Mathematics of Telecommunications
Telecommunications is one of the key enabling technologies of our modern information-based society. It has completely changed our way of life during the last few decades, especially due to the widespread use of the internet. New services and real-time applications have caused a sharp increase in demand for high bitrates and availability, and the efficiency and reliability of telecommunication networks becomes more and more important. Already today, Voice over IP, Peer-to-Peer, IP-TV and Video-on-demand applications are responsible for the lion's share of internet traffic. Mobile data traffic has also grown enormously, due to new technologies such as UMTS and LTE.
A structural understanding of the underlying problems is nowadays indispensable for the planning and operation of telecommunication networks. This is enabled by mathematical optimization. New challenges raise new and ever more complex questions which might include stochastic aspects, the planning over multiple network layers, or energy efficiency.
We are providing mathematical models and solution techniques for the planning and optimization of both fixed and mobile telecommunication networks, taking various technologies and deployment strategies into account: IP, MPLS, OSPF, Ethernet, WDM, and FTTx variants, as well as GSM, UMTS, LTE, and WLAN.
To this end, we apply a wide variety of mathematical theory: Depending on the problem, game theory, graph algorithms, mixed integer programming, or stochastic models might come into play.