# Variable Speed Limit and Ramp Metering for Mixed Traffic Flows: A Review and Open Questions
## 3 Research and Implementation
### Impact of AVs and CAVs on the Fundamental Diagram
In [77], the flow-density relation, Time-to-Collision (\(TTC\)), acceleration rate distributions, and speed difference distributions were analyzed under different penetration rates of CAVs from 0% to 100% and with two different time headways. The total number of incidental situations in the mixed traffic flow under different CAV penetration rates was reduced. The traffic flow was significantly increased by about 2000 veh/h in the case of the desired time headway of 0.5 s, while in the case of 1.1 s, the increase was measured to be close to 500 veh/h. The results of acceleration rate distributions and speed difference distributions of the mixed traffic flow indicate that the increase in penetration rates of CAVs smoothed both acceleration and speed significantly. In [78], lane capacity was analyzed for different AV and CAV penetration rates. Lane capacity was increased by 8.6% when the AV penetration was increased from 0% to 100%. When the CAV penetration rate was increased from 0% to 100%, lane capacity was increased by 188.2%. When the mixed traffic flow consists of CAVs and HDVs, the lane capacity increases approximately linearly from 2046 veh/h/lane to 6450 veh/h/lane as the CAV penetration rate increased from 0% to 100%. In [79], the influence of AVs in mixed traffic flow and the influence of autonomous driving levels on the fundamental diagram were analyzed. The results show that as the AV penetration rate increased with higher automation level, the capacity of the overall network increased and the \(\rho_{c}\) value on a single road was higher. The \(\rho_{c}\) value was increased by almost 48% from no AVs to 100% AVs in mixed traffic flow. In [80], Cellular Automata (CA) model was used to analyze the impact of CAVs on the fundamental diagram on a single-lane road. CA was used to partition the road into cells, where a vehicle may or may not be present in a cell. The results show that with 70% of CAVs, the \(\rho_{c}\) value was increased by about 37%, while the capacity under the \(\rho_{c}\) was increased by about 42%. In [81], the impact of AVs with different penetration rates on the fundamental diagram was analyzed. As the AV penetration rate increased, the speed-density curve shifted to the right, resulting in a higher \(\rho_{c}\) value. Therefore, increasing the AV penetration rate increased the mean speed at the same density, thus increasing the traffic flow. The free-flow speed was increased by about 34% with 100% AV penetration rate, while the increase in capacity under \(\rho_{c}\) was measured to approximately 30%. In [82], the impact on traffic flow and density of Connected Vehicles (CVs) and AVs was analyzed under different penetration rates from 0% to 100% and three scenarios. In the first scenario, the effect of CV penetration rate was tested. The mainline flow was set to 1800 veh/h/lane in the first and second set of simulations. The throughput was increased as the CV and AV penetration rates increased. At low penetration rates of 0% to 50%, the results on the relationship between flow and density were inconsistent. At higher penetration rates, no breakdown or scatter was observed in the flow-density relationship. The second scenario analyzed the effects of AVs on throughput and scatter in the flow-density relationship. The results were similar to the first scenario, with the exception of a smaller scatter at 50% and 70% AV penetration rates. The third scenario analyzed the simultaneous effects of AVs and CVs on throughput and scatter in flow-density relation. Six combinations of different penetration rates of CVs and AVs were analyzed. The mainline flow was set to 2200 veh/h/lane. The scatter in flow-density relationship was increased once the number of CVs surpassed the number of AVs, except in the scenario with a high CV penetration rate. In [83], another analysis of the impact of AVs on fundamental parameters (\(q\), \(\rho\) and \(\overline{v}\)) was performed.