We have presented a modeling framework for the simulation of freezing processes involving an arbitrary number of densely packed vials up to pallet scale. Instantiations of this model qualitatively predict all experimental trends observed in the engineering run data of the Janssen COVID-19 vaccine. The findings imply that stochastic ice nucleation is an essential aspect of the freezing process and that a mechanistic description of it is required in order to fully understand, and eventually optimize, the process.