# Research on Queue Equilibrium Control Algorithm of Urban Traffic Based on Game Theory
## 4 Simulation Verification  
To verify the feasibility of the proposed algorithm, this paper implements the queuing equilibrium control algorithm based on game theory in Matlab and compares it with algorithms in other papers. Two groups of experiments are carried out: 1. using the queuing equilibrium game control algorithm in this paper; 2. using the MA-DD-DACC queuing strength balance control algorithm. As shown in Figures 1 and 2, it can be found that MA-DD-DACC can ensure the balanced queuing strength (the number of queuing vehicles/the length of its link) and clear the intersection at the same time. The time taken is 651 s. However, most of the time, the line in each direction does not fill the lane, and the experience of each vehicle in the line will have greater significance. The algorithm in this paper takes the number of queues as the index. Each phase competes with the other over the green time and finally clears the entire intersection, which takes 639 s. The experimental parameters are shown in Table 1, where the flow rate of each phase is translated successively \(\frac{pi}{4}\) by the cosine function. We use the traffic simulation software VISSIM to carry out the experiments. The intersection of Nanhuan Road and Yanping Road in Changping District in Beijing is selected as the simulation intersection, and the simulation time is 10 a.m. to 11 a.m. (during the off-peak period). The filed traffic data in the intersection is applied as the vehicle inputs and routes ratio of VISSIM, as shown in Table 2. The vehicle composition of all directions is similar in the intersection, as shown in Table 3. The original signal timing and the magnetic detector data of the intersection are obtained by the traffic management department. The original intersection timing plan is shown in Table 4. The magnetic detector is located 120 m from the stop line in the east-west direction and 50 m from the stop line in the north-south direction. The east-west direction is the main road, so the conflict zone in the priority of east-west is higher than that of north-south. Figure 1: The queuing index of MA-DD-DACC algorithm. Figure 2: The queuing index of the game equilibrium algorithm in this paper. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **East Import** & **North Import** & **West Import** & **South Import** \\ \hline Arrival flow \(q\)/pcu-h\({}^{-1}\) & & (1.5 + cos(x * pi/4:0.2:(1 + x/4) * pi)) * 200 & \\ \hline Initial cycle \(C_{0}\)/s (maximum cycle \(C_{\text{max}}\)/s) & & 128 (120) & \\ \hline Initial queue \(D_{0}\)/pcu & 10 & 20 & 30 & 40 \\ \hline Saturation flow \(S\)/pcu-h\({}^{-1}\) & 1880 & 1880 & 1880 & 1880 \\ \hline Initial green light time \(g\)/s & 10 & 10 & 10 & 10 \\ \hline Lost time \(t_{L}\)/s & 2 & 2 & 2 & 2 \\ \hline Maximum queue length \(l_{\text{max}}\)/pcu & 100 & 200 & 300 & 400 \\ \hline Maximum green light time \(g_{\text{max}}\)/s & 70 & 70 & 70 & 70 \\ \hline Minimum green light time \(g_{\text{min}}\)/s & 10 & 10 & 10 & 10 \\ \hline Quotiely alpha & 0.99 & 0.99 & 0.99 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The equilibrium control simulation parameter table. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **East** & **North** & **West** & **South** \\ \hline Vehicle Inputs & 974 & 306 & 998 & 285 \\ \hline \multirow{4}{*}{Routes ratio} & Straight & 0.87 & 0.85 & 0.84 & 0.57 \\ \cline{2-4}  & Left-turn & 0.09 & 0.05 & 0.14 & 0.14 \\ \cline{2-4}  & Right-turn & 0.02 & 0.1 & 0.02 & 0.29 \\ \cline{2-4}  & U-turn & 0.02 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The vehicle inputs and routes ratio of VISSIM. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Rel.Flow** & **Des.Speed** \\ \hline
100.Car & 0.900 & 50(48.0, 58.0) \\ \hline
200.HGV & 0.100 & 40(40.0, 45.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The traffic composition of VISSIM. (GA algorithm) with the goal of best matching the number of vehicles passing through the each direction of the intersection.