cumlative_usage

This repository contains a Python script that models the cumulative cloud storage usage using an exponential function. The script fits an exponential model to daily usage data and plots the cumulative usage over a period of days.[default= 7 days]

Requirements

Python 3.x
NumPy
SciPy
Matplotlib

Installation

Clone the repository:

git clone https://github.com/yourusername/cumulative-cloud-storage-usage.git

Navigate to the project directory:
```
cd cumulative-cloud-storage-usage
```
Install the required packages:
```
pip install numpy scipy matplotlib
```

Usage

Run the script to see the cumulative usage plot:

python cumulative_usage_model.py

Script Overview

The script performs the following steps:

Data Preparation:

Define the number of days and daily usage.
Calculate the cumulative usage.

Model Definition:

Define the exponential model for cumulative usage.

Model Fitting:

Fit the model to the data to determine the parameters 𝐴 and 𝑘.

Plotting:

Plot the actual cumulative usage and the model's cumulative usage.

Guidance

1. Mission

Introduction

In a world overflowing with pay-as-you-go services, such as AWS, Azure, and OCI, you can probably check cumulative metrics... But wouldn’t you like to know the formulas and graphs representing cumulative usage?

(No, it's just that I thought it would make a good Qiita article, not that I always think this way... haha)

Challenge

Assume cumulative usage of 28 GB over 7 days. Set daily usage as [3, 3, 5, 2, 8, 4, 2]. The goal is to find a function that returns the following values (in GB) for the given number of days. 🐎🐎🐎

$$F(1) = 3$$

$$F(7) = 28$$

2. Mathematics

This is nonlinear. Once you realize it’s not a linear graph, using an exponential function usually works well.

Let the machine handle fitting in the nonlinear function model!🚀🚀🚀

Search for the specific values of the parameter constants (A, k) through fitting.

$$Assumption: A, k \in \mathbb{R}$$

𝐹(𝑡): The integral of daily usage 𝑓(𝑡) representing cumulative usage (GB)

$$F(t) = A \cdot e^{kt} - A$$

𝑓(𝑡): The derivative of cumulative usage

$$f(t) = A \cdot k \cdot e^{kt}$$

3. Implementation

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

# Number of days
days = np.array([1, 2, 3, 4, 5, 6, 7])
# Daily usage
daily_usage = np.array([3, 3, 5, 2, 8, 4, 2])
# Cumulative usage
cumulative_usage = np.cumsum(daily_usage)

# Cumulative usage model
def cumulative_model(t, A, k):
    return A * np.exp(k * t) - A

# Fitting
params, covariance = curve_fit(cumulative_model, days, cumulative_usage, p0=[1, 0.1])
A, k = params
print(f"A: {A}, k: {k}")

# Plotting the graph
plt.figure(figsize=(10, 6))
plt.plot(days, cumulative_usage, 'o', label='Cumulative Usage (Observed)')
plt.plot(days, cumulative_model(days, A, k), '-', label='Cumulative Usage (Model)')
plt.xlabel('Days')
plt.ylabel('Cumulative Usage (GB)')
plt.legend()
plt.title(f'Cumulative Usage Model: A={A:.2f}, k={k:.2f}')
plt.grid(True)
plt.show()

4. Results

Exponential Function Parameters (A, k)

𝐴=56.14 𝑘=0.0584 👩‍💻👩‍💻👩‍💻

$$Cumulative Usage (GB): F(t) = 56.14 \cdot e^{0.0584t} - 56.14$$

$$Daily Usage (GB): f(t) = 56.14 \cdot 0.0584 \cdot e^{0.0584t}$$

Here's what the graph looks like

It may look linear due to the small data sample, but it is a nonlinear function. 🧑‍💻🧑‍💻🧑‍💻

myon-bioinformatics/cumlative_usage