Fog computing offloads latency critical application services running on the Cloud in close proximity to end-user devices onto resources located at the edge of the network. The research in this paper is motivated towards characterising and estimating the time taken to offload a service using containers, which is investigated in the context of the `Save and Load' container migration technique. To this end, the research addresses questions such as whether fog offloading can be accurately modelled and which system and network related parameters influence offloading. These are addressed by exploring a catalogue of 21 different metrics both at the system and process levels that is used as input to four estimation techniques using collective model and individual models to predict the time taken for offloading. The study is pursued by collecting over 1.1 million data points and the preliminary results indicate that offloading can be modelled accurately.