Scripts

• 1.3 Handshaking protocol [ipynb]

• 2.1 Little's law [ipynb]
• 2.2 Two-dimensional random variables [ipynb]
• 2.3 Transform methods [ipynb]
• 2.4 Mixture distribution [ipynb]
• 2.4 Discrete random variable and convolution [ipynb]

• 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]

• 4.1 M/M/n-0 loss system: Erlang-B formula [ipynb]
• 4.2 M/M/n delay system: Erlang-C formula [ipynb]
• 4.3 Engset model and Engset formula [ipynb]
• 4.4 Customer retrial model [ipynb]
• 4.5 M/M/1/K-PS processor sharing system [ipynb]
• State transition diagram to Markov model [ipynb]

• 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]

• 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]

• 7.1 Video streaming QoE [ipynb]
• 7.3 M/D/1 vs. nD/D/1 [ipynb]
• 7.4 Energy efficiency of IoT and Kleinrock's power metric [ipynb]
• 7.6 Overload control model [ipynb]

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