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Help with Modelling a large system of probabilities
02-07-2018, 10:50 AM (This post was last modified: 02-07-2018 10:51 AM by pier4r.)
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RE: Help with Modelling a large system of probabilities
Interesting problem (how many interesting problems are posted here, and I miss the majority of them).

I learned that some can proceed by large improvements at once, I have to go very slowly, step by step.
At first I would check the real world reports, to get an idea about the success rate (being within the SLA) of each system.
Even without real world stats one could work with assumptions. I mean in the Engineering course I learned that unless we need extra precision, it is ok to know a range of values where things works (or, conversely, don't).

So you said that there are normal queries, that could be considered executed on each system independently from the others and then queries that depends on other systems.
For the first type of queries (the independ ones), you already have the solution. The probability of going over the SLA is a Bernoulli trial.
If the probability to succeed is P (assumed or computed), then to fail is (1-P). Then the SLA fails when one system fails, when two system fails, when three, etc.. then all.

This is:

\[ \sum_{n=1}^{2400} P^{2400-n} \cdot (1-P)^n \]

so the probability of succeeding is:

\[ 1 - \sum_{n=1}^{2400} P^{2400-n} \cdot (1-P)^n \]

And this is for the simple queries. For the more complicated queries, either you go through the rabbit hole of dependent variables (I myself have little ideas about those) or again: simplify unless you need that high precision (or you want to know).
So for depended queries again we need to set assumptions.
How often do they happen? Often enough that we need to care for them?
If they happen, can we model them like a chain of dependencies? Can be that one system may ask many others but each independently so the chain is at most of length 1 (longer lengths may be not so frequent)?

Wikis are great, Contribute :)
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RE: Help with Modelling a large system of probabilities - pier4r - 02-07-2018 10:50 AM

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