On optimal freeway ramp control policies for congested trac corridors

This paper examines the conditions for which ramp metering can be bene®cial to the overall system in terms of travel time savings for a simple trac corridor that consists of a freeway and a set of parallel arterials connected by entrance ramps. The focus is on analyzing state and control relationships to arrive at general analytical results regarding optimal metering policies, rather than on either developing speci®c control algorithms or solving a speci®c application. The analysis is concerned with the general behavior of the system under ramp control and trac diversion. The analysis assumes that time-varying trac demands that originate from various locations are destined for a single location and that the freeway is uniformly congested throughout the control period. Under these assumptions, some general results are obtained regarding the e€ectiveness of ramp metering for various trac diversion propensities and di€erentials between freeway and arterial trac conditions. It is shown that the optimal ramp control policies are determined by the magnitudes of two co-state vectors that depend on trac conditions on the freeway and its alternative, and the drivers diversion propensity. The results of two limiting cases imply that when the freeway is uniformly congested ramp control is counter-productive unless diversion occurs, and where drivers have a high propensity to divert, the optimal policy is dependent on the travel speed on the freeway alternative and on the wave speed of backward propagating waves on the freeway.# 1999 Elsevier Science Ltd. All rights reserved.