  With the simultaneous rise of energy costs and demand for cloud computing,
efficient control of data centers becomes crucial. In the data center control
problem, one needs to plan at every time step how many servers to switch on or
off in order to meet stochastic job arrivals while trying to minimize
electricity consumption. This problem becomes particularly challenging when
servers can be of various types and jobs from different classes can only be
served by certain types of server, as it is often the case in real data
centers. We model this problem as a robust Markov Decision Process (i.e., the
transition function is not assumed to be known precisely). We give sufficient
conditions (which seem to be reasonable and satisfied in practice) guaranteeing
that an optimal threshold policy exists. This property can then be exploited in
the design of an efficient solving method, which we provide. Finally, we
present some experimental results demonstrating the practicability of our
approach and compare with a previous related approach based on model predictive
control.
