Self-healing Troublebuster software 

When we encounter a software functionality failure or a performance issue, we troubleshoot it based on well known patterns and techniques. At the heart of these diagnosis and mitigation technique is a monitoring process and a remedial process. The monitoring process is one which we take to diagnose the health, or monitor a system based on logs and counters or get alerts/feedback from the system itself. The remedial process is one which takes corrective action based on the predetermined root causes. A set of well known causes have a corresponding resolution.  

For example, take a disk usage activity. If there is a  quota for the storage size, the activity may very well use up all the quota and software relying on the storage may  run into disk space issue. A corresponding monitoring process may alert based on the usage threshold. A suitable mitigation in this case would be to increase the storage size. 

In this practical example, much of the process mentioned is mostly manual today because they are not often encountered. However a storage provider serving the  large set of such customers may want to help automate it for their customers. So a customer can set a policy to remind theselves or a system to take the same corrective action.  

Consequently we transition from a manual process such as follows : 

 

To one that involves  

As follows: 

                                                                      

 


#geometryproblem

et P be a polygon that is convex and symmetric to some point O. Prove that for some

parallelogram R satisfying P  R we have

|R| / |P| <= sqrt(2)

where |R| and |P| denote the area of the sets R and P, respectively.
Let us draw parallelograms R1 such that the midpoints of the sides of R1 are the points on the Polygon P.
Let R2 be inner parallelogram joining the midpoints of the sides of R1
Let R3 be the smallest parallelogram bounding P that is parallel to the midpoint connectors.
R2 is a subset of R3.
An affine one-to-one maps of the plane preserves the ratios of areas of subsets of the plane. A parallelogram can be transformed to a square with an affine map.
If we take a as the side of R2 and b and c as the distances of R3 from R2,
the areas of R1, R2, R3 can be written as
|R1| = 2a^2
|R3| = (a+2b)(a+2c)
and |P| >= a^2 | 2.ab/2 + 2.ac/2 = a(a+b+c)
If we assume the contrary of the given inequality in the question and substitute the above areas, we see that we get a contradiction.
Therefore the given inequality holds.
Intuitively, we may also bound the ratio to something less than 1.5.