2 research outputs found
An algebraic analysis of storage fragmentation
PhD thesisStorage fragmentation, the splitting of available computer memory space
into separate gaps by allocations and deal locations of various sized blocks
with consequent loss of utilisation due to reduced ability to satisfy
reque~ts, has ~roved difficult to analyse. Most previous studies rely on
simulation, and nearly all of the few published analyses that do not, simplify
the combinatorial complexity that arises by some averaging assumption.
After a survey of these results, an exact analytical approach to the
study of storage allocation and fragmentation is presented. A model of an
allocation scheme of a kind common in many computing systems is described.
Requests from a saturated fi rst come fi rst served queue for varyi ng amounts of
contiguous storage are satisfied as soon as sufficient space becomes available
in a storage memory of fixed total size. A placement algorithm decides which
free locations to allocate if a choice is possible. After a variable time,
allocated requests are completed and their occupied storage is freed again.
In general, the avail ab 1 e space becomes fragmented because allocated requests
are not relocated ~r moved around in stora~e.
The model's behaviour and in particul~r the storage utilisation are
studied under conditions in which the model is a finite homogeneous Markov
chain. The algebraic structure of its sparse transition matrix is discovered
to have a striki~g recursive pattern, allowing the steady state equation to be
simplified considerably and unexpectedly to a simple and direct statement of
the effect of the choice of placement algorithm on the steady state. Possible
developments and uses of this simplified analysis are indicated, and some
investigated. The exact probabilistic behaviour of models of relatively small
memory sizes is computed, and different placement algorithms are compared with
each other and with the analytic results which are derived for the
corresponding model in which relocation is allowed