mm1cke 0.4.1

cke solver for mm1 queues

A Continuous Kolmogorov Equation (CKE) solver for M/M/1 queueing systems.

Overview

mm1cke provides a fast and accurate solver for the transient behavior of M/M/1 queues using the continuous Kolmogorov equations (CKE). It is designed for researchers and practitioners in operations research, queueing theory, and performance analysis.

Features

• Transient analysis of M/M/1 queues

• Vectorized and efficient implementation

• Outputs results as Polars DataFrames

• Easy integration with scientific Python stack

Installation

Install with pip:

pip install mm1cke

Requirements

• Python >= 3.11

• simpy >= 4.1, < 5

• matplotlib >= 3.10, < 4

• polars >= 1.30, < 4

• rich >= 14

• scipy >= 1.15

• seaborn >= 0.13

• pydantic >= 2.11

Usage Example

from mm1cke import TransientCase, solve_transient

case = TransientCase(L_0=9, λ=0.88, μ=1, ls_max=500, time_step=0.5)
probs_df = solve_transient(case)
print(probs_df)

# Calculate performance measures (mean and coefficient of variation)
from mm1cke.utils import calculate_performance_measures
plot_df = calculate_performance_measures(probs_df)
print(plot_df)

# Plotting (optional)
import seaborn as sns
import matplotlib.pyplot as plt
ax = sns.lineplot(plot_df, x="t", y="e_l_s")
plt.show()

API Reference

• mm1cke.TransientCase: Configuration for a transient M/M/1 queue case.

• mm1cke.solve_transient(case: TransientCase) -> polars.DataFrame: Solves the transient CKE for the given case.

• mm1cke.utils.calculate_performance_measures(probs_df: polars.DataFrame): Computes mean and coefficient of variation of the queue length over time.

Project Links

• Homepage: https://github.com/smz70/MM1CKE

• Bug Tracker: https://github.com/smz70/MM1CKE/issues

License

MIT License. See LICENSE file for details.