  In multitasking operating systems, requests for free memory are traditionally
modeled as a stochastic counting process with independent,
exponentially-distributed interarrival times because of the analytic simplicity
such Poisson models afford. We analyze the distribution of several million unix
page commits to show that although this approach could be valid over relatively
long timespans, the behavior of the arrival process over shorter periods is
decidedly not Poisson. We find that this result holds regardless of the
originator of the request: unlike network packets, there is little difference
between system- and user-level page-request distributions. We believe this to
be due to the bursty nature of page allocations, which tend to occur in either
small or extremely large increments. Burstiness and persistent variance have
recently been found in self-similar processes in computer networks, but we show
that although page commits are both bursty and possess high variance over long
timescales, they are probably not self-similar. These results suggest that
altogether different models are needed for fine-grained analysis of memory
systems, an important consideration not only for understanding behavior but
also for the design of online control systems.
