A study of two onramp metering schemes for congested freeways

We investigate the stability of a nonlinear (piecewise linear and possibly discontinuous) model of a freeway onramp, controlled by two popular onramp metering schemes: alinea and percent-occupancy. The freeway model is based on Daganzo's cell-transmission model and can be understood as a hybrid system switching among several discrete-time linear dynamics equations. It is shown, under conditions placed on the upstream mainline demand and on the controller parameters, that both of these controllers are capable of rejecting congestion near the onramp. In addition, we illustrate how the use of downstream measurements allows alinea to robustly drive the freeway to a predetermined uncongested desired state.