This paper analyses the picking performance of a robotic mobile fulfilment system (RMFS) and proposes a Simulation Framework of RMFS based on cellular automata (SFRMFSCA). Many previous RMFS simulation platforms stipulate all aisles to be set up in a fixed directional road network for oneway lines. The warehouse robot had to travel an unnecessarily long distance to perform tasks. We relax the one-way constraint on aisles and cross aisles in the warehouse and allocate the right of way among the warehouse aisles and cross-aisles intersection by referring the idea of traffic light and traffic flow control to the RMFS warehouse scenario. To improve the efficiency of RMFS order picking, this paper designs a comprehensive strategy combining adaptive traffic light update rule, deadlock detection and recovery algorithm, and traffic control to improve the traffic flow of the system. A series of numerical experiments show that the comprehensive strategy designed in this paper can effectively improve the order picking efficiency of RMFS and reduce the probability of scale deadlock. These results and strategies provide a useful reference for designers who initially set up the RMFS warehouse.