I came up with the question of how one might optimally choose the order of drivers so as to maximize the number of consecutive points obtained. This question is similar to computing the probability of achieving a run of heads when flipping a coin some number of times, except this is a continuous time situation with changing parameters based on who is driving.
Anyway, I'm thinking of perhaps writing some python code to take a given ordering of drivers and simulate the expected number of consecutive points obtained over the entire run by using the following assumptions:
1. Shifts are 12 hours (though this could be easily modified)
2. The run lasts for the length of DB8
3. No repeated drivers at least until 6.5 days have passed
4. After a bit of research, it seems reasonable to model the probability distribution for the time before a crash for each driver as an expontential distribution
Code: Select all
F(t) = (1/beta)*exp(-t/beta)Then, for a given ordered list of drivers, I would sample times before a crash from the distribution F(t) until the sum of those times exceeds the shift time of the driver. Then proceed to the next driver in the list, and so on, until the run is over, all while keeping track of the maximum number of consecutive points obtained. Do this experiment many times (say 1000) and take the average to get the expected number of consecutive points for the given ordering of drivers.
Anyway, this is as far as I've taken this line of thinking in my head so far. Statistics is not my area of research, but I figured it was an interesting problem to think about regardless. My intuition tells me that perhaps the best ordering of drivers is to simply put them in increasing order of crash to hours driven ratios.
