A Python package for simulating and analyzing queueing systems (QS) and networks.
- 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.
- 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.
pip install most-queueOr install from the repository:
pip install -e .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.
| # | 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 |
| # | 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 |
| # | 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 |
| # | 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 |
| # | 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 |
| # | 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 |
- Queueing theory
- Simulation
- Numerical methods
- Queueing networks
- Performance analysis
- Cloud computing
- Call center optimization
- Transportation systems
- Network traffic
- Python package
Contributions are welcome!
- Open an issue for bugs or suggestions.
- Submit a pull request for feature enhancements.
- Contact me at [email protected] for questions.