Going Rogue Waiting for Palin

(Posted 12/05/2009, edited 12/06/2009)

Just How Long Does One have to wait in Line to Get Their “Going Rouge” book signed?

A few thoughts:

Consider a Problem, likely a differential equation with:

Boundary Condition1: At some time, the number of people in line equals zero
(edit(12/06/2009): Actually the time is unknown. We want to know this to answer the just how long does one have to wait problem. )
Boundary Condition2: At some later time, the number of people in line equals zero
(edit(12/06/2009): this is not really what we wanted to know, but it might be helpful if we wanted to model part 3 (see below))

**edit(12/06/2009) These two edits may mess up the boundary conditions somewhat. It looks like we might have to look at boundary conditions. Data gathering would be most appropriate, but would be cumbersome if it had to be done for each time the model is run (say the the famous person is changed). This would sort of defeat the purpose if the model was to be universal, and not require a whole lot of input and effort. I am thinking about statistics and using a normal variate somewhere (even for the mean of something), but I don't know how to do that off the top of my head. I think it might be doable, it might just take a little time. This sounds like a tough problem.

Solve this as a 3 part problem :

Part1: For the time before 7pm Thursday when the line is forming. Consider the rate of people joining per unit time. The line forms when the rate is zero. The rate may peak at some point.
Notes: This would depend on the population density about the location, the mobility of the population to Hastings (given obstacles such as traffic, road layout etc.), the proportion of people in the region that would go see Sarah Palin, and how crazy people are (i.e. what they perceive is a good time to go) which could depend on the popularity of Sarah Palin. The region’s boundaries would have to be defined as a point where the density of people going to see Sarah Palin would drop below a certain level. I suspect this may be modeled using catalytic reactor theory, and/or theory used by industrial engineers and concert organizers. (Suspected Keywords that come to mind: Catalytic Reactor, Industrial Engineering, Statistics, {Barnum and Bailey Circus, LiveNation, various production companies (theater, concert), The Walt Disney Company, Six Flags} (or at least people who consult for them), UPS, Wal-Mart, Mathematicians) Consider effects like mobile devices, and their dispersal of information that could discourage people from joining the line.

Part2: For the time between 7pm and the time when all the wristbands have been passed out.
Notes:
It is suspected that People will leave the line while additional People that will join the line after 7pm. Consider effects like mobile devices, and their dispersal of information that could discourage people from joining the line.

Part3: Time at which all the wristbands are all passed out, and people begin to leave.
Notes: This is a dispersion type problem. People may find out that the wristbands are gone in a manner like wave propogation, which could be much faster than a walk or a run. Consider effects like mobile devices, and their dispersal of information.