Modeling turn-taking speed while considering speaker characteristics and the relationships between speakers is essential for realizing dialogue systems capable of natural interactions. In this study, we focused on dialogue participants’ roles, relationships, and personality, analyzing and modeling turn-taking speeds observed in real conversations. The analysis confirmed that the expression of these attributes—role, relationship, and personality—is closely associated with turn-taking speed. Based on these findings, we constructed a model that predicts the distribution of turn-taking speeds according to each attribute using a gamma distribution. Evaluation results demonstrated that appropriate parameter fitting to the three-parameter gamma distribution enables effective modeling of turn-taking speeds based on participants’ roles, relationships, and characteristics.