Yep but how far in advance, a week a month a year!
The message is not very helpful when I have a dead MBP.
Slots are opened 3 days in advance. ie If you were to try to book today, it would allow slots to be booked for today, tomorrow and Saturday. If you try tomorrow, you will then have the opportunity to book slots for Sunday. If it says all appointments are booked then there is nothing you can really do.
If you live close then maybe pop in to the store and ask whether a stand by appointment would be possible. Stand By appointments won't always be available however.
Be aware that if you do get a stand by appointment, you may not be waiting for long, but on the other hand you could be there till the store closes without being seen. It won't ever guarantee you the chance to see a Genii.
It may seem a little disheartening that you need an appointment but are struggling to get one, but they run it like that for the customers benefit. The only other way customers could be seen would be with a queue which would work out much much worse for customer experience.
If appointments are really that tight, rest assured that the store will be aware and will be doing what they can to increase availability.
