How can we measure Fragmentation/ discontinuity in a system?
We can count number and types of discontinuities. Also the fractal dimension might be useful in a sense that it's definitions / techniques might be adaptable.
It depends exactly what you mean by "fragmentation in system" - but one simple formula you could use would be:
(free - freemax)
---------------- x 100% (or 100% for free=0)
free = total number of bytes free
freemax = size of largest free block
That way, if all memory is in one big block, the fragmentation is 0%, and if memory is all carved up into hundreds of tiny blocks, it will be close to 100%.
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