based on that, you go from 11.0.3 to 11.11.8. There will be downtime needed. Otherwise, for zero downtime, or almost zero downtime, you have do to every single upgrade from 11.0.3 which would be hundreds of them.
So better, follow the upgrade path as per the docs:
13.1.11 - > latest
and make sure also as per upgrade docs, after doing each version upgrade, check for background migrations before continuing the next upgrade:
the command for checking is at the link. So in summary.
- Upgrade 11.0.3 to 11.11.8.
- Check background migrations. When result is zero, the next upgrade can be started.
and repeat for each upgrade. Make sure you have a backup of your server in case something goes wrong, because then it’s easier to restore the system and start again.