Queueing Systems: Simulation & Numerical Methods

A Python package for simulating and analyzing queueing systems (QS) and networks.

About

This repository focuses on solving steady-state problems in queueing theory.

Key Features:

• Simulate various types of queueing systems and networks.
• Numerical methods for solving queueing theory problems.
• Analyze system performance metrics such as waiting times, soujourn times, load factor and etc.

Use Cases

• Modeling cloud computing infrastructure.
• Designing efficient call centers.
• Optimizing transportation systems.
• Network traffic analysis.

Contributing

Contributions are welcome! If you find any issues or have suggestions, please open an issue. Your pull requests are also appreciated. You can write me at [email protected]

---

Installation

Install most-queue with pip

  pip install most-queue

---

Description of the Project

Most_queue consists of two main parts:

• most_queue.theory contains programs that implement methods for calculating queueing theory models.
• most_queue.sim contains simulation programs.

See examples in the tests folder:

FIFO QS

#	Kendall Notations	Description	Example	Tutorial
1.	Ek/D/c	Numerical calculation of a multi-channel system Ek/D/n	link
2.	GI/M/1	Solving for QS GI/M/1	link
3.	GI/M/c	Solving for QS GI/M/c	link
4.	M/D/c	Solving for QS M/D/c	link	link
5.	M/G/1	Solving for QS M/G/1	link
6.	M/H2/c	Numerical calculation of QS M/H2/c by the Takahashi-Takami method with complex parameters when approximating the serving time by the H2-distribution	link	link
7.	M/M/c/r	Solving for QS M/M/c/r	link	link

QS with priorities

#	Kendall Notations	Description	Example	Tutorial
1.	M/Ph/c/PR	Numerical calculation of QS M/Ph/c with 2 classes and PR - priority. Based on the approximation of busy periods	link
2.	M/M/c/PR	Numerical calculation of QS M/M/c with 2 classes, PR - priority by the Takahashi-Takami numerical method based on the approximation of the busy period by the Cox distribution	link
3.	M/M/c/PR	Numerical calculation of QS M/M/c with 3 classes, PR - priority by the Takahashi-Takami numerical method based on the approximation of busy period by the Cox distribution	link
4.	M/G/1/PR	Calculating QS with preemtive priorities (single-channel).	link	link
5.	M/G/1/NP	Calculating QS with non-preemtive priorities (single-channel).	link	link
6.	M/G/c/Priority	Calculating QS with NP and PR (multi-channel) by method of relation	link	link

Fork-Join QS

#	Kendall Notations	Description	Example	Tutorial
1.	M/M/c/Fork-Join	Solving for Fork-Join queueing system	link
1.	M/G/c/Split-Join	Solving for Split-Join queueing system	link

QS with Batch Arrival

#	Kendall Notations	Description	Example	Tutorial
1.	Mx/M/1	Solving for the of Mx/M/1 QS with batch arrival	link

QS with Vacations

#	Kendall Notations	Description	Example	Tutorial
1.	M/H2/c	Numerical calculation of the M/H2/c system with H2-warming using the Takahasi-Takagi method.	link	link
2.	M/G/1	Solving for QS M/G/1 with warm-up
3.	M/Ph/c	Multichannel queuing system with H2-serving time, H2-warm-up, H2-cold delay and H2-cold (vacations). The system uses complex parameters, which allows you to calculate systems with arbitrary serving, warm-up, cold-delay and cold variation coefficients	link
4.	M/M/c	Multichannel queuing system with exp serving time, H2-warm-up and H2-cold (vacations). The system uses complex parameters, which allows to calculate systems with arbitrary warm-up and cold variation coefficients	link

QS with Impatience

#	Kendall Notations	Description	Example	Tutorial
1.	M/M/1/D	Solving for M/M/1 with exponential impatience	link

Closed QS (with finite number of sources)

#	Kendall Notations	Description	Example	Tutorial
1.	M/M/1/N	Solving for the Engset model for M/M/1 with a finite number of sources.	link

Queuing Networks

#	Kendall Notations	Description	Example	Tutorial
1.	General Network	Numerical calculation of queuing network with priorities in nodes	link

Usage

• Look here for examples
• Look here for jupyter tutorials