Counter Size and Counter Overflow

Counter Size

  • We must select counters large enough for avoiding overflow.
  • Size is 4 bits/counter suggested by Poisson approximation.
  • Average load implementing k = (ln 2)m/n counters is ln 2.
  • Probability a counter has load minimum 16:≈e-ln2(ln 2)16/16!≈6.78E-17
  • We consider 4 bits/counter for comparisons.

Counter Overflow

  • When a counter does overflow, it may be arrived at its maximum value.
  • This situation can later cause a false negative only if eventually the counter goes down to 0 when it should have remained at nonzero.
  • The expected time to this situation is very large but is something we need to keep in mind for any application that does not permit false negatives.
  • For avoiding counter overflow, its size must be sufficiently large. It was found that 4 bits per counter are sufficient.