[Bug 1214482] Re: Not-grouping dependent packages in Phased Updates changes propability distribution for entire group of dependent packages.

[Marek Wrzosek]

Extending this Linux packages example. What if some proprietary device driver called X? This driver is not from Linux source package, but every update of Linux will cause the need of rebuilding X's deb packages. Sources are independent but deb packages of X depends on Linux's deb packages. If you change RNG's probability distribution from uniform to normal, then probability distribution will stay normal, but parameters will change (e.g. average).
You can compare this two m-files:
uniform.m:

figure(1)
hist(rand(1,100000),100,1)
for i = 2:10
 figure(i)
 hist(max(rand(i,100000)),100,1)
endfor

normal.m:

figure(1)
hist(randn(1,100000),100,1)
for i = 2:10
 figure(i)
 hist(max(randn(i,100000)),100,1)
endfor

If you combine normal distribution with seeding RNG with (source package name, update version, client-machine-id), then this will keep number of random variables to low values and combined probability distribution will be closer to normal.
In this scenario Linux's packages probability distribution will be normal (because it is independent) and X's will be like for i = 2 from 'normal.m' file. You can calculate parameters of probability distributions for dependent groups of deb packages (coming from the same source packages) using lists of installed packages from users that report bugs.

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https://bugs.launchpad.net/bugs/1214482

Title:
  Not-grouping dependent packages in Phased Updates changes propability
  distribution for entire group of dependent packages.

Status in “update-manager” package in Ubuntu:
  New

Bug description:
  I assume that you decided for uniform distribution in the random
  number generator. If group of dependent packages is installed only
  when all phased-update-percentage values (for each package) are
  smaller than the present percentage on server - it will change
  probability distribution for the whole group of packages.

  Just run this:

  figure(1)
  hist(rand(1,100000))
  for i = 2:10
  	figure(i)
  	hist(max(rand(i,100000)))
  endfor

  in octave and look at histograms for i>1 (i is the number of dependent
  packages).

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