Hmmm, I think that for every environment and every situation, there exists a minimum density of pens such that the average time it takes for a someone looking for a pen is less than the amount of time before frustration sets in.
- d = minimum density of pens
- p = density of people
- v = average velocity of user
- t = mean time between pen usage
- f = time it takes for user to get frustrated
- k = konstant
d = p • k • v² / f / t
For me, I think that d is around 0.25 pens/m² in my standard environment.
Now to calculate how the probability density function relates to the pen density function and write it up in a portable document format.