Continuous Estimated Time of Arrival I'm trying to create a model for when a shipped product will arrive at its destination. There are several stages the delivery goes through, so it's not just drive time from point A to point B. My first model looks at the status of the product on the first stage and uses average time deliveries for that product time to predict the # of minutes after the first stage that the product will be delivered.
I want to make another model that gives more of a continuous prediction, taking into account how long the delivery has been in a certain stage. For example, if most deliveries are done with the first stage after 15 minutes and it's been 10 minutes, the model should account for that in the eta. 
How would I approach this? I can feed in the # of minutes it's been in the stage as an input but it seems like I can come up with a huge amount of data for each example.
Sorry if this isn't a clear question.
If I understand correctly (not sure), it looks to me like you don't need a model which can predict at any time, you just need:


a model which predicts the ETA at any stage given information about the past stages. The easiest way to do that is probably to just train a different model for each stage, since the number of stages is fixed.
Then between two stages the ETA can be updated in a deterministic way: if the last stage was passed at time $t$ and the predicted ETA was say 10mn, then at time $t'$ the ETA is just 10mn - $(t'-t)$.