## 2 Related Works  
### VSL and LCC Traffic Control Methods  
VSL systems are primarily categorized into open-loop and closed-loop control. Initially, open-loop control was favored for its simple structure and ease of maintenance, as it operates based on feedforward characteristics. For instance, [PERSON] et al. [7] proposed a VSL method using a collision prediction model to evaluate highway collision risks, demonstrating that variable speed limits significantly reduce overall collision probability compared to fixed speed limits. Optimal control is a typical open-loop method designed for dynamic systems. [PERSON] et al. [8] proposed an optimal VSL strategy for connected and automated vehicles using optimal control methods, showing significant improvements in traffic efficiency and emission reductions in simulations. However, due to the lack of feedback in open-loop control, systems are highly susceptible to disturbances and exhibit poor stability. Therefore, many researchers have shifted toward closed-loop control. [PERSON] et al. [9] employed a proportional-integral feedback regulator for highway traffic control, validated with real road data from Germany, showing substantial improvements in performance metrics.  
Model Predictive Control (MPC) methods represent another control category, predicting traffic flow trends to enable preemptive congestion control. [PERSON] et al. [10] first applied MPC to VSL, with subsequent research expanding this approach. New MPC types and hierarchical control methods based on discrete LWR models have been developed and validated in microsimulation environments to effectively mitigate highway congestion waves [11]. [PERSON] et al. [12] introduced a fast MPC method for VSL coordination, addressing highway congestion waves by considering the linear properties of classical discrete first-order models and congestion wave propagation characteristics.  
VSL research in traffic operations focuses on enhancing road traffic efficiency and safety. Studies indicate that VSL can boost traffic efficiency by 10% to 40% [13], especially when optimizing total travel time. However, recent studies on VSL effectiveness present mixed results [14], questioning VSL's impact on traffic efficiency under high-demand conditions. This disparity is attributed to highly disordered and randomly changing traffic flows at congestion bottlenecks.  
To address VSL's limitations in traffic efficiency improvement, research has increasingly integrated VSL with other active control methods. Current studies on ramp control often integrate VSL with Ramp Metering (RM) [15; 16]. While VSL-RM strategies enhance traffic efficiency and safety more than VSL alone, ramp queue lengths can overflow when mainline traffic is heavy.  
With advancements in vehicle-to-everything (V2X) technology and intelligent transportation systems, integrated control of connected vehicles can be achieved through spatial management, combining lane change control. [PERSON] et al. [17] proposed an integrated VSL and LCC method using an MPC framework in heterogeneous multi-lane CTM, optimizing the weighted sum of TTS and TTD in each control cycle. This method maximizes traffic efficiency by determining lane change numbers and speed limits while considering their interactions. [PERSON] et al. [18] applied MTFC as a VSL strategy at lane-drop bottlenecks, treating lane change as a linear quadratic optimal control problem and implementing results every 10 s in an Aimsun microsimulation model.