Wolfgang König

Benedikt Jahnel, Paul Keeler

Christina van de Sand

Members of the group from left to right: Wolfgang König, Robert Patterson, Paul Keeler, Benedikt Jahnel

Present day telecommunication networks are ill equipped for the rapidly growing demand for mobile data transfers. With the fifth generation of mobile networks, paradigmatic shifts in the design of the network are on the agenda. A critical aspect here is the role of infrastructure. Multilayered cellular networks with possible incorporation of relaying mechanisms are under investigation not only in the scientific community, but also in industry. All these new designs have in common a rapid increase of degrees of freedom in the system. The central role of (expensive) base stations is reduced in favour of an increasingly important rôle of (cheap) relays. In particular, also the users of the system will be attached a relay functionality in the system. As a result, the network becomes more and more decentralised. First implementations of peer-to-peer (P2P) communications for public use are already available. Exploring the possible benefits of such new architectures is in full swing in the academic and the industrial research.

One promising way to cope with the new and more complex structures that arise is to exploit probabilistic methods. Indeed, fundamental ansatzes from stochastic geometry (e.g., spatial Poisson processes, continuum percolation theory, ...) are widely used for modelling the spatial locations of the users, the relays and the base stations and their basic connectivity properties. For the description of temporal developments, standard methods from stochastic processes (stochastic interacting particle processes like bootstrap percolation or the contact process) are commonly used to model the spread of information through a network.

Contribution of the Institute

The WIAS has performed mathematical research on connectivity and capacity problems in mobile relay-augmented probabilistic models over a period of four years within the Leibniz Group "Probabilistic methods for mobile ad-hoc networks" together with the Leibniz-Institute "Innovations for High Performance Microelectronics" (IHP) and in other collaborations. Its expertise includes dynamic modelling of message propagation in dense networks, bottleneck behaviour in Device-to-Device (D2D) systems, connection times in large networks without infrastructure and wifi-augmented mobil urban communications models.
Metropolitan street system with random users and additional boxes
Fig1. - Metropolitan street system with random users and additional relay boxes.


One of the highlights of the past years is an industry collaboration with a large European telecommunications company with the goal to better understand large scale D2D networks build on realistic street models.

Drainage network
Fig2. - Directed drainage network in a single cell.