Predicting the behavior of DNA molecules in vitro is one of the most fundamental issues on DNA computing, but is also known to be quite difficult. Shiozaki et al. proposed a probabilistic model that can simulate many features of biochemical experiments in terms of the reaction rate , although there are several differences between the biochemical experiments and the computational simulations on the model. In this paper, we extend the model to support base pairs construction among k DNA sequences, which plays an essential role in realizing branch migrations. The simulation results have much more similarities to the biochemical experiments results than ones on the previous model, which implies that the analysis of the model may give some insight about the reaction rate. Through the analysis, we conclude this paper by giving a guideline for designing DNA sequences that can quickly react.