I feel like you could align a lot of the incentives here with an X cent “line charge” or something similar?
You get 10min, 5min push notifications, then if you aren’t in the store within 1 min of your spot in line being called, you forfeit the X cents. But if you are then they give you a discount on whatever your buy so the “line charge” nets out.
However, I’m not sure if there exists an X such that
A) you’ll risk it for the convenience
but
B) it’s enough to actually compensate the store if you don’t go
(Could be some interesting behavioral econ approaches there, maybe?)