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This paper studies steady-state traffic flow on a ring road with up- anddown- slopes using a semi-discrete model. By exploiting the relations betweenthe semi-discrete and the continuum models, a steady-state solution is uniquelydetermined for a given total number of vehicles on the ring road. The solutionis exact and always stable with respect to the first-order continuum model,whereas it is a good approximation with respect to the semi-discrete modelprovided that the involved equilibrium constant states are linearly stable. Inan otherwise case, the instability of one or more equilibria could triggerstop-and-go waves propagating in certain road sections or throughout the ringroad. The indicated results are reasonable and thus physically significant fora better understanding of real traffic flow on an inhomogeneous road.

Steady-state traffic flow on a ring road with up- and down- slopes