This paper proposes a mathematical model to analyze the behavior of an asynchronous parallel evolutionary algorithm (APEA) and demonstrates its validity through the comparison of the theoretical result with the simulation one. The proposed model considers the transition of the probability density of solutions in the population and the slave nodes in the parallel computing environment during the optimization process of an APEA. This paper demonstrates the convergence state of the population and the slave nodes on the flat fitness landscape by using the proposed model. From the result of the comparison between the theoretical result acquired by the proposed model and the simulation one, the validity of the proposed model is confirmed. Additionally, it is revealed that an APEA is necessarily biased toward the search area having a shorter evaluation time regardless of the fitness landscape. This paper finally shows a possible attempt to avoid the evaluation time bias on APEAs and demonstrates its effectiveness in the simulation experiment.