Memory occupancy patterns in garbage collection systems

Some programming languages and computer systems use dynamic memory allocation with garbage collection. It would be useful to understand how the utilization of memory depends on the stochastic parameters describing the size and life distributions of the cells. We consider a class of dynamic storage allocation systems which use a first-fit strategy to allocate cells and perform noncompacting garbage collections to recover free memory space when memory becomes fully occupied. A formula is derived for the expected number of holes (available cells) in memory immediately following a garbage collection which specializes to an analogue of Knuth's 'Fifty Percent' rule for nongarbage-collection systems. Simulations confirm the rule for exponentially distributed cell lifetimes. Other lifetime distributions are discussed. The memory-size requirements for noncompacting garbage collection are also analyzed.

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