# A Carbon Benefits-Based Signal Control Method in a Connected Environment
## 4 Methodology
### Control Structure  
The control architecture is illustrated in Figure 2. The control system operates within a defined rolling time window, initiating its functions as the designated execution interval commences. It performs data acquisition and identifies CBCVs within the control zone. Following this, the traffic signal control optimization module is activated. This module dispatches command signals to both the traffic controller and CBCVs for execution. Subsequently, the carbon benefit calculation module is activated for evaluation. This control sequence is perpetuated in a rolling time window format. Below are the details of the aforementioned modules.  
* **Data collection module:** This module collects historical signal timing, determines vehicles positions within the control area, and identifies the IDs of CBCVs.
* **Signal control optimization module:** This module provides the signal timing plan and speed guidance to CBCVs.  
\begin{table}
\begin{tabular}{c l c} \hline \hline
**Notations** & **Explanation** & **Unit** \\ \hline \(D_{\omega_{1}}\) & The delay of vehicle \(\omega_{k}\) during passing through the intersection & s \\ \(u_{k}^{i}\) & The start time of the \(i\)-th green time for phase \(k\) & \\ \(\sigma_{k}^{i}\) & The end time of the \(i\)-th green time for phase \(k\) & \\ \(N\) & The number of optimization cycles & \\ \(x^{\omega_{k}}\) & The distance between vehicle \(\omega_{k}\) and the stop line & m \\ \(\Delta t\) & The planning time interval. & s \\ \(t_{0}\) & The start time of the control algorithm. & \\ \(h_{\omega_{k}}\) & The time when vehicle \(\omega_{k}\) crosses the stop line in trajectory & s \\ \(t_{c}^{\omega_{k}}\) & The time when the vehicle \(\omega_{k}\) passes the stop line under & s \\  & signal control & s \\ \(t_{a}^{\omega_{k}}\) & The time taken by the vehicle \(\omega_{k}\) to accelerate from crossing & s \\  & the stop line to its desired speed & \\ \(t_{free}^{\omega_{k}}\) & The time the vehicle spends in free flow to reach the point & s \\  & where it achieves \(t_{a}^{\omega_{k}}\) & m/s \\ \(v_{c}\) & The speed of the vehicle as it crosses the stop line & m/s \\ \(\tau_{l}\) & The speed limit on the road & m/s \\ \(L\) & The length of the control area & m \\ \(t_{clar}\) & The clearance time required during phase switching & s \\ \(S_{min}\) & The minimum green time duration & s \\ \(S_{max}\) & The maximum green time duration & s \\ \(\tau_{\omega}\) & Execution cycle of the rolling horizon scheme & s \\ \(\tau_{n}\) & The safety interval in the rolling horizon scheme & s \\ \(\alpha\) & The weight of the stop time & \\ \(\Omega_{\omega_{1}}^{k^{c}}\) & The set of vehicles guided by CBCVs \(\omega_{k}^{c}\) & \\ \(\tau_{cf}\) & Time lag in the Newswell model & s \\ \(d_{cf}\) & Spatial lag in the Newswell model & m \\ \(N_{sg}\Delta t\) & The transmission interval for speed instructions & g \\ \(a_{L}^{\omega_{k}}\) & Maximum deceleration of the vehicle & m/s\({}^{2}\) \\ \(a_{ll}^{\omega_{k}}\) & Maximum acceleration of the vehicle & m/s\({}^{2}\) \\ \(v_{sg}^{\omega_{k}^{c}}(t)\) & The set of target speed for vehicle \(\omega_{k}^{c}\) & m/s \\ \(v_{\omega_{1}}^{\omega_{1}^{c}}(t)\) & The set of actual speed of vehicle \(\omega_{k}^{c}\) & \\ \(TH\) & The threshold for judging whether the vehicle has complied & \\  & with the speed guidance. & \\ \(R(\omega_{k}^{c})\) & The carbon reward amount allocated to \(\omega_{k}^{c}\) & \\ \(CE(\omega_{k}^{c})\) & The reduction in carbon emissions by vehicle \(\omega_{k}^{c}\) & g \\ \(\mathcal{CP}\) & The incentive amount per unit of carbon emission reduction & \\ \(CE^{\omega_{1}^{c}}\) & The emissions of all vehicles within the group \(\Omega^{k^{c}}\) & g \\ \(CE^{\omega_{1}^{c}}_{opt}\) & The emissions of all vehicles within the group \(\Omega^{k^{c}}\) & g \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._* **Carbon benefit calculation module:** This module evaluates the execution performance of CBCVs based on speed guidance and computes their carbon benefits.