## Worst Case Mobility in Ad Hoc Networks

Christian Schindelhauer, Tamás Lukovszki, Stefan Rührup, Klaus
Volbert

#### Abstract

We investigate distributed algorithms for mobile ad hoc networks for
moving radio stations in a worst case scenario. We consider two models
to find a reasonable restriction on the worst-case mobility. In the
pedestrian model we assume a maximum speed *v*_{max} of the radio
station, while in the vehicular model we assume a maximum
acceleration *a*_{max} of the points.

Our goal is to maintain persistent routes with nice network
properties like hop-distance, energy-consumption, congestions and
number of interferences. A route is persistent, if we can guarantee
that all edges of this route can be uphold for a given time span
*Delta*, which is a parameter denoting the minimum time the mobile
networks needs to adopt changes, i.e. update routing tables, change
directory entrees, etc.

We present distributed algorithms based on a gird clustering
technique and a high-dimensional representation of the dynamical
start situation. We measure the optimality of the output of our
algorithm by comparing it with the optimal choice of persistent
routes under the same circumstances with respect to pedestrian or
vehicular worst-case movements.