Queuing Theory

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ver stand in a long line waiting ... waiting ... waiting? Why do we have to wait? Often, the reason is all too apparent but in some circumstances it simply isn't necessary.

Take the case of amusement parks

Here's a business that routinely cuts its own throat on any hot Saturday afternoon in the summer. There might be 12,000 people in the park and 5,000 of them are standing in hot, dusty lines getting thirsty and "pissed off" that they are offered a cool drink while trapped in line (for only $3.00 a pop).

Why are they there? Why can't they get a piece of paper saying that they are in line? ... then go somewhere else, come back when their place in line has moved up to the front, and rejoin ... or something similar.

Is there a better way?

You bet your sweet ass, lil' momma' !
    Some relevant parameters:
  • No one can be denied the right to get into line for any ride under normal operating conditions ... as many times as they want or are willing to stand for.
  • No one should be absolutely required to stand in line to get on a popular ride no matter how busy it is.
  • No business should antagonize its customeers by making them stand in line to obtain the product they have already paid for as the price of admission.
  • The amount of time that a person will tolerate standing in line (in this amusement park example) is approximately ten times longer than the duration of the ride, i.e. a 2 minute roller-coaster ride demands less than 20 minutes wait time.
Now, some of these conditions seem to contradict others but they really don't if you are willing to "innovate" (as Bill says).

This is my solution and I am aware that some real life experiment and trials are necessary to fine tune.

When a person arrives, the ticket purchased has the name of some popular ride and a time to get on - without waiting. A 15 minute window during which, if that person arrives at the ride entrance designated "Reservations" , he gets into the "short line" composed of other people who arrived at their designated window. This line is something like the wheel chair line where handicapped people get on AT ONCE with no waiting and everyone just looks on and sighs, "I sure wish ... I ... was paralyzed".

There is another line.

This other line is the standard line. Get in it if you wish and wait as long as it takes as many times as you want.

The distinction is that the reserved line is much shorter because the people arrive "just in time" (like the Japanese car manufacturing innovation).

The ride operaters load half from one line and half from the other. Thus, they both keep moving. The half and half mode is adjustable to meet whatever need arises ... like nobody in the Reservation line ... or, ride out-of-order temporarily, etc.

If you don't like the reservation given to you on arrival, you may trade it to someone else (or sell it?!) ... just whatever.


To implement this type of no-line solution, the proprietors of the park must do experimental trials on perhaps one main ride on maybe one day a week to ascertain what exact form the system should have. If found workable, expand to every day then to other rides ... gradually. It is important to ease this in slowly because the people who are not now in line will be somewhere else using their new free time to do something ... what? If they go to other less congested rides, those rides may become more congested, etc.

One must also bear in mind the time of day. You may not be able to give a late arrival the same deal as the early morning arrival (and may not need to if attendance slacks off considerably near closing time). Also, if a ride going full bore all day at peak efficiency can accomodate only 12,000 riders, you can't please everybody in principle if your attendance for the day is 20,000. But this will rarely be the case except perhaps with brand new rides. In general, not everyone even wants to get on the most popular ride, let alone actually tries to get on.

Also, there is the ever present "season ticket holder" consideration to deal with.


My view here is (based on personal experience) is that the customers will be well pleased with such an arrangement ... AND ... will be well served by the business which "doesn't make us wait".

Above is from 10-28-98

Well, here it is ... new for 2001 ... finally !

"Adding to the excitement of two new rides, Six Flags Over Georgia is actually increasing the amount of time guests can enjoy the park with its new virtual queuing technology - Fast Lane. Six Flags Over Georgia is the first U.S. theme park to implement a system that replaces long waits with a computerized "virtual line," scheduling ride times for park visitors who can then return to the ride just minutes before boarding." - from http://www.sixflags.com/georgia


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