Scripts
An implementation of the models in the book is available as interactive notebooks. The scripts will help students to better understand the impact of parameters
on performance characteristics, will avoid common pitfalls in the implementation,
and provide means for numerical robust and efficient implementations for researchers in the domain.
Chapter 1: Introduction
- 1.3 Handshaking protocol [ipynb]
Chapter 2: Fundamentals
Chapter 3: Stochastic Processes
- 3.2 Renewal processes [ipynb]
- 3.3 Poisson processes [ipynb]
- 3.5 Markov processes: nonstationary and stationary analysis [ipynb]
- 3.5 M(x)/M/2-1 delay-loss system [ipynb]
- 3.5 M(x)/M/K-0 loss system [ipynb]
Chapter 4: Markovian Systems
Chapter 5: Non-Markovian Systems
- 5.2 Power method for DTMC [ipynb]
- 5.3 M/GI/1-S delay-loss system: power method and Eigenvalue problem [ipynb]
- 5.4 GI/M/1 delay system: geometric approach [ipynb]
- 5.5 Model with batch service and threshold control [ipynb]
- 5.6 Kingman's approximation [ipynb]
Chapter 6: Discrete-Time Analysis
- Module DiscreteTimeAnalysis: documentation [download] [pip install discreteTimeAnalysis]
- 6.1 Recurrence time distribution [ipynb]
- 6.2 Z-Transform, DFT and convolution [ipynb]
- 6.3 GEOM(1)/GI/1 waiting time [ipynb]
- 6.4 GI/GI/1 waiting time [ipynb]
- 6.4.8 Idle time distribution [ipynb]
- 6.4 Discretized M/GI/1 queue [ipynb]
Chapter 7: Applications
Python Modules
Module DiscreteTimeAnalysis: The module provides a class for finite discrete distributions which are utilized for discrete-time analysis. For example, discrete-time GI/GI/1 systems can be analyzed with functions of the module.
- documentation
- [download]
- [pip install discreteTimeAnalysis]
- Example 6.4 GI/GI/1 waiting time [ipynb]
- Example 6.4.8 Idle time distribution [ipynb]
- Example 7.6 Overload control model [ipynb]
Module MarkovModelModule: A directed graph class for modeling continuous-time Markov chains (CTMCs) as StateTransitionGraph. This allows easy (visual) checking of Markov models, visualization as transition graph, and Markov simulation (e.g. for large models). The analysis allows symbolic computation of closed formulas, as well as efficient computation of numerical values for steady-state probabilities and probabilities in the transient phase.
- module documentation
- module download
- Example 1: M/M/n-0 loss system [ipynb] - visulization, animation, steady-state probabilities
- Example 2: M/M/1 with N-Policy (video buffer) [ipynb] - two-dimensional state space
- Example 3: M/M/1-0 loss system [ipynb] - symbolic computation, transient probabilities