most-queue

Queueing Systems: Simulation & Numerical Methods 🔄

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

Most-Queue 2.0 Release Notes

• New similar API for both simulation and calculation classes:

# ... initialize NUM_OF_CHANNELS and other parameters ...

# run calculation
tt = MGnCalc(n=NUM_OF_CHANNELS)

tt.set_sources(l=ARRIVAL_RATE)
tt.set_servers(b=b)

calc_results = tt.run()

# run simulation
qs = QsSim(NUM_OF_CHANNELS)

qs.set_sources(ARRIVAL_RATE, "M")
qs.set_servers(gamma_params, "Gamma")

sim_results = qs.run(NUM_OF_JOBS)

See more examples in tests and tutorials folders.

• Refactored code for better readability and maintainability.

🔍 Key Features

• Simulation: Model various types of queueing systems and networks.
• Numerical Methods: Solve steady-state problems in queueing theory.
• Performance Metrics: Analyze waiting times, sojourn times, load factors, and more.

📌 Use Cases

• Cloud Computing: Model infrastructure scalability and performance.
• Call Centers: Optimize staffing and customer wait times.
• Transportation: Improve traffic flow and logistics.
• Network Traffic: Analyze and predict data flow patterns.

📦 Installation

  pip install most-queue

Or install from the repository:

  pip install -e .

📚 Project Overview

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.

🧪 Example Use Cases

FIFO Queueing Systems

#	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

Queueing Systems 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/G/1/PR	Calculating QS with preemtive priorities (single-channel).	link	link
4.	M/G/1/NP	Calculating QS with non-preemtive priorities (single-channel).	link	link
5.	M/G/c/Priority	Calculating QS with NP and PR (multi-channel) by method of relation	link	link

Queueing Systems with Vacations

#	Kendall Notations	Description	Example	Tutorial
1.	M/H2/c	Numerical calculation of the M/H2/c system with H2-warming using the Takahashi-Takami 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

Queueing Systems with Negative arrivals

#	Kendall Notations	Description	Example	Tutorial
1.	M/G/1 RCS	Exact calculation of sojourn time for M/G/1 with RCS (remove customer from service) negative arrivals. Service time approximates by H2 or Gamma distribution	link
2.	M/G/c RCS	Numerical calculation of M/G/c with RCS negative arrivals. Service time approximates by H2 distribution	link
3.	M/G/c disaster	Numerical calculation of M/G/c with disaster (remove all customer from service and queue by negative arrival). Service time approximates by H2 distribution	link

Fork-Join Queueing Systems

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

Others

#	Kendall Notations	Description	Example	Tutorial
1.	Mx/M/1	Solving for the of Mx/M/1 QS with batch arrival	link
2.	M/M/1/D	Solving for M/M/1 with exponential impatience	link
3.	M/M/1/N	Solving for the Engset model for M/M/1 with a finite number of sources.	link
4.	Queuing Network	Numerical calculation of queuing network	link
5.	Queuing Network with Priorities	Numerical calculation of queuing network with priorities in nodes	link	link
6.	Queuing Network Optimization	Optimization of queuing network transition matrix	link

🔍 Search & Indexing Keywords

• Queueing theory
• Simulation
• Numerical methods
• Queueing networks
• Performance analysis
• Cloud computing
• Call center optimization
• Transportation systems
• Network traffic
• Python package

📁 Examples & Tutorials

• Look tests for examples with comparison of theoretical and simulation results.
• Look tutorials for jupyter tutorials

👥 Contributing

Contributions are welcome!

• Open an issue for bugs or suggestions.
• Submit a pull request for feature enhancements.
• Contact me at [e-mail] for questions.