  Azure (the cloud service provided by Microsoft) is composed of physical
computing units which are called nodes. These nodes are controlled by a
software component called Fabric Controller (FC), which can consider the nodes
to be in one of many different states such as Ready, Unhealthy, Booting, etc.
Some of these states correspond to a node being unresponsive to FCs requests.
When a node goes unresponsive for more than a set threshold, FC intervenes and
reboots the node. We minimized the downtime caused by the intervention
threshold when a node switches to the Unhealthy state by fitting various
heavy-tail probability distributions. We consider using features of the node to
customize the organic recovery model to the individual nodes that go unhealthy.
This regression approach allows us to use information about the node like
hardware, software versions, historical performance indicators, etc. to inform
the organic recovery model and hence the optimal threshold. In another
direction, we consider generalizing this to an arbitrary number of thresholds
within the node state machine (or Markov chain). When the states become
intertwined in ways that different thresholds start affecting each other, we
can't simply optimize each of them in isolation. For best results, we must
consider this as an optimization problem in many variables (the number of
thresholds). We no longer have a nice closed form solution for this more
complex problem like we did with one threshold, but we can still use numerical
techniques (gradient descent) to solve it.
