coscia 17 dealt with the derivation and the analysis of a new mathematical model, modeled by stochastic games, for vehicular traffic along a one-way road obtained by the coupling of a uniform and an adaptive discretization. Zhang 18 used Braess’ paradox and road traffic ability to evaluate the impact of the opening of the urban microcirculation system on the surrounding roads in residential areas.…”

“…The traditional solution method has the characteristics of convenient and fast calculation, but the accuracy of the result is often limited, and the more precise calculation results push us to improve the traditional solution method. 17 In addition, considering the preciseness of the method, we should apply the model to the real street network to verify the improvement effect of the solution.…”

Modeling Complex Systems with Particles Refuge by Thermostatted Kinetic Theory Methods

“…Indeed the environmental action or external agents can affect the whole dynamics and abrupt changes can occur; for example, the behavior pattern carried out by animal swarms can be disturbed by the attack of a predator; tumor growth can be controlled and avoided by the action of an external vaccine at the cellular scale. The interested reader in a deeper understanding of these topics is referred to papers [5][6][7][8][9][10][11][12][13][14][15] and the references cited therein.…”