Fairly common complaint this time of year. The tough part is, when a shop is full, a shop is full!
All of my bays and guys are booked solid right now for 5-6 days in advance from open to close, and it's not snowing yet.
We've been working with other tire shops in town to handle the load, they send some to me, I send some to them.
The challenge is, if you try to rush, you make mistakes. its important for customers to understand that this is winter tire season, and 3-7 days is common everywhere. I communicate with all of the tire shops here every few days, and we're all the same.
As far as cancellations or no shows, it does happen for sure. The way we handle customers in a hurry situation is that they must leave the vehicle with me, and if we have a no show, we slide it in. If the car isn't there at that minute, it can't be done. By the time you call a customer, they drive in, it's too late. If the customer in a hurry is willing to leave their vehicle for 24 hours, there's a good chance we can find a free slot. They simply can't sit and wait for it, they could wait all day.