Class-Specific Variable Speed Limit for Traffic Flow Optimization on Road Networks

This paper presents a novel approach to traffic management in road networks, consisting in time-varying class-specific variable speed limit (VSL) restricted to a fraction of road users. In particular, we present a macroscopic approach where traffic dynamics is described by a multi-class Lighthill-Whitham-Richards (LWR) model, with two classes of users (controlled and uncontrolled vehicles). The model can be applied to a general road network and our goal is to optimize traffic performance by minimizing both the average travel time in the network and the total time spent in virtual buffers at the network entries to prevent spill-back scenarios. The optimization is performed by acting on different ratios of controlled vehicles, and we compare the performance of the proposed control strategy with a classical inflow control at the entries of the network. The numerical tests show that class-specific speed control outperforms inflow control, and highlight the importance of tailored traffic control strategies for road networks, offering insights into optimizing mobility, safety, and traffic efficiency.