In the experiment proposed by Konno et al. (in press) about constructing a symbolic communication system, it had been confirmed that the emergence process includes three stages corresponding to three test conditions: no messaging, synchronous messaging and asynchronous messaging, respectively. To investigate the mechanism of the emergence of symbolic communication system, an agent-based model is built using reinforcement learning. The simulation result shows that: 1) for synchronous messaging condition, the number of rounds taken to get enough points to win tends to grow when increasing the size of selectable symbols; 2) for asynchronous messaging condition, the number of rounds before success remains stable even though more selectable symbols are offered. We thus conclude that the size of selectable symbols has a negative effect on the formation of symbolic communication system under the synchronous messaging condition, while has no effect under the asynchronous messaging condition.