# Coordinated Control Method of Bus Signal Priority and Speed Adjustment Based on Stop-Skipping
## 3 Model Building
### Assumptions  
1. The environment of the waiting facilities at each station is the same.
2. Buses pass on dedicated bus lanes.
3. The bus vehicle is not fully loaded, and the bus ride demand will be satisfied as long as it stops at the station.
4. Passengers waiting at the station will wait until they enter the bus, and the last bus will not refuse passengers.
5. The same station cannot be skipped twice by vehicles passing by.
6. The vehicle-road coordination system can detect the running state of the vehicle and provide real-time two-way communication for the bus and the signal controller.
7. This study ignores the impact of social vehicles, and there is no bus queue at the intersection.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Definition and Description** \\ \hline Sets & \\ \(I\) & The set of buses. \\ \(J\) & The set of stations. \\ \(X\) & The set of intersections. \\ Parameters & \\ \(i\) & \(i\in I,i=1,2,3,\ldots,m\), \(m\) represents the maximum number of bus. \\ \(j\) & \(j\in J,j=1,2,3,\ldots,n\), \(n\) represents the maximum number of station. \\ \(x\) & \(x\in X,x=1,2,3,\ldots,q,q\) represents the maximum number of intersection. \\ \(t_{0}\) & The departure moment of the first bus on the line. \\ \(t_{ij}\) & The time when the bus \(i\) runs from the first station to the station \(j\). \\ \(t^{\prime}_{ij}\) & The departure time of bus \(i\) at station \(j\) on the line. \\ \(t_{i,x}\) & The moment when bus \(i\) arrives at intersection \(x\). \\ \(\bar{t}\) & The average time of picking-up or dropping-off per passenger. \\ \(\tau_{i,j}\) & The stop time of bus \(i\) at station \(j\) on the line. \\ \(\mu\) & The time of bus acceleration and deceleration. \\ \(\eta\) & The coefficient of passengers waiting stations. \\ \(h\) & The departure interval of buses on the line. \\ \(h_{j}\) & The headway of two adjacent buses at station \(j\). \\ \(h_{0}\) & The safe distance between two adjacent buses. \\ \(\varphi_{i,x}\) & The delay time of bus \(i\) arriving at intersection \(x\) is the remaining red-light time. \\ \(r_{i,x}\) & The extended or advanced green-light time for bus \(i\) to arrive at intersection \(x\). \\ \(r_{1}\) & The red-light time for phase 1. \\ \(r_{2}\) & The red-light time for phase 2. \\ \(R\) & The signal period of the intersection. \\ \(d_{ij}\) & The distance of bus \(i\) from the departure station to station \(j\). \\ \(s_{j,x}\) & The distance from station \(j\) to intersection \(x\). \\ \(v\) & The average speed of the bus. \\ \(\sigma\) & The adjusted speed of the bus. \\ \(L^{p}_{i,j}\) & The number of passengers on bus \(i\) when it arrives at station \(j\). \\ \(D^{l}_{i,j}\) & The number of people entering bus \(i\) when it arrives at station \(j\). \\ \(A^{p}_{i,j}\) & The number of people exiting bus \(i\) when it arrives at station \(j\). \\ \(W_{i,j}\) & The number of people waiting for bus \(i\) at station \(j\). \\ \(\lambda\) & The time value factor for cost reduction. \\ \(Q\) & The capacity of the bus. \\ \(\Delta C\) & The operating cost of bus stops at the station. \\ Decision variables & \\ \(Z_{i,j}\) & \(Z_{i,j}=1\), if bus \(i\) stops at station \(j\), and \(Z_{i,j}=0\), otherwise. \\ \(\gamma_{i,x}\) & \(Y_{i,x}=1\), if bus \(i\) stops at intersection \(x\), and \(Y_{i,x}=0\), otherwise. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notation.