Tower of Hanoi scheme
At a glance
You can set up the following parameters of a Tower of Hanoi scheme.
Schedule parameters are set as follows
Number of levels: 4
This is how the first 14 days (or 14 sessions) of this scheme’s schedule look. Shaded numbers denote backup levels.
Backups of different levels have different types:
A cleanup mechanism ensures that only the most recent backups of each level are kept. Here is how the archive looks on day 8, a day before creating a new full backup.
The scheme allows for efficient data storage: more backups accumulate toward the current time. Having four backups, we could recover data as of today, yesterday, half a week, or a week ago.
The number of days we can go back in the archive is different on different days. The minimum number of days we are guaranteed to have is called the roll-back period.
The following table shows full backup and roll-back periods for schemes of various levels.
Adding a level doubles the full backup and roll-back periods.
To see why the number of recovery days varies, let us return to the previous example.
Here are the backups we have on day 12 (numbers in gray denote deleted backups).
A new level 3 differential backup has not yet been created, so the backup of day five is still stored. Since it depends on the full backup of day one, that backup is available as well. This enables us to go as far back as 11 days, which is the best-case scenario.
The following day, however, a new third-level differential backup is created, and the old full backup is deleted.
This gives us only a four day recovery interval, which turns out to be the worst-case scenario.
On day 14, the interval is five days. It increases on subsequent days before decreasing again, and so on.
The roll-back period shows how many days we are guaranteed to have even in the worst case. For a four-level scheme, it is four days.