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most-queue

Software package for calculation and simulation of queuing systems

2.4
pipPyPI
Maintainers
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Queueing Systems: Simulation & Numerical Methods 🔄

Queue

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

GitHub commit activity

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 NotationsDescriptionExampleTutorial
1.Ek/D/cNumerical calculation of a multi-channel system Ek/D/nlink
2.GI/M/1Solving for QS GI/M/1link
3.GI/M/cSolving for QS GI/M/clink
4.M/D/cSolving for QS M/D/clinklink
5.M/G/1Solving for QS M/G/1link
6.M/H2/cNumerical calculation of QS M/H2/c by the Takahashi-Takami method with complex parameters when approximating the serving time by the H2-distributionlinklink
7.M/M/c/rSolving for QS M/M/c/rlinklink

Queueing Systems with Priorities

#Kendall NotationsDescriptionExampleTutorial
1.M/Ph/c/PRNumerical calculation of QS M/Ph/c with 2 classes and PR - priority. Based on the approximation of busy periodslink
2.M/M/c/PRNumerical 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 distributionlink
3.M/G/1/PRCalculating QS with preemtive priorities (single-channel).linklink
4.M/G/1/NPCalculating QS with non-preemtive priorities (single-channel).linklink
5.M/G/c/PriorityCalculating QS with NP and PR (multi-channel) by method of relationlinklink

Queueing Systems with Vacations

#Kendall NotationsDescriptionExampleTutorial
1.M/H2/cNumerical calculation of the M/H2/c system with H2-warming using the Takahashi-Takami method.linklink
2.M/G/1Solving for QS M/G/1 with warm-up
3.M/Ph/cMultichannel 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 coefficientslink
4.M/M/cMultichannel 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 coefficientslink

Queueing Systems with Negative arrivals

#Kendall NotationsDescriptionExampleTutorial
1.M/G/1 RCSExact calculation of sojourn time for M/G/1 with RCS (remove customer from service) negative arrivals. Service time approximates by H2 or Gamma distributionlink
2.M/G/c RCSNumerical calculation of M/G/c with RCS negative arrivals. Service time approximates by H2 distributionlink
3.M/G/c disasterNumerical calculation of M/G/c with disaster (remove all customer from service and queue by negative arrival). Service time approximates by H2 distributionlink

Fork-Join Queueing Systems

#Kendall NotationsDescriptionExampleTutorial
1.M/M/c/Fork-JoinSolving for Fork-Join queueing systemlink
2.M/G/c/Split-JoinSolving for Split-Join queueing systemlink

Others

#Kendall NotationsDescriptionExampleTutorial
1.Mx/M/1Solving for the of Mx/M/1 QS with batch arrivallink
2.M/M/1/DSolving for M/M/1 with exponential impatiencelink
3.M/M/1/NSolving for the Engset model for M/M/1 with a finite number of sources.link
4.Queuing NetworkNumerical calculation of queuing networklink
5.Queuing Network with PrioritiesNumerical calculation of queuing network with priorities in nodeslinklink
6.Queuing Network OptimizationOptimization of queuing network transition matrixlink

🔍 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 xabarov1985@gmail.com for questions.

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