Fluid Approximation for Controlled Stochastic Networks with Delayed Dynamics

The exiting developments in communication networks within the last
20 years give rise to many challenging routing, scheduling or admission
control problems. Classical methods from queueing theory often fail to provide
adequate answers to these stochastic control problems for networks of realistic size.
Therefore,
tools like fluid or Brownian approximation were introduced to examine
stochastic networks. This thesis
develops extensions of the fluid approximation to networks with
delayed dynamics operating in a random environment. In particular,
a detailed analysis of the relation between the stochastic control
problem and its fluid analogue is given, and it is demonstrated how the
solution of the fluid problem can be used to gain insight into the original problem.