# Variable Speed Limit and Ramp Metering for Mixed Traffic Flows: A Review and Open Questions
## 3 Research and Implementation
### Merging Control Approaches in Mixed Traffic Flows
#### 3.5.1 Optimization-Based Methods for Merging Control  
The problem of optimal coordination of CAVs at merging roadways formulated as an unconstrained optimal control problem by applying the Hamiltonian analysis to derive an analytical, closed-form solution was analyzed in [100]. Different scenarios were tested regarding mainline and on-ramp speed and density. The overall cumulative fuel consumption with imposed control was improved by 48.1% for the case with different initial speeds for each road compared to the baseline scenario. The \(TTT\) was also improved by 13.5%.  
In [101], the authors proposed an optimization framework and an analytical closed-form solution for online coordination of CAVs at on-ramp merging zones formulated as a nonlinear optimization problem. At a distance of 250 m to 500 m before the merging area, the optimized acceleration information for each vehicle is sent back to the related vehicles at the next decision interval (10 s intervals), which strictly apply the given information. This approach was compared with the gradual speed limit by reducing the speeds to 50 km/h and 70 km/h at 0-250 m and 250-500 m before the merging area, and with no control scenario. Low (300 veh/h), medium (500 veh/h), and high (700 veh/h) demand scenarios for on-ramp and mainline flow were tested. The proposed approach reduced the average delay time per vehicle to almost 0 s and increased the average speed up to 95 km/h. For gradual speed limit and no control scenarios, the average delay time per vehicle under high on-ramp demand was measured to be up to 225 s and 255 s, respectively. The average speed was measured close to 15 km/h for both scenarios.  
In [107], a hybrid approach was developed combining the hierarchical and distributed approaches for merging control. A Road Side Unit (RSU) was placed at the slot selection point and acted as a proxy between the mainline vehicles and the on-ramp vehicles. The RSU was utilized to locate the mainline vehicles and coordinate with them via V2V communication to determine suitable merging slots. These slots are marked as occupied for the vehicles and thus stored as a determined merging slot. Once the slot becomes free, the RSU distributes the slot information to the merging vehicle. The proposed approach does not suffer from system overload at very high traffic demand. Under medium mainline traffic conditions of 3600 veh/h, the slot-based approach with cooperation achieved a 106% increase in throughput compared to HDV-only flows. Under heavy mainline traffic conditions of 4700 veh/h, a throughput increase of 452% was measured for the slot-based driving with cooperation.  
In [109], an MPC-based path planner was proposed to automatically decide the mode of maneuvers under a unified optimization framework for AVs in structured driving environments. A convex relaxation approach was used to determine the LC and lane-keeping maneuvers. Various simulation scenarios were tested in a simulation, including LC, lane keeping, ramp merging, and intersection crossing. The proposed path planner performance was effective in generating a safe and comfortable path for AVs in all tested scenarios.  
In [110], a learning-based method for estimating vehicle intentions in ramp merging scenarios without over-the-air communication between vehicles was presented. The intention estimation is generated from a Probabilistic Graphical Model (PGM) that organizes historical data and latent intentions and determines predictions of real driving trajectories to learn transition models. The PGM-based intention estimation is augmented with ACC model to generate appropriate acceleration and deceleration behavior. The proposed method performance was evaluated on real merging data as well as with a designed merging control in simulation. The proposed method had the lowest failure rate and improved intention estimation in the merging control. It is computationally efficient and does not require acceleration information about other vehicles.