Predicting when a partition in Oracle database will be archived
I'd suggest first visualize your data.

The time to archive a partition could be defined as a difference between the partition start (first possible insert) and archiving time (last possible update).

Plot the total distribution of this data for some time interval - check if it follows some distribution. Is the average, median or sd meaningful?

Make a boxplot for each hour to see inter quartile interval and the outliers.

Plot it as a time series - does it have a trend or daily/weekly pattern?

In your simple set up (with one predictor and one response) this will give you impression about the accuracy that you can expect from a model. The choose of the model depends on the result of the visualization.

I personally would start with the simplest models:


all partition archived after $N$ hours;
independent model for each hour predicting say $.9$ quantile of some
history interval;
more advanced 2.: consider the weekday and/or trend and/or
ignoring outliers.


Always check the accuracy and stop if expectations are met.