FP+ Let's look at the math...

[sixbitslocum]

There are plenty of threads addressing FP+ and the perceived benefits vs. issues. I've been following some of them, as much as I can bear to, but being a bit of a nerd I keep thinking about the math of the situation, and some of the reports we are getting don't seem to add up. For example, there can't be both fewer fastpasses AND longer fastpass lines. I'd like to start a thread that looks at FP+ from a purely logical, mathematical standpoint because I'm sure that is how the Disney team is looking at it.

Before I start, I will apologize for the length of the post. For those of you who get through the whole thing, I hope it inspires thoughful discussion, rather than argument. Also, I want to point out that all numbers I use are made up. I have no live data to go on and have just chosen estimated numbers to illustrate my points.

Let's start with a basic premise. Let's assume both before and after FP+, the number of rides remains the same (more or less) and the number of riders who can ride the ride in an hour stays the same. So if Space Mountain can handle 1500 riders an hour (my made up number), then that is true whether the riders are fastpass riders or standby riders. If we can agree on this, then the next step is to look at the breakdown between FP riders vs. Standby riders.

Let's look at a few scenarios. First, in the days before fastpass, every line was a standby line and you were always at the mercy of the number of people who wanted to ride the ride at the same time you did. Those 1500 people still rode Space Mountain, but they all may have waited 60 minutes to do so. I'm sure everyone will agree that the original FP improved this because it allowed some of those 1500 people to do other things while they waited. Let's say that 20% of the 1500 (300 people) ended up getting fastpasses. Those 300 people only had to wait in line 10 minutes. Even though the remaining line has 1200 people left, they are still being intermingled with the FP riders so they are still waiting 60 minutes each, but overall there was less wait time for the group as a whole. Now, let's look at the opposite extreme. Let's assume that in a not too distant future, everyone has a fastpass to Space Mountain and there are no longer any standby lines. Each of the 1500 people has a virtual spot in line reserved for them and can return to the ride with almost no wait. In this case, the wait time for the group as a whole has drastically been reduced. The two extremes demonstrate how either everyone can wait 60 minutes or everyone can wait for 10 minutes and the same number of riders (1500) ride Space Mountain in that hour.

I believe that is the direction Disney is headed with FP+. With the paper FP system, it would have been very difficult to manage, (as well as killed forests of trees to provide the paper), but with everyone having instant access to the great fastpass system in the sky through the cell phones that they are all carrying, you CAN achieve a world of "all fastpass, all the time". I believe the current FP+ system is the stepping stone to that improved system. I know FP+ currently only allows for 3 fastpasses per day, but remember, it is a program in its infancy. It needs time to grow and work out the kinks. Data needs to be collected. As the program matures, it will be far easier adding additional fastpasses per day than it would be to take them away. Over time I think we will get to the point where you will be able to ride each ride using fastpasses that you arranged before you even walked in the front gate.

I don't want to argue the merits of having to book a time for everything and not being able to just enjoy your vacation. Although I talk about "all fastpass, all the time", I believe there will still always be standby lines for those who don't want to participate or who just want to wing it. I just think that instead of the split being 20% fastpass/80% standby it will move more toward 80% fastpass/20% standby and the average wait time for the collective group will be shorter.

I had a class in college that touched on "queuing theory" and ever since then, I've always admired how Disney manages to process so many people through the parks while keeping waits to a minimum. I have to believe that being the company that introduced FastPass, they have perhaps some of the best experience and expertise in the industry at managing wait times. Based on the mathmatical results they collect during the beta phase, I think they will be able to fine tune FP+ to provide for shorter wait times for everyone. Disney doesn't just spend half a billion dollars on something that they haven't done extensive mathmatical simulations on. I think there are going to be some rough patches in the short term until the transition is complete, but I really think that once we all get on the other side we're going to see the benefits.

I think we all just need to have a little faith, trust, and.... uhh... oh, I can never remember that last thing.

 

[sharonabe]

I have a feeling I'm not quite up to the math here, but I do have a few questions.

So, keeping with the goal of 20% SB and 80% FP, would that mean there would only be 1200 FP available during a given hour? If all 1200 show up at the ride at the same time, i.e. the beginning of the FP window, wouldn't you go back to the 60 min wait for those who are a few minutes behind the rush? I would think they would have to start staggering the windows. Staying with your fake numbers, 200 FP for 1:00-2:00, 200 for 1:10-2:10...oh wait a minute, now we're in the next hour, so how do we get only 1200 in that hour?

I knew my math wouldn't keep up.

 

[surferdave]

I'm afraid your basic premise (and opening example) is flawed. FP+ lines move more slowly because of the time it takes to scan the bands with the orbs. This becomes the limiting throughput factor for many rides when a FP+ line backs up and has priority over the SB line.

This means that (1) you can have both fewer fastpasses and longer fastpass lines, because FP+ take longer to process than FP-, and (2) the throughput of attractions is not the same whether the riders are fastpass riders or standby riders.

 

[seashoreCM]

Scanning of the wristbands is not the limiting factor. The Fastpass (plus) queue areas have been filling up solidly all the way to the outside and beyond.

The problem is that the system is inherently sensitive to bunched arrivals and consequent delays if the number of fastpasses issued is close to the number of fastpasses that can be accepted during the time period in question.

I am guessing that issuing fastpasses to use about 60% of the ride capacity each hour (perhaps broken down by 5 to 10 minute intevals)_ while accepting fastpasses up to 85% of the ride capacity every 5 minutes will give acceptable results (except after parades) although I have not taken any classes in queuing theory.

Oh, by the way, if scanning of wristbands does impact the movement of the fastpass queue adversely then it would not be necessary to meter the merge point between fastpass and standby. Letting fastpass riders have absolute priority at that junction would then never reach the maximum fastpass to standby ratio scheduled for that time of day.

Disney hints: http://www.cockam.com/fastsave.htm

 

[CassieF]

I have a feeling I'm not quite up to the math here, but I do have a few questions.

So, keeping with the goal of 20% SB and 80% FP, would that mean there would only be 1200 FP available during a given hour? If all 1200 show up at the ride at the same time, i.e. the beginning of the FP window, wouldn't you go back to the 60 min wait for those who are a few minutes behind the rush? I would think they would have to start staggering the windows. Staying with your fake numbers, 200 FP for 1:00-2:00, 200 for 1:10-2:10...oh wait a minute, now we're in the next hour, so how do we get only 1200 in that hour?

I knew my math wouldn't keep up.

You are on the right track, only you'd have to make the return windows smaller. So, instead of 1200-100, 1210-110 you would have the first 200 at 1200-1210, second at 1210-1220, etc.

 

[Silock]

Putting most of the math aside, and how complicated it gets when you have bunched arrivals instead of a steady stream of people--

I don't really care if the new system reduces my wait time drastically if I only get to ride three rides. Even if they double the FPs and give me six FPs, only six attractions in a day isn't worth the price of admission.

 

[clsteve]

I'd like to start a thread that looks at FP+ from a purely logical, mathematical standpoint because I'm sure that is how the Disney team is looking at it.

but with everyone having instant access to the great fastpass system in the sky through the cell phones that they are all carrying, you CAN achieve a world of "all fastpass, all the time".

I think you hit the problem right from the start and are absolutely correct, from a purely logical and mathematical standpoint- as is Disney.

But, people don't react to models in purely logical and mathematical ways- as we are seeing. There are too many variables in play: language barriers, infrastructure issues, each individual's tech-savviness, CM ability, ergonomics, herd mentality and crowd theory, heck, even weather.

There's no doubt that the models looked amazing on the drawing boards and white boards and still do. It's those pesky guests that keep breaking them....

 

[sharonabe]

Putting most of the math aside, and how complicated it gets when you have bunched arrivals instead of a steady stream of people--

I don't really care if the new system reduces my wait time drastically if I only get to ride three rides. Even if they double the FPs and give me six FPs, only six attractions in a day isn't worth the price of admission.

You can ride more than the number of FPs you have. FP just lets you ride those three with little wait. We are one of those families that only used 3 or 4 FP- in a day, but we rode more than those 3 or 4.

 

[DisneyAllyC]

I hate math

 

[Shaden]

You are leaving out HUGE problems.

Your potential theory only works not only if the ride capacity is filled for the entire day, but if it is filled at the exact minute they next ride (spaceship) arrives to take the next group. You would have to have FP+ return times to the minute, or the 5 minute or something. Its very possible that 80% of the people with FP+s from 12-1 show up at 12:30. in that case the last people to arrive there have about a 1 hour wait, the impact this has on the SB lines, is far worse.

Secondly, you don't account for the standby lines, or anyone who wants to ride an attraction more than once, despite the fact you suggest they will always be there, and they will be. There is, particularly on busy days, an unlimited supply of people who want to ride SB. You have no account for how this impacts lines/waits etc.

 

[Laketravis]

3 < 6

 

[kapoof]

I hate math

Me too...also I don't think the lines for some of the headlines are all that short.

 

[magicbob]

3 < 6

3=1

 

[Laketravis]

And if you want to get fancy and all with the math, the Erlang C formula used in telecom could prove useful.

Substitute "Guests" for calls and "Ride Slots" for agents/servers.

The Erlang C formula expresses the probability that an arriving customer will need to queue (as opposed to immediately being served). Erlang C assumes an infinite population of sources, which jointly offer traffic of A erlangs to N servers. However, if all the servers are busy when a request arrives from a source, the request is queued. An unlimited number of requests may be held in the queue in this way simultaneously. This formula calculates the probability of queuing offered traffic, assuming that blocked calls stay in the system until they can be handled. The Erlang C formula assumes that callers never hang up while in queue, that all calls begin and end in the same time period being considered, and that callers never try to call back after having hung up while in queue. These deficiencies make the formula predict that more agents should be used than are really needed to maintain a desired service level.

P_W = {{\frac{A^N}{N!} \frac{N}{N - A}} \over \sum_{i=0}^{N-1} \frac{A^i}{i!} + \frac{A^N}{N!} \frac{N}{N - A}}

where:
A is the total traffic offered in units of erlangs
N is the number of servers
PW is the probability that a customer has to wait for service.

It is assumed that the call arrivals can be modeled by a Poisson process and that call holding times are described by a negative exponential distribution.

 

[magicbob]

You just made my brain hurt!

 

[AmyB2006]

3 < 6

Ah, the obvious.


I'll tell you what I found interesting. I was just at Disney over Princess weekend. We showed up for our Soarin' FP at 12:27 pm. Our actual FP time was 11:40 to 12:40. There was a line of people probably 30 deep waiting about 10 feet from the actual entrance of the FP queue.

So I walked up with our bands, and our good FPs, for 12:27 pm, and started to scan and go into the queue, per the CM instructions waving me on through.

Apparently the line of people waiting had FPs that didn't start until 12:30 pm. Then a few of them started complaining... "why are they cutting the line?" "It doesn't start until 12:30". I'm like, "mine started at 11:40... have a nice day".

Two things I don't get here, why would you create and stand in a line before your actual FP time like this, and why would you confront someone "going ahead" of you if they have a valid FP? The whole point of the FP is so you can wait in line less, not more. They're waiting in line, to enter the FP queue, to wait in another line.

I think scenarios like this only add to the line problem. Did people do this before with paper FP? I never really used paper FP so I'm not sure if this was a common occurrence.

Anyway, this is what happens if everybody shows up at once for the exact time their FP starts. I know they stagger some of the times, but I think they need to stagger them more.

 

[MaryKatesMom]

There is also the psychology of the perceived value of what that FP+ cost. Meaning if it is a cold snowy night you are far less likely to use a free ticket to any event over a paid ticket.

SE is an example for us. If we felt like walking all the way through Epcot we would visit it toward the end of the day when it would have a short SB line. However, possessing a FP+ (one of only three I purchased with my ticket) I will definitely make the effort to ride the attraction. I have now made the SB line longer.

The effect FP+ has on SB lines is of great interest to me because we've done the parks so many times. There are very few rides worth the wait time.

 

[MaryKatesMom]

Ah, the obvious.


I'll tell you what I found interesting. I was just at Disney over Princess weekend. We showed up for our Soarin' FP at 12:27 pm. Our actual FP time was 11:40 to 12:40. There was a line of people probably 30 deep waiting about 10 feet from the actual entrance of the FP queue.

So I walked up with our bands, and our good FPs, for 12:27 pm, and started to scan and go into the queue, per the CM instructions waving me on through.

Apparently the line of people waiting had FPs that didn't start until 12:30 pm. Then a few of them started complaining... "why are they cutting the line?" "It doesn't start until 12:30". I'm like, "mine started at 11:40... have a nice day".

Two things I don't get here, why would you create and stand in a line before your actual FP time like this, and why would you confront someone "going ahead" of you if they have a valid FP? The whole point of the FP is so you can wait in line less, not more. They're waiting in line, to enter the FP queue, to wait in another line.

I think scenarios like this only add to the line problem. Did people do this before with paper FP? I never really used paper FP so I'm not sure if this was a common occurrence.

Anyway, this is what happens if everybody shows up at once for the exact time their FP starts. I know they stagger some of the times, but I think they need to stagger them more.

Yes this was always a problem. RnR always seemed the worst to me because you approach the FP line at only one angle.

That is the other thing I worry about. What if everything I want to do says a SB line of 60 minutes, for example but my FP time is WAAAAY on the other side of the park in 30 minutes, and who hasn't had the experience of getting in a SB line that is way off its estimated wait? What exactly can you do for 20 minutes by RnR except get something to eat?

 

[ChrisFL]

FP+, crowds, times, I think all would require a powerful computer to really calculate the advantages/disadvantages, and that still leaves out human psychology.

 

[magicbob]

Yes this was always a problem. RnR always seemed the worst to me because you approach the FP line at only one angle.

That is the other thing I worry about. What if everything I want to do says a SB line of 60 minutes, for example but my FP time is WAAAAY on the other side of the park in 30 minutes, and who hasn't had the experience of getting in a SB line that is way off its estimated wait? What exactly can you do for 20 minutes by RnR except get something to eat?

Or shop. Don't forget about shopping.

Anyone seeing the trend yet?