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.