Computing Jobs

Swan Job Growth Model Specification

1. Introduction

Swan's decentralized computing ecosystem is built upon a foundation of job growth and management. This document outlines the mathematical model used to predict and understand the growth of jobs within the Swan platform. The model takes into account the natural growth of jobs and the influence of incentives provided to job creators. Furthermore, it emphasizes the significance of Swan jobs in the overall system.

2. Importance of Swan Jobs for the System

Swan jobs serve as the backbone of the decentralized computing ecosystem. They play a pivotal role in the following ways:

• Revenue Generation for Providers: Swan jobs are a primary source of income for providers. As more jobs are placed and executed, providers earn more, ensuring their active participation and commitment to the platform.

• Revenue Stream for Swan: While Swan supports and incentivizes job creators, it also benefits by earning a fraction from the job placements. This revenue is essential for the sustenance and further development of the platform.

• Foundation of the Ecosystem: Jobs are the core transactions in Swan's decentralized computing ecosystem. They drive the interactions between creators and providers, ensuring a dynamic and thriving community.

• Incentive for Quality and Growth: The matching incentives provided by Swan not only encourage more job placements but also ensure the quality of jobs. This dual benefit ensures a healthy growth trajectory for the platform.

3. Components of the Model

3.1 Initial Jobs Growth (Logistic Growth Curve)

The logistic growth curve models the natural growth of jobs without any external incentives.

Equation:

$$J_{initial}(x) = \frac{L_{initial}}{1 + e^{-k_{initial} \times (x - x_{0_{initial}})}}$$

3.2 Jobs from Incentive (Exponential Decay)

This component models the jobs created due to incentives provided by the platform.

Equation:

$$J_{incentive}(x) = a \times e^{b \times J_{initial}(x)}$$

3.3 Total Jobs

The total number of jobs is the sum of the initial jobs and the jobs from incentives, capped at a maximum capacity.

Equation:

$$J_{total}(x) = min(J_{initial}(x) + J_{incentive}(x), capacity)$$

4. Simulation Code

import numpy as np
import matplotlib.pyplot as plt

# Parameters
L_initial = 80  # Carrying capacity for initial jobs
k_initial = 0.1  # Growth rate for initial jobs
x_0_initial = 50  # Midpoint of the growth curve
a = 40  # Maximum possible number of jobs from incentives
b = -0.05  # Decay rate
capacity = 120  # Maximum number of jobs allowed

# Simulation
x = np.linspace(0, 200, 400)
J_initial = L_initial / (1 + np.exp(-k_initial * (x - x_0_initial)))
J_incentive = a * np.exp(b * J_initial)
J_total = np.minimum(J_initial + J_incentive, capacity)

# Plot
plt.figure(figsize=(10, 6))
plt.plot(x, J_initial, label="Initial Jobs")
plt.plot(x, J_incentive, label="Jobs from Incentive")
plt.plot(x, J_total, label="Total Jobs", linestyle='--')
plt.xlabel("Time")
plt.ylabel("Number of Jobs")
plt.title("Swan Job Growth Model")
plt.legend()
plt.grid(True)
plt.show()

5. Conclusion

The Swan Job Growth Model provides a comprehensive framework to understand, predict, and manage the growth of jobs on the platform. By emphasizing the importance of Swan jobs in the ecosystem, it underscores the platform's potential for both job creators and providers. The model, combined with the platform's strategic incentives, ensures a sustainable and prosperous decentralized computing ecosystem.