Numerical Calculation of Multichannel Queues with Warm-Up, Cooling and Delay in Cooling Start

Overview

This repository contains numerical calculations and simulation code for multichannel queue systems with:

• Vacation periods (warm-up, cooling)
• Delayed cooling start
• Different service time distributions

Abstract:

A method is proposed for obtaining probabilities of states, initial moments of waiting and sojourn times of applications in a multi-channel queueing system with hyperexponential service times, warm-up, cooling, and delay before cooling starts. The parameters of the hyperexponential distribution are generally complex, which allows setting arbitrary variation coefficients of the specified distributions (including less than one). Numerical calculation results are presented in comparison with simulation modeling results, confirming the high accuracy and correctness of the proposed solution.

Paper Reference

PDF | DOI

Requirements

💻 Python 3.8+

• Dependencies in requirements.txt

Installation

git clone https://github.com/username/repo.git
cd repo
pip install -r requirements.txt

Usage

Main Scripts

Compare Calculations vs Simulations

python run_one_calc_vs_sim.py 

Waiting Time Analysis

🚀 Run all calculations and simulations with base_parameters.yaml parameters:

python main.py 

All results are saved in the results directory with 'exp_' prefix.

Find Best Cooling Delay

🥇 Optimize cooling delay for a given set of parameters and utilization factor: look at the script find_best_delay.py for more details on

Results

📊 Visualizations and quantitative results in results/ directory.

Contributing

1. Fork repository :git:
2. Create issue before changes
3. Pull requests welcome!

Issues

Report bugs, request features or ask questions in Issues.

License

📄 MIT License

Related Repositories

🔗 Check out related projects:

• Queueing Systems: Simulation & Numerical Methods