A cooperative control algorithm based on an assignment model is proposed for the merging areas of urban roads and highways, specifically designed for connected and automated vehicles. The primary objective of this algorithm is to optimize the positional distribution and operational speed of mainline vehicles located upstream of the merging area, thereby reserving the space resources of the outer lane of the mainline for ramp vehicles to merge effectively. The algorithm generates virtual slots based on the positions of vehicles on the roadway. To minimize the vehicles lane-changing time, a time cost matrix is created, an assignment model is established, and the Hungarian algorithm is emploed to solve this model. Utilizing the Python-SUMO simulation platform, two scenarios-free traffic and congested traffic-are simulated to evaluate the peformance of the proposed model. The results show that the proposed cooperative control algorithm can significantly reduces the occurrence of traffic deceleration waves and improve driving efficiency. In free traffic conditions, the driving time and fuel consumption can be reduced by 18% and 20.03%; in congested traffic scenarios, the driving time can be reduced by 13.47%, while fuel consumption can be reduced by 13.82%. The research results have important practical value for traffic control in merging areas for connected and automated vehicles.