A Dynamic Programming Approach to Optimal Lane Merging of Connected and Autonomous Vehicles

Lane merging is one of the major sources causing traffic congestion and delay. With the help of vehicle-to-vehicle or vehicle-to-infrastructure communication and autonomous driving technology, there are opportunities to alleviate congestion and delay resulting from lane merging. In this paper, we first summarize modern features and requirements for lane merging, along with the advance of vehicular technology. We then formulate and propose a dynamic programming algorithm to find the optimal solution for a two-lane merging scenario. It schedules the passing order for vehicles while minimizing the time needed for all vehicles to go through the merging point (equivalent to the time that the last vehicle goes through the merging point). We further extend the problem to a consecutive lane-merging scenario. We show the difficulty to apply the original dynamic programming to the consecutive lane-merging scenario and propose an improved version to solve it. Experimental results show that our dynamic programming algorithm can efficiently minimize the time needed for all vehicles to go through the merging point and reduce the average delay of all vehicles, compared with some greedy methods.