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Simulation, Petri-net and Queuing Models

General Topic

Queuing models are based on a theoretical framework that enables the mathematical analysis of waiting lines and related service processes. The solutions are derived from Markov models for various types of queuing systems and they possess a low computational complexity. Typical computed performance measures are delay times, utilizations, mean number of jobs in the system or more general the probability of encountering the system in certain states. Queuing models have applications in diverse fields, including computer networks, traffic engineering and the design of factories, shops or offices.
A Petri-net is a graphical/mathematical modeling language for the description of distributed systems. Like industry standards such as UML activity diagrams, BPMN and EPCs, Petri nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution. Unlike these standards, Petri nets have an exact mathematical definition of their execution semantics, with a well-developed mathematical theory for process analysis (cited from Wikipedia). Performance measures for Petri-net based models can be computed via simulation and numerical methods. Typical computed performance measures are state probabilities and system throughputs. Additionally Petri-nets are offering methods for analyzing the structure and behavior of a system – Keywords in this respect are state reachability, system liveness and boundedness.
The word simulation is very ambiguous. In my case the important key words are discrete event simulation, event scheduling / process oriented simulation and Monte Carlo simulation.
In a discrete event simulation the operation of a system is represented as a chronological sequence of events. Each event changes the system state. The event scheduling simulation method directly relies on the principle of chronological events. An extension of this method is the process oriented simulation which provides advanced means of process interactions like waiting for processes and for free resources or master/slave relationships. Both methods can be used for modeling systems with a very high degree of freedom. Downsides are the computational complexity and that solutions are prone to errors due to a high implementation effort.
The Monte Carlo simulation is a stochastic numerical method based on the generation of pseudo random numbers. It is often used for simulating physical and mathematical systems when it is unfeasible or impossible to compute an exact result with a deterministic algorithm. The method can be used readily, if the domain of possible inputs is known but the generation of accurate results requires a large amount of random experiments for complex problems.

Company

Between April 2004 and August 2011 I worked as a research assistant in the research group “Systems Modelling” of the faculty of Economics and Business Administration at the University of Duisburg-Essen. The research field of our research group included modeling and performance evaluation of computer- and communication systems. Techniques used were stochastic Petri-nets, Markov chains, queuing networks and discrete event simulation. My research interests included Common Radio Resource Management (CRRM), stability analysis of communication networks and since the year 2010 optimization problems in smart grid infrastructures. My work at the university was connected to a PhD. thesis that has been supervised by Prof. Dr. Bruno Müller-Clostermann.

Task

During my work at the University of Duisburg-Essen I took care for several different tutorial courses for lectures given by Prof. Dr. Bruno Müller-Clostermann. My responsibilities included not only the giving of tutorials but also the arrangement of instructors and rooms as well as the preparation of exercise materials and online courses. Additionally I have supervised several seminars, project works and B.Sc./M.Sc. theses. Please see this link for information on my research activities.

Gained Experience

Because of the teaching of fundamentals courses for models used in computer science I have gained a comprehensive overview on topics like formal languages, state machines, mathematical logic and graph theory. Furthermore, the teaching of advanced courses has deepened my theoretical knowledge in generalized stochastic Petri-nets, queuing models, Marcov models and simulation methods. The responsibility for online courses and for the arrangement and quality control of up to 15 parallel tutorial courses per term as well as the supervision of project works and theses has developed my time management and organizational skills. I have attended several voluntary qualification courses to further enhance my skills in different areas. Among several English language trainings I also have completed the university didactics certificate (which includes theoretical and practical aspects of didactics, time management, group dynamics and communication) and I have attended general knowledge seminars like vocal training, conflict management training, project management training and others.

Please see my curriculum vitae for a complete list of my qualifications and tool experiences and see the publications section for a list of supervised theses.