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We consider Ramp Metering (RM) at the microscopic level subject to vehiclefollowing safety constraints for a freeway with arbitrary number of on- andoff-ramps. The arrival times of vehicles to the on-ramps, as well as theirdestinations are modeled by exogenous stochastic processes. Once a vehicle isreleased from an on-ramp, it accelerates towards the free flow speed if it isnot obstructed by another vehicle; once it gets close to another vehicle, itadopts a safe gap vehicle following behavior. The vehicle exits the freewayonce it reaches its destination off-ramp. We design traffic-responsive RMpolicies that maximize the throughput. For a given routing matrix, thethroughput of a RM policy is characterized by the set of on-ramp arrival ratesfor which the expected queue size at all the on-ramps remain bounded. Theproposed RM policies work in synchronous cycles during which an on-ramp doesnot release more vehicles than its queue size at the beginning of the cycle.Moreover, all the policies operate under vehicle following safety constraints,where new vehicles are released only if there is sufficient gap betweenvehicles on the mainline at the moment of release. We provide three mechanismsunder which each on-ramp: (i) pauses release for a time interval at the end ofa cycle, or (ii) adjusts the release rate during a cycle, or (iii) adopts aconservative safe gap criterion for release during a cycle. All the proposedpolicies are reactive, meaning that they only require real-time trafficmeasurements without the need for demand prediction. The throughput of thesepolicies is characterized by studying stochastic stability of the inducedMarkov chains, and is proven to be maximized when the merging speed at all theon-ramps equals the free flow speed. Simulations are provided to illustrate theperformance of our policies and compare with a well-known RM policy from theliterature.

Ramp Metering to Maximize Freeway Throughput under Vehicle Safety Constraints