Markoff chains, call centers and Google's PageRank: on the theory and applications of matrices

This training course will show that matrices are used both in mathematical theory and in current practical applications. First, matrices are considered as mathematical objects in their own right. Elementary properties will be recalled, but some more complex questions will also be addressed.

Matrices can be used to model random movements (Markoff chains). The long-term behavior of these processes can be predicted or controlled from properties of the matrix.

Markoff chains in turn play a role in so-called page ranking, which Google, for example, uses to determine which pages are 'at the top' in Internet searches. The resulting matrices and other interesting details of this process are presented.

Call centers are playing a growing role in business and services, even if we as consumers don't always like it. Markoff chains are used here to model the formation and reduction of queues and to calculate waiting times.

Program

Materials

• Presentation by Dr. Pralle
• Lecture by Prof. Kolonko
• Collection of applets for the lecture by Prof. Kolonko
• Lecture by Dr. Sandmann
• Lecture by Dr. Herzog (slides)
• Lecture by Dr. Herzog (handout)