Semester Assignment Star Trek

Captain's log, stardate 47465.1

The Enterprise is trapped in a gravity well emanating from a nearby rift in the space-time continuum and is being slowly dragged into it. If we get too close to it, the ship will be destroyed. The warp engines, which we need in order to escape from the gravity well, are damaged. An engineering team is working hard to repair them, but the high levels of plasma in the engine room are very hazardous to their health. A nearby shower of antimatter particles has come within the influence of the gravity well and is moving rapidly towards us. I fear that some of the particles will hit us, causing damage to our shield. Furthermore, there is a high level of deadly Theta radiation in the space surrounding the ship. Only when our shields are at full power can they prevent this radiation from entering the ship. I have sent out a distress signal and the USS Saratoga has responded. She will arrive at our position in just four hours. We must survive until that time or repair our warp engines.
I have assembled a meeting of the senior officers to assess our situation. You can find their reports below.

Agent-based Addition
As if this was not already enough, the enemy is sending attack drones to our position that are also weakening our shield. However, our autonomous drone interceptor ship is trying to minimize their numbers.

Your assignment:

You are the Ship's Science Officer. The Captain requires a strategy for splitting the available power between the two essential tasks of recharging the shields and pulling the enterprise out of the rift. Use the ship's computer to provide the Captain with the answers he needs. Time is of the essence!
The basic time unit is minute.

As a first task you should answer the following questions under the assumption that the energy is split equally between the two systems:
(Use a fixed power distribution of 30:70 [Shields:Engines])
1. What is the probability that...
  - the Enterprise will be rescued by the USS Saratoga?
  - the engineering team will repair the warp drive?
  - the crew will die of Theta radiation poisoning?
  - the ship will be destroyed because the shield energy level has reached 0?
2. What is the average shield energy level over the whole simulation time?
3. What is the shield energy level after 2 hours?
4. How many antimatter particles will hit the shield?
5. Whats the enterprise's speed?
6. How long on average does it take to repair the warp drive?
7. How often does our interceptor ship miss a drone?
8. How many drones are destroyed successfully?
Add an interaction possibility for the user to be able to dynamically distribute the available energy between shields and engines.
Your main goal is to increase the survival probability of the crew as much as possible. Your second task is therefore to devise a strategy for splitting the energy between the two systems.

Senior officers' situation reports

Astrometric lab:

Antimatter particles will hit the shield at exponentially distributed intervals, with a mean interval of 15 minutes, starting immediately.
Each hit will drain between 5 and 10 units of energy from the shields, uniformly distributed.
The level of Theta radiation in the space around the ship is 100 units.

Ship technical specifications:

The energy output to the shields and impulse engines is 100 units.
This energy can be allocated as needed, using all of the energy for either recharging the shield or powering the impulse engines, or it can be split arbitrarily between the two systems.
The shield charging rate is proportional to the total energy allocated for this task with a proportionality constant of 0.003.
Theta radiation penetrates the shields at a rate which is proportional to the product of the difference between the current shield energy level and the maximum shield energy level and to the difference between the radiation level inside and outside the ship. The proportionality constant is 0.0002.
The maximum shield energy level is 100 units.
The ship's mass is 1 unit.

Chief Medical Officer:

Any Theta radiation which gets through the shields will increase the level of radiation inside the ship.
Because of the high levels of plasma currently in the engine room, the repair team can only spend 22 minutes at a time working there before they have to go to sick bay to be treated. After medical treatment, the engineers can return to work.
Treatment for plasma burns is carried out in two steps. There is one bed in the sickbay for each step.
The Starfleet medical database contains times for carrying out the treatment. The times are valid both for step 1 and for step 2. They are available in accompanying file SFMDB341874003.

Chief Engineer:

The repair crew consists of eight engineers. For safety reasons, they always enter and leave the engine room all togehter.
It is about 2½ hours work to repair the warp engines. The estimate is normal distributed with an standard error of 20 minutes.
The overall repair time will be longer, because the repair crew needs periodical medical treatment.

Ops.:

The radiation level inside the ship is currently 0 units.
Shields are currently at maximum.
Work on repairing the warp engine has just started.

Navigation:

The rift in the space time continuum is pulling the ship towards it. The force is inversely proportional to the square of the distance from the ship to the rift. The proportionality constant is 1.0.
The impulse engines are trying to move us away from the rift. Their force is equal to the allocated impulse engine power multiplied by 0.0001.
The ship is currently at a distance of 14.18 units from the rift.
The ship's velocity is currently 0 units/minute.

Tactical / Communications:

The USS Saratoga has been informed of our situation and is on her way. She will arrive at our position in 240 minutes.

Possible outcomes:

The ship will be destroyed if it gets closer than 0.1 units to the rift.
The ship will be destroyed if the shield level reaches 0 units.
A Theta radiation level of 90 units and above is lethal for the crew.
If the warp drive is repaired the enterprise escapes.
If the USS Saratoga arrives the crew will be saved.

Details of Attacking Drones (to be implemented using agent based modeling)

We assume that the space around the ship can be abstracted to a 2D area of 500m x 500m continuous space. All interactions between the attackers and the drone interceptor are assumed to happen within this area.

Drone Interceptor Ship Officer:

The drone interceptor ship moves with a speed of 1.5 m/s patrolling the area around the ship.
A patrol route is not defined so it can move randomly or systematically.
It can shoot at enemy attack drones that are within the attack range of 60m.
A shot hits an attack drone with a probability of 80%, destroying the attack drone.
If the shot misses the attack drone, the shot hits the shield of the Enterprise, immediately decreasing the shield level by 2.
After a shot it takes 30 seconds to recharge the weapon.

Enemy Scouting Report:

The attack drones are arriving at the ship with a rate of 20 per hour (exponentially distributed).
After arrival they randomly move around with a speed of 1m/s and attack the shield.
Therefore the shield level decreases by 0.02 times the number of attack drones at the hull per minute.
There are already 5 enemy attack drones attacking the ship.