Virtual queue for theme park rides

Design a virtual queue for a theme park's 12 most popular rides. Instead of standing in line, a guest joins a ride's queue in the park app, sees their place and an estimated return time that update live, and gets a push notification when it is their turn, with 15 minutes to arrive. Each ride boards about 1,200 riders an hour, a guest can hold one virtual place at a time, and ride operators can pause a queue when a ride breaks down. On a busy day 40,000 guests use the app, and when the park opens thousands try to join in the first minute. Describe the data model, how places and return times are computed, how updates reach phones, and what happens when a ride pauses.