# Optimal Frequency Homework: Maximizing Air/Ground Queues

• zzmanzz
In summary, the conversation discusses how to maximize the thresholds for air and ground queues while keeping the constraint of no more than one plane in each queue at the end of a 10 second loop. It is suggested to use a simulation to find the maximum thresholds, as it may be difficult to mathematically link the thresholds to the queues. However, it is noted that maintaining the constraint with 100% certainty may not be possible, and the weight given to each threshold in terms of "maximizing both" is unclear.
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]

A simulation is probably faster.

zzmanzz said:
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"?

## 1. What is the purpose of "Optimal Frequency Homework"?

The purpose of "Optimal Frequency Homework" is to find the best frequency for air and ground queues, in order to maximize their efficiency. This can help reduce wait times, increase throughput, and improve overall operations.

## 2. How is the optimal frequency determined?

The optimal frequency is determined through mathematical calculations and simulations. Factors such as queue length, arrival rate, and service rate are taken into account to find the frequency that will result in the most efficient use of resources.

## 3. What are the benefits of using "Optimal Frequency Homework"?

The benefits of using "Optimal Frequency Homework" include reduced wait times for customers, increased efficiency of operations, and improved utilization of resources. This can ultimately lead to cost savings and improved customer satisfaction.

## 4. Can "Optimal Frequency Homework" be applied to any type of queue?

Yes, "Optimal Frequency Homework" can be applied to any type of queue, including air and ground queues. It can also be applied to different industries such as transportation, healthcare, and retail.

## 5. How often should "Optimal Frequency Homework" be conducted?

The frequency of conducting "Optimal Frequency Homework" will depend on the specific industry and operations. It is recommended to periodically review and update the optimal frequency to ensure that it is still providing the most efficient results.

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