Globally optimal solutions to the on-ramp metering problem - Part 1

A mathematical programming approach to the freeway on-ramp metering problem is formulated. The objective function is a linear combination of mainline and on-ramp flows, termed the generalized total travel time. The underlying freeway model - the asymmetric cell transmission model (ACTM) - is similar to the original cell transmission model (CTM), except that the merge law of the CTM has been replaced with additional terms weighted by the influence parameters. It is shown that an appropriate selection of the model parameters and boundary conditions guarantees a physically reasonable evolution of the ACTM. It is also shown that the resulting nonlinear optimization problem can be solved globally, by solving an equivalent linear program, whenever the cost weights are generated by a proposed numerical algorithm.