# Variable Speed Limit and Ramp Metering for Mixed Traffic Flows: A Review and Open Questions
## 3 Research and Implementation
### VSL in Mixed Traffic Flows
#### 3.4.1 Optimization-Based Methods for VSL  
An integrated VSL and Lane Change (LC) control framework for motorway bottlenecks with mixed traffic flows was proposed in [85]. The Model Predictive Control (MPC)-based framework considers the interaction between VSL and LC to maximize traffic efficiency. An improved multiclass Cell-Transmission Model (CTM) that considers the effects of LC behavior was proposed to predict the traffic state. The Genetic Algorithm (GA)-based method was used to find the optimal values of VSL and LC settings simultaneously. The simulations were performed under three different traffic demand values, 1000 veh/h/2 lanes, 2000 veh/h/2 lanes, and 3000 veh/h/2 lanes with 100% CAV penetration rate. The proposed control method significantly reduced \(TTS\) by 23.86% to 44.62%, outperforming the VSL-only control, which reduced \(TTS\) by 6.43% to 13.84% compared to the no control scenario. The problem of controlling the speed of a number of AVs before entering a speed reduction zone on a motorway was analyzed in [87]. The problem of deriving the optimal acceleration and deceleration of each AV was solved by the proposed optimal control method applying Hamiltonian analysis. The main objective was to minimize the acceleration or deceleration for each vehicle entering the controlled segment until the specified time. By minimizing the acceleration or deceleration of each vehicle, fuel consumption and emissions were reduced. The effectiveness of this approach was evaluated using three different traffic demand levels. It was compared to the no control HDV scenario, VSL algorithm (using shock wave theory proposed in [105]), and a modified vehicular-based SPeeD HARMonization (SPD-HARM) algorithm proposed in [106]. Fuel consumption for each vehicle was reduced by 19% to 22% compared to the no control HDV scenario, by 12% to 17% compared to the VSL algorithm, and by 18% to 34% compared to the SPD-HARM algorithm. \(TT\) was improved by 26% to 30% compared to the baseline scenario, by 3% to 19% compared to the VSL algorithm, and 31% to 39% compared to the vehicular-based SPD-HARM algorithm. In [88], the authors proposed an optimal VSL strategy in a CAV environment for a motorway corridor with multiple bottlenecks using an extended CTM that takes into account capacity drop and mixed traffic flow, including HDVs, heavy vehicles, and AVs. The GA optimization process for the developed VSL control strategy was conducted in four steps. The first step involves the collection of motorway detector-based data in each cell, including traffic flow, speed, and density. The second step refers to the traffic state prediction in the selected motorway cells during the next control horizon based on the collected traffic data. The third step is the optimization process, which computes the objective function according to the predicted traffic data. The objective function value of each individual in the population is evaluated, and a new population is generated using the mutation and crossover operators. Two stopping criteria were used for the GA, including a maximum number of generations and the average relative change between the best objective function value at the current iteration and the values achieved up to the current iteration. The proposed VSL control with V2V, V2I, and I2V communication outperforms the VSL-only control. Better performance was achieved with increasing CAV penetration rate. Seven different simulation scenarios were compared with a scenario with 100% HDVs and no VSL control. The scenario with 10% CAVs, I2V, V2I, VSL control, and the extended CTM showed the best results, reducing \(TTT\), delays, number of stops, and emissions by 35.6%, 67.9%, 65.9% and 7.6%, respectively. In [92], AVs were used as actuators for Cooperative VSL (C-VSL), receiving speed limits directly from the controller and following them strictly. For a mixed traffic flow scenario, C-VSL was tested together with Point-level VSL (P-VSL), which was developed to inform HDVs that have a speed acceptance factor about the posted speed limit.