In a previous article, I discussed the Psychology of Queueing and my experience at Disneyland while on vacation with my family. In this post, I want to briefly talk about FastPass at Disneyland, in the context of Queueing.

FastPass is a feature that Disneyland offers its customers, wherein a customer is invited to obtain a pass, redeemable only at a certain time and ends at a certain time. The idea is that during those times, theoretically, the lines will be shorter and the wait time will be shorter also. Below is a picture of what that looks like at Disneyland.

As you can see from the picture above, the customers are invited to return between 4:25PM to 5:25PM, with the idea that the wait time will be shorter. Disneyland calls this offering FastPass.

As I thought more about FastPass, I think it is a simple Queueing calculation; If I’m thinking about this correctly, then, we need to know the following items:

- λ = Arrival Rate, or more specific, the time between arrivals. For most queues, we can assume that the arrival distribution can be approximated by a Poisson distribution; which means that the time between arrivals are not deterministic, but random.
- μ = Service Rate, or more specific the time for a arrival to be serviced.

Then, Disneyland probably has historical data on when this particular ride is least congested, and I’m assuming it’s between the hours of 4:25PM and 5:25PM. Disneyland, then, can calculate, given historical congestion data and the Arrival Rate and the Service Rate, the probability of N arrivals during this 60 minute period:

(P

_{n}= (λT)^{n}/n!)e^{-λT}

Where T is period T, in our Disneyland example, it is 60 minutes.

Let’s assume that Arrival Rate = 15, and we want to know the probability of 4 arrivals during this 60 minute period. Then, we get the following:

(P

_{4}= (15*1.0)^{4}/4!)e^{-15*1.0}

The result of the equation above would give a % of probability of 4 arrivals during a 60 minute period.

**Does FastPass Work?**

I’m not sure. Our family went on plenty of rides and, on some, I saw noticed that FastPass seemed to work, whereas on others, FastPass was no faster than the regular line.

Like most things, the equations we come up with are clean and neat. But, when they meet everyday life and empirical data, things get a little muddy and much more complex.

**Enough Pontificating**

We had a great vacation at Disneyland. We’re already planning our next vacation — we’re thinking Hawaii. I can’t wait.

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