We study an exclusion process with multiple dynamic roadblocks.Each roadblock can move diffusively forward or backward with different rates,as well as unbind from/rebind to a free site.By Monte Carlo simulations,the two moving types are investigated in combination of roadblock number.The case of only diffusive roadblocks shows an asymmetric current-density relation.The case of only long-range jumping roadblocks presents that flux decreases with increasing roadblock number.
This paper uses the Taylor expansion to seek an approximate Kortewegde Vries equation(KdV) solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.
