  We introduce the mobile server problem, inspired by current trends to move
computational tasks from cloud structures to multiple devices close to the end
user. An example for this are embedded systems in autonomous cars that
communicate in order to coordinate their actions.
  Our model is a variant of the classical Page Migration Problem. More
formally, we consider a mobile server holding a data page. The server can move
in the Euclidean space (of arbitrary dimension). In every round, requests for
data items from the page pop up at arbitrary points in the space. The requests
are served, each at a cost of the distance from the requesting point and the
server, and the mobile server may move, at a cost $D$ times the distance
traveled for some constant $D$. We assume a maximum distance $m$ the server is
allowed to move per round.
  We show that no online algorithm can achieve a competitive ratio independent
of the length of the input sequence in this setting. Hence we augment the
maximum movement distance of the online algorithms to $(1+\delta)$ times the
maximum distance of the offline solution. We provide a deterministic algorithm
which is simple to describe and works for multiple variants of our problem. The
algorithm achieves almost tight competitive ratios independent of the length of
the input sequence.
  Our Algorithm also achieves a constant competitive ratio without resource
augmentation in a variant where the distance between two consecutive requests
is restricted to a constant smaller than the limit for the server.
