A group of mathematical models for the investigation of the impact of the median to the relative risk of interurban road segments is presented in this paper. Several generalized linear models have been estimated using alternative distributional assumptions regarding the error structure, namely the Poisson, quasi-Poisson, and negative binomial distributions. While the Poisson distribution fails to capture the overdispersion that is observed in the data, the quasi-Poisson and negative binomial distributions lead to models that do not violate the basic statistical assumptions. From the results of the application of these models, it is verified in a sample of road segments from the Patras-Athens-Thessaloniki motorway in Greece that the relative risk increases nonlinearly with the increase in traffic flow, while the existence of a median results in the net reduction of the relative risk of road segments.