## 3 Experimental Setup
### Scenario 3: MP-Based Scenario at the Signalized Intersection  
For comparison, we implemented another scenario of intersection management based on max pressure (MP), as shown in part (b) of Figure 9. This was a feedback-based signal control algorithm that stabilized the queue length and maximized throughput. This controller did not need to know about the current or future traffic volume of the network. It only required the real-time measurement of the queue length in all directions to and from the intersection. The signal control plan consisted of 4 phases with duration based on the MP algorithm. In this scenario, 24 area detectors were placed in 24 lanes to and from the intersection to measure the queue length per lane. The intersection (n) is presented as a graph with links \(\mathrm{z}\ \in\ \mathrm{Z}\), including the incoming link set (\(\mathrm{I_{n}}\)) and outgoing link set (\(\mathrm{O_{n}}\)). The equation that describes the evolution of queue length for link z is expressed as follows:  
\[\mathrm{x_{z}\ (\ t\ +\ 1\ )}=\ \mathrm{x_{z}\ (t)}\ +\ \mathrm{T_{t\ \rightarrow\ (t+1)}\ [\ q_{z}\ (t)\ -s_{z}\ (t)\ +\ d_{z}\ (t)\ -u_{z}\ (t)]} \tag{11}\]  
Here,  
* \(\mathrm{x_{z}\ (t)}\) is the number of vehicles in link z to link m at the end of the discrete-time t.
* \(\mathrm{q_{z}\ (t)}\) and \(\mathrm{u_{z}\ (t)}\) are the inflow and outflow in the same period. * \(\mathrm{d_{z}\ (t)}\) and \(\mathrm{s_{z}\ (t)}\) are the demand and saturation flow in this link. The state \(\mathrm{x_{z}\ (k_{n})}\) of each link is determined based on the number of vehicles in the queue length according to real-time measurement. The pressure of this link can be calculated as follows: \[\mathrm{P_{z}\ (k_{n})}\ =\ \left[\frac{\mathrm{x_{z}\ (k_{n})}}{\mathrm{x_{z,\ max}}}\ -\ \sum_{\mathrm{w\ \in\ \mathrm{O_{n}}}}\frac{\beta_{\mathrm{\ i,\ w}\ \mathrm{x_{w}\ (k_{n})}}}{\mathrm{x_{w,\ max}}}\ \ g_{ \mathrm{\mathrm{r_{n},\ j}\ (k_{n})}}\right]\mathrm{S_{z}}\] (12) Here,
* \(\mathrm{x_{z,\ max}}\) and \(\mathrm{x_{w,\ max}}\) are the storage capacity of link z and link w.
* \(\beta_{\mathrm{\ i,\ w}\ }\) is the turning movement rate with \(\mathrm{i}\ \in\ \mathrm{I_{n}}\) and \(\mathrm{w}\ \in\ \mathrm{O_{n}}\). * \(\mathrm{k_{n}}\) is the control discrete time index. * \(\mathrm{g_{n,j}}\) is the green time of stage j. Pressure in each direction is defined as the difference between the upstream and downstream queue length. In this case, the output links are exiting links with infinite capacity, and the second term in Equation (12) becomes zero. Thus, the pressure of each link is simply equal to the queue length multiplied by the saturation ratio (\(S_{z}\)). The pressure of each stage j of the intersection can be determined as  
\[\mathrm{P_{n,j}\ (\ k_{n})}\ =\ \max\left\{\ 0,\ \sum_{\mathrm{z\ \in\ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\
u_{j}}}}}}}}\ \mathrm{P_{z}\ (k_{n})}\right\} \tag{13}\]  
The total effective green time for intersection n (\(\mathrm{G_{n}}\)) could be obtained by  
\[\mathrm{G_{n}\ =\ \mathrm{C_{n}\ -\ L_{n}\ -\ \sum_{j\ \in\ \mathrm{F_{n}}}g_{n,\ j,\ min}}\ \ \ \ \ \mathrm{with\ n\ \in\ \mathrm{N}} \tag{14}\]  
\(\mathrm{g_{n,\ j,\ min}}\) is the minimum green time for stage j of intersection n. This value is taken in the ATSC-based scenario as 10 s. Moreover, \(\mathrm{g_{n,\ j}\ (\ k_{n})}\) is the green time spent in phase j with the constraint  
\[\mathrm{g_{n,\ j}\ (\ k_{n})}\ \geq\ \mathrm{g_{n,\ j,\ min}} \tag{15}\]  
The number of vehicles in the queue length at each lane was extracted from the 24 area detectors on each lane. Based on the collected data, the IMS continuously calculated the pressure for the 4 phases and determined the stage with MP. After the minimum green time of the current phase has expired, the IMS checked whether the current phase has maximumpressure. If the current phase was the MP phase, the IMS prolonged the current phase until the other phase had MP. Conversely, if the current phase was not the MP phase, then the IMS shifted the current phase to the MP phase.