FIND model

This directory provides a Python implementation of the FIND model and protocol.

The provided code allows to calculate the probability for each node in a clique to become active in any slot, the probability for any individual link to be discovered in any slot as well as the network discovery latency.

Installation

Depending on your setup, install the python package together with the requirements for the examples using

pipenv install neslab.find[examples]

or

pip install neslab.find[examples]

Usage

Instantiate the model with a uniform distribution with scale 10 and three nodes with charging times of 100, 125 and 200 that become active for the first time without an offset:

import matplotlib.pyplot as plt
from neslab.find import Model

m = Model(10, "Uniform", [100, 125, 200], offset=0)

Compute for every node the probability of being active in a slot and plot the results:

act = m.activity()
plt.plot(act[:2000])
plt.show()

Compute the cumulative distribution function (cdf) of the slot in which each of the three links between the three nodes is discovered and plot the results:

cdfs = m.cdf()
plt.plot(cdfs)
plt.show()

Compute the fraction of discovered links and plot the result:

dff = m.disco_frac()
plt.plot(dff)
plt.show()

Compute the discovery latency:

lat = m.disco_latency())
print(f"Discovery latency: {lat} slots")

Examples

We provide more involved example scripts in the examples directory:

To compare the probability of activity and the cdf of the corresponding discovery latency of two nodes with a charging time of 30 and 60 slots, using a uniform delay distribution, call

python examples/plot_example.py

To compare the discovery latency of two nodes when using different distributions across a range of their scale parameters, run

python examples/compare_dists.py

To plot the discovery latency of a clique of nodes over the node density, run

python examples/plot_density.py

To optimize the scale parameter of the geometric distribution to a range of charging times, run

python examples/optimize_scale.py

Reproduce key results

We used the code provided in this directory to gain the insights presented in section 2 of our paper. We invite you to reproduce our results with the scripts provided in the reproducibility directory. Some of the calculations take significant computing resources and require a high performance computing system with a large number of CPUs.