# Research on Queue Equilibrium Control Algorithm of Urban Traffic Based on Game Theory
## 1 Introduction  
The signal control is one of the key factors that impact road performance and traffic congestion. A reasonable optimization strategy of signal control at the intersection can alleviate urban road congestion and improve traffic efficiency. To alleviate traffic pressure, researchers have proposed many advanced traffic signal control methods according to different control standards. In 1958, the famous [PERSON]'s signal plan [1] was put forward, which was mainly used to calculate the green split to reduce the delay. Subsequently, SCAT [2] and SCOOT [3; 4; 5] adaptive traffic signal optimization systems were proposed and widely applied in the world. [PERSON] et al. developed a new hybrid neural network (SPSA-NN) for distributed real-time control of intersections in road networks. The experimental results show that the algorithm can significantly reduce the delay and stop of vehicles in road networks. However, this algorithm requires a large number of training samples [6]. In recent years, reinforcement learning has become the mainstream method in urban traffic signal control research. [PERSON] et al. proposed an adaptive traffic signal control scheme for urban road networks based on multi-agent reinforcement learning (MARL). A delay time estimation model was adopted to predict the total delay of vehicles in each road section, and traffic signals are adaptively controlled according to the computation [7]. [PERSON] et al. proposed an adaptive traffic signal control system that is trained by the function approximation reinforcement learning technology. In the process, they developed a dynamic and random traffic simulation method that will slightly increase the delay of left-turning vehicles [8]. [PERSON] et al. used an immune network algorithm to conduct an optimization study in the intersection after traffic disturbance events [9]. Based on data-driven intelligent transportation systems (D2 ITSs), [PERSON] et al. designed the MA-DD-DACC method combined with real-time queue-length data to ensure queuing strength (the number of queuing vehicles/the length of its link) balance between multiple signal phases and proved that the algorithm could make the queue intensitybalance error remain bounded by using [PERSON]'s stability analysis, but most of the time, the vehicles in the queues in each direction do not saturate the road and lane space, and the number of queuing-vehicles balance will have greater significance [10]. The traffic condition change of a local road network can be regarded as uncertain competition conditions in the game, so it is appropriate to use the Nash equilibrium to improve the existing intersection signal control strategy. [PERSON] et al. developed a Nash negotiation game theory framework for the intersection phase that uses each signal phase as a game player competing for the green light release and realized phase-free and cycle-free distributed real-time signal control. However, the algorithm is not friendly for driving and is not good for vehicle-to-infrastructure cooperative control [11]. [PERSON] et al. designed a traffic signal control multi-agent coordination framework based on deep reinforcement learning methods, which corrected actions by using spatial difference coordination methods. They proved that the model could converge to the Nash equilibrium [12]. The [PERSON] and [PERSON] game theory models were used to balance the flow of a single intersection and road network in the previous study [13; 14; 15; 16]. The cooperative game was utilized to optimize vehicles distribution among multiple intersections [17]. [PERSON] et al. used the two-layer cooperation game model to control the single intersection, but this method is only applicable to the two-phase intersection [18]. In this paper, the game theory is introduced into the intersection signal control to realize the coordination and optimization of control.