document: Modeling self-consistent multi-class dynamic traffic flow In this study , we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model . The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model . The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes , especially motorcyclists . The dispersion model , which is a nonlinear Poisson equation , is derived from the car-following theory and the equilibrium assumption . Under the concept that all kinds of users share the finite section , the density is distributed on a road by the dispersion model . In addition , the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation . Multiplying Boltzmann equation by the zeroth , first - and second-order moment functions , integrating both side of the equation and using chain rules , we can derive continuity , motion and variance equation , respectively . However , the second-order moment function , which is the square of the individual velocity , is employed by previous researches does not have physical meaning in traffic flow
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