Simulation

In many cases, practical problems are mathematically so complex that they cannot (yet) be solved analytically. In these cases, event-oriented stochastic simulation is used, which in principle can be used to investigate any stochastic problems. However, complex problems can sometimes lead to very long simulation runtimes, which limits the usefulness of the results, especially if the simulation has to be repeated many times as part of an optimization.

Interactive pages on integration simulation

Generating of uniformly distributed random numbers

Generating of uniformly distributed random numbers

The basis for many (stochastic) simulations are random numbers. With the help of the linear congruence generator, equally distributed pseudo-random numbers can be generated on an interval.

Dice roll simulator

Dice roll simulator

The dice roll simulator can be used to try out how the measured mean values slowly stabilize against the theoretical expected values.

(Counting) densities of certain distributions

(Counting) densities of certain distributions

This webapp allows to generate measured values according to certain distributions and to compare the histograms with the theoretical (count) densities.

Simulation of a homogeneous Markov chain (in discrete time)

Simulation of a homogeneous Markov chain (in discrete time)

In this webapp, the behavior of a discrete-time Markov chain with up to 6 states can be studied.

Simulation of a homogeneous Markov chain (in continuous time)

Simulation of a homogeneous Markov chain (in continuous time)

For continuous-time Markov chains, transitions can occur at any time. Therefore, the definition of the transitions must be done via rates.

Simulation of a M/G/1 queue

Simulation of a M/G/1 queue

In dieser Webapp wird der zeitliche Verlauf der Anzahl an Kunden im System in einem M/G/1-Modell dargestellt.

Simulation software

TU Clausthal offers a number of simulation programs via the Simulation Science Center. All of these are open source programs that can be used free of charge:

Queueing Simulator

Queueing Simulator

Opensource Java application for modeling and simulation of complex queueing networks

Callcenter Simulator

Callcenter Simulator

Opensource Java application for analysis and optimization of complex call center networks consisting of several sub-call centers and several caller groups

Mini Callcenter Simulator

Mini Callcenter Simulator

Opensource Java application for simulation of simple queueing models

Mini Queueing Simulator

Mini Queueing Simulator

Opensource webapp for modeling and simulation of queueing networks

G/G/c/K+G Simulator

G/G/c/K+G Simulator

Opensource webapp for simulation of G/G/c/K+G queue models

Queueing Calculator

Queueing Calculator

Opensource webapp for calculating the characteristics of different queue models (Erlang-B, Erlang-C, Pollaczek-Chintschin, Allen-Cunneen)

QueueSim (Python)

QueueSim (Python)

Opensource Python library (incl. examples in the form of Jupyter notebooks) for creating simulation models in Python

Literature

Simulation mit dem Warteschlangensimulator - Mathematische Modellierung und Simulation von Produktions- und Logistikprozessen
Einband des Buches Simulation mit dem Warteschlangensimulator

Simulation mit dem Warteschlangensimulator - Mathematische Modellierung und Simulation von Produktions- und Logistikprozessen

A. Herzog, Springer, 2021 (in German language)

Callcenter-Analyse und -Management Modellierung und Optimierung mit Warteschlangensystemen
Einband des Buches Callcenter Analyse und Management

Callcenter-Analyse und -Management Modellierung und Optimierung mit Warteschlangensystemen

A. Herzog, Springer, 2017 (in German language)