M/M/1 Queue (Cinema) Calculator

Cinema and attraction queue time

To get a rough wait, take the average service time × people in front of you and divide by how many servers work in parallel. The usual numbers look like this: buying a ticket runs about 30 s, popcorn/concessions take 1-2 min, and theatre entry (the ticket scan) is around 10 s. A single-queue, multiple-server setup, the Disney "snake" line, ends up with the same average as several parallel queues, but its variance is far lower, so you almost never get stuck behind the slowest customer. Little's Law puts a formula on this: L = λ · W, where L is the average number in queue, λ the arrival rate, and W the mean time spent in queue. Example: 20 people ahead, 30 s per ticket, 2 booths open → wait ≈ 20 · 0.5 / 2 = 5 min. Real queues bring randomness into it (someone changes their mind, a payment fails), so plan for a 20-30% buffer on top.

Applications

It comes in handy at box offices, theme parks (Disney FastPass+, Universal Express, Beto Carrero), supermarket checkouts, airport check-in and security, plus restaurant and bakery counters. The same math shows up in cashier sizing, call-centre staffing and ITSM incident management, where the question is how many attendants you need to hold a target wait.

FAQ

Single queue or multiple queues? One queue feeding several servers gives the same mean time but much less variance, which is why it tends to win on fairness and on how customers feel about the wait.

Why does the wait grow faster than the number of people? Service time isn't constant, it varies from one customer to the next, and that randomness piles up, especially once utilisation runs high.

Does opening one more booth halve the wait? Roughly, yes, as long as arrivals don't grow to match. The closer λ sits to capacity, the more an extra server buys you compared with a quiet period.

How do parks estimate "45 min from here"? Sensors and ticket scans read the real flow, and the number on the sign keeps getting refreshed from Little's Law as conditions change.