## CASIMIR

### MORE ON THE CASIMIR PROGRAMME

This project fits into the Casimir programme. This is a programme, funded by NWO to intensify the exchange of knowledge between private institutions (in this case: industry) and public institutions (in this case: universities). Part of this programme is that the Casimir-researcher (in this project: Maurits de Graaf - Thales Nederland, Division Land & Joint Systems) works part-time (1 day/week) at the University of Twente (EWI � Chair: SOR). The project started on 1-1-2006 and ends on 31-12-2009.

The project goal is to maximize the lifetime of wireless networks (such as those applied for the emergency services) by reducing the energy consumption, without reducing the reliability of the network. To that order the ad-hoc networks are modelled as random graphs. This is a theoretical mathematical investigation of which the results may be applicable in products that Thales will be developing in the future.

Collaboration is important in this project. In various constellations collaborations are taking place with students and staff from the University of Twente. To put these into perspective, let us briefly sketch the network lifetime problem in a battery powered network.

## NETWORK LIFETIME PROBLEM

In a typical setting, we assume broadcast traffic that is generated by one (more generally: a subset) of the nodes. The two main variables that we consider are: (1) the settings of the transmission powers of the nodes; and (2) the set of nodes that forward the traffic on the multi-hop path from one node to its destination(s). For the first aspect, we assume the transmission powers to be variable, one aim is to reduce the transmit powers as much as possible, without losing connectivity of the network. The second aspect is the selection of relay nodes. In a multi-hop network these are the nodes on a path from the source to a destination. If there are multiple paths from a source to a destination then these can be alternated, taking into account the remaining battery capacity of the nodes, in order to maximise the network lifetime.

## RESEARCH TOPICS

The following research topics will be addressed in the programme, in collaboration with members from SOR:

- Improvement of OLSR selection method for relay nodes. In this setting we assume fixed transmit powers and aim to select relay nodes in the OLSR protocol so that the network lifetime is maximised.
- Analysis of the Minimum Spanning Tree. Given a graph, the problem is to assign transmit powers to the nodes so that the resulting graph is connected and the sum of the transmit powers is minimized. The minimum spanning tree heuristic provides a reasonably good solution for this problem. We will analyse the average case performance of this heuristic.
- Dynamic Master Selection algorithm. Suppose the network in which only one node is able to relay the traffic (the 'master radio' in a radio network). We address the problem of selecting this master and varying the transmit powers so that the lifetime of the network is maximized.
- Performance of wireless networks. Analysis of the throughput of multi-hop wireless networks, taking into account the interference that is present in such networks.