We consider Ramp Metering (RM) at the microscopic level subject to vehicle following safety constraints for a 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 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 expected queue size at all the on-ramps remain bounded. 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 sufficient gap between vehicles on the mainline at the moment of release. We provide three mechanisms under which each on-ramp: (i) pauses release for a time interval at the end of a cycle, or (ii) adjusts 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 at 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.

翻译：我们考虑在微观层面受车辆跟驰安全约束的匝道控制（Ramp Metering, RM）问题，研究对象为具有任意数量入口与出口匝道的高速公路。车辆到达入口匝道的时间及其目的地均由外生随机过程建模。车辆一旦从入口匝道释放，若前方无其他车辆阻挡，则加速至自由流速度；一旦接近前车，则采用安全跟驰间隙模式行驶。车辆到达目标出口匝道后即驶离高速公路。我们设计了响应实时交通状况的RM策略，以最大化通行能力。在给定路由矩阵条件下，RM策略的通行能力由一组入口匝道到达率刻画：在此到达率下，所有入口匝道的期望队列长度保持有界。所提出的RM策略以同步周期运行，每个周期内入口匝道释放的车辆数不超过该周期起始时的队列长度。此外，所有策略均在车辆跟驰安全约束下运行：仅当主线上车辆间存在足够间隙时，才释放新车辆。我们提供了三种机制，使每个入口匝道：(i) 在周期末暂停释放一段时间，或 (ii) 在周期内调整释放率，或 (iii) 在周期内采用保守的安全间隙标准进行车辆释放。所有策略均为反应式，即仅需实时交通测量数据，无需需求预测。通过研究所诱导马尔可夫链的随机稳定性，我们刻画了这些策略的通行能力，并证明当所有入口匝道的汇入速度等于自由流速度时，通行能力达到最大。最后通过仿真验证了所提策略的性能，并与文献中经典RM策略进行了对比。