Variability dependent modeling provides a way of handling the impact of some variability sources in the modeling. In many cases, the variability factor is estimated in a deterministic way, leading to a mere selection of the most adequate model. However, there are always some uncertainty in the estimation of the variability sources which may induce a sub optimal model selection. This paper considers the context of a speaking rate dependent modeling approach, and shows that the uncertainty on the speech segment boundaries, which translates in an uncertainty on the speaking rate estimation, can be handled in the training process and/or in the decoding process. Preliminary results reported here are promising for dealing with variability estimation uncertainty.