Optimal Frequency Homework: Maximizing Air/Ground Queues

[zzmanzz]

Homework Statement

I want to apologize in advance as there are a few steps in this problem.[/B]
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.

Homework Equations

We are given

p = m/n (p = probability, m = planes, n = time.[/B]

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[/B]

 

[mfb]

A simulation is probably faster.

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

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