It's an interesting topic to ponder.
I don't think queue times are an indicator of popularity per se. Particularly the app queue times, seeing as those can often be inaccurate to wildly varying degrees. Using queue times as a sole indicator forgets the key element of throughput.
With that being said, what I think queue times do indicate is how much demand is outstripping supply by. Let's consider two major coasters, Coaster A and Coaster B. Coaster A has a throughput of 1,800pph and Coaster B has a throughput of 1,200pph. If we have 1,800 people go to each ride at a uniform rate across a period of 1 hour, Coaster A will have a 0 minute queue while Coaster B will have a 30 minute queue by the end of the hour. If we repeat this for another hour, Coaster A will maintain a 0 minute queue while Coaster B will have a 60 minute queue after 2 hours. This might sound odd when they each have the same number of people going to them, but consider this; 1,800 people are flocking to both rides during the hour, which equates to roughly a person every two seconds if people flock to them at a uniform rate. The key difference here is that Coaster A can service a person every two seconds and 1,800 people every hour, whereas Coaster B can't. Coaster B can only service a person every three seconds, or 1,200 people every hour. So if we look at a 5 minute period where 150 people turn up to each ride, Coaster A has serviced all 150 people across the 5 minute period, while Coaster B has only serviced 100 out of the 150 people and there is still a backlog of 50 people to service. As more people flock to each ride, Coaster A will just keep gobbling them up perfectly without a backlog left while Coaster B's backlog will just keep growing with time.
Let's apply this to some real-world Alton Towers examples. Let's go with two dark rides of vastly differing throughputs; Gangsta Granny and The Curse at Alton Manor. If we assume Gangsta Granny has a throughput of 400pph and Alton Manor has a throughput of 1,800pph (rough ballpark guesses), and the same 1,800 people flock to each at a uniform rate across a period of 1 hour, Alton Manor will remain walk-on at the end of the hour, whereas Gangsta Granny will have amassed a 3.5 hour, or 210 minute, queue by the end of the hour. This is because Alton Manor has no backlog, whereas Gangsta Granny has a backlog of 1,400 people left to service from the hour.
So if Alton Manor averages a 5 minute queue across a day and Gangsta Granny averages a 60 minute queue across the same day, Alton Manor will have vastly more people riding it each hour on average than Gangsta Granny, despite it initially seeming like Gangsta Granny is more popular:
- Alton Manor: 5 minute queue at 1,800pph = Backlog of 150 people, total of 1,950 riders queueing per hour
- Gangsta Granny: 60 minute queue at 400pph = Backlog of 400 people, total of 800 riders queueing per hour
Of course this isn't a perfect analogy, as people don't flock to rides at a uniform rate and this also assumes that every seat is filled on all rides, but you get my basic point.
Basically, the queue times are an indicator of how much demand is outstripping supply by. So the ride with the longest queue time is not the one that's most popular, but instead the one that is servicing its level of demand most poorly.
