Multi-traffic Signal-Control Synchronization

In this chapter, we provide a brand-new paradigm for combining game theory and the extraproximal approach to represent the multi-traffic signal-control synchronization problem. The intersection’s goal is to reduce queuing time, and finding the best signal timing strategy, or assigning a green period to each signal phase, is a challenge for signal controllers. The game’s players are referred to as signal controllers. Finding a green period at each junction seeks to reduce signal and queuing delays. The issue poses two inherent limitations: (a) the number of arriving and departing vehicles varies for each street of the intersection; and (b) for every intersection, the period of time allowed for vehicles to reach the green light is equal to the duration of the red light. A leader-follower Stackelberg game model is determined by the first restriction: streets with higher traffic demand more green time. The most recent constraint created a simultaneous game-solution as a better evaluation of the actual circumstance. The study then demonstrates that the Nash equilibrium provides the solution in order to take use of the game’s structure. To solve the problem computationally and determine the best signal timing distribution, we present the c-variable technique. The extraproximal approach is a two-stage iterative process. In the first phase, an approximate equilibrium point is calculated, and in the second step, the previous step is adjusted. The game is described in terms of linked nonlinear programming issues that use the Lagrange principle. To guarantee the convergence of the cost-functions to a Nash equilibrium point, the Tikhonov regularization approach is used. The extraproximal approach is also developed using Markov chains. The three way intersection example serves as a good demonstration of the method’s use. Our contributions have significant effects on the applications in the real world.