Ramp Metering to Maximize Freeway Throughput under Vehicle Safety Constraints

We consider Ramp Metering (RM) at the microscopic level subject to vehicle following safety constraints for a single freeway with arbitrary number of on- and off-ramps. The arrival times of vehicles to the on-ramps, as well as their destinations are modeled by exogenous stochastic processes. Once a vehicle is released from an on-ramp, it accelerates towards the free flow speed if it is not obstructed by another vehicle; once it gets close to another vehicle, it adopts a safe gap vehicle following behavior. The vehicle exits the freeway once it reaches its destination off-ramp. We design traffic-responsive RM policies that maximize the freeway throughput. For a given routing matrix, the throughput of a RM policy is characterized by the set of on-ramp arrival rates for which the queue sizes at all the on-ramps remain bounded in expectation. The proposed RM policies work in synchronous cycles during which an on-ramp does not 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 enough gap on the mainline at the moment of release. We provide three policies under which each on-ramp: (i) pauses release for a time interval at the end of a cycle, or (ii) modulates the release rate during a cycle, or (iii) adopts a conservative safe gap criterion for release during a cycle. All the proposed policies are reactive, meaning that they only require real-time traffic measurements without the need for demand prediction. The throughput of these policies is characterized by studying stochastic stability of the induced Markov chains, and is proven to be maximized when the merging speed of all the on-ramps equals the free flow speed. Simulations are provided to illustrate the performance of our policies and compare with a well-known RM policy from the literature.