# Optimal Frequency

1. Oct 19, 2014

### zzmanzz

1. The problem statement, all variables and given/known data

I want to apologize in advance as there are a few steps in this problem.

1.For each second, 2 planes join the air queue if randomAir1 < AirQueueThreshold and randomAir2 < AirQueueThreshold.
2. For each second, 1 plane joins a ground queue if randomGround < GroundQueueThreshold.
3. Air has priority over the ground. - that is, if both queues have 1 plane in them and runway is vacant, the one in the air lands.
4. It takes 2 seconds to land/take off.

I'm trying to maximize AirQueueThreshold and GroundQueueThreshold but keep airQueue <= 1 and GroundQueue <=1 at the end of a 10 second loop.

2. Relevant equations

We are given

p = m/n (p = probability, m = planes, n = time.

3. The attempt at a solution

is it easier just to run the simulation a bunch of times for 10 seconds and finding the maximum thresholds or is there a mathematical (straightforward) way to link the thresholds to the queues?

Thanks and sorry for any ambiguity.

Regards,
Z

2. Oct 19, 2014

### Staff: Mentor

A simulation is probably faster.

You cannot keep that constraint with 100% certainty, and how do you weight the different thresholds (and the success rate) in terms "maximize both"?