Equilibrium analysis and comparison for general CTMs and LCTMs

In this paper, we study the equilibriums of the general Cell transmission models (CTM) and the general Lagged Cell transmission models (LCTM). Theoretical analyses show that different CTMs and LCTMs converge to a two-segment almost piecewise-linear equilibrium state with similar shapes, although the variety of the traffic flow-density relationships (fundamental diagram, FD) and the existence of the lagged effect lead to different patterns of convergence trajectories and speeds. These results indicate the usefulness of the CTMs and LTCMs in practice, especially when we are interested on the formations and dissipations of traffic congestions.