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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 the subject of simulation

Generation of uniformly distributed random numbers

Random numbers form the basis for many (stochastic) simulations. With the help of the linear congruential generator, pseudo-random numbers that are evenly…

Dice roll simulator

The dice simulator allows you to see how the measured mean values slowly stabilize against the theoretical expected values.

(Counting) densities of certain distributions

This web app allows you to generate measured values according to specific distributions and compare the histograms with the theoretical (count) densities.

Simulation of a homogeneous Markov chain (in discrete time)

This web app allows you to examine the behavior of a discrete-time Markov chain with up to 6 states.

Simulation of a homogeneous Markov chain (in continuous time)

In continuous-time Markov chains, transitions can occur at any time. Therefore, transitions must be defined in terms of rates.

Simulation of a M/G/1 queue

This web app displays the chronological progression of the number of customers in the system in an M/G/1 model.

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

Open source Java application for modeling and simulating complex queueing networks

Call center simulator

Open source Java application for analyzing and optimizing complex call center networks consisting of several sub-call centers and several caller groups

Mini call center simulator

Open source Java application for simulating simple queueing models

Mini Queueing Simulator

Open source web application for modeling and simulating queueing networks

G/G/c/K+G Simulator

Open source web app for simulating G/G/c/K+G queueing models

Queueing Calculator

Open source web application for calculating the parameters of various queueing models (Erlang-B, Erlang-C, Pollaczek-Chintschin, Allen-Cunneen)

QueueSim (Python)

Open source Python library (including examples in the form of Jupyter notebooks) for creating simulation models in Python

Literature

Simulation with the queue simulator - Mathematical modeling and simulation of production and…

A. Herzog, Springer, 2021

Call center analysis and management: Modeling and optimization with queuing systems

A. Herzog, Springer, 2017