Distributed storage monte-carlo simuation

A monte-carlo simulation to model failures in a distributed storage system.

Math StackExchange question: https://math.stackexchange.com/q/3217875/31502

In broad strokes, the simulation proceeds as follows:

Partition NUM_MACHINES into NUM_PARTITIONS separate groups. This simulation uses partition to refer to separate groups instead of cell used by the math StackExchange question.
Uniformly distribute NUM_DATA pieces of data to all subsets of machines such that:
1. Every subset of machines reside in the same partition.
2. Every subset has exactly a size of NUM_REPLICAS.
Generate machine failure start times pulling samples from an exponential distribution.
Get the cumulative sum of the failure times to generate subsequent failure times for a machine. Meaning, turn [1, 3, 2, 7] into [1, 4, 6, 13].
Create an outage for a machine by adding the time to repair to the failure start time. The time to repair is drawn from a normal distribution.
Find all outages where N machines are down at the same time. This is an outage clique. When N == NUM_REPLICAS, this means we might have an outage for some subset of data.
Find all outage cliques where each machine in the clique hosts the same piece of data. The found cliques mean some data is completely unavailable.
Display the outage cliques start time, duration, and machines in the clique.

Running the simulation:

git clone https://github.com/jschaf/cellarch.git
cd cellarch

# Create a venv dir in the cellarch dir.
python3 -m venv venv
source venv/bin/activate

# Verify the venv python is used.
which python

pip install -r requirements.txt 

# Run it
python montecarlo.py