  Much research in the last two decades has focused on Virtual Topology
Reconfiguration (VTR) problem. However, most of the proposed methods either has
low controllability, or the analysis of a control parameter is limited to
empirical analysis. In this paper, we present a highly tunable Virtual Topology
(VT) controller. First, we analyze the controllability of two previously
proposed VTR algorithms: a heuristic method and a neural networks based method.
Then we present insights on how to transform these VTR methods to their tunable
versions. To benefit from the controllability, an optimality analysis of the
control parameter is needed. In the second part of the paper, through a
probabilistic analysis we find an optimal parameter for the neural network
based method. We validated our analysis through simulations. We propose this
highly tunable method as a new VTR algorithm.
