This is actually something that I spent a lot of time trying to get right. Currently when a user selects their tickets and clicks 'Checkout', all other sessions they have open will be cancelled and their reserved tickets released.
This still doesn't stop people from completing the checkout process and then starting again though. It's a tricky thing to prevent as most preventative measures are easily circumvented by users.
Looks interesting and nicely done from the screenshots, but there's massive friction to take a real look. There should be a link to a live demo, front and center.
I had an issue with eventbrite where if the tickets are free people will just open several tabs and order 10 at once.
Is there some kind of IP checking ?