  Dynamic Spectrum Access systems exploit temporarily available spectrum
(`white spaces') and can spread transmissions over a number of non-contiguous
sub-channels. Such methods are highly beneficial in terms of spectrum
utilization. However, excessive fragmentation degrades performance and hence
off-sets the benefits. Thus, there is a need to study these processes so as to
determine how to ensure acceptable levels of fragmentation. Hence, we present
experimental and analytical results derived from a mathematical model. We model
a system operating at capacity serving requests for bandwidth by assigning a
collection of gaps (sub-channels) with no limitations on the fragment size. Our
main theoretical result shows that even if fragments can be arbitrarily small,
the system does not degrade with time. Namely, the average total number of
fragments remains bounded. Within the very difficult class of dynamic
fragmentation models (including models of storage fragmentation), this result
appears to be the first of its kind. Extensive experimental results describe
behavior, at times unexpected, of fragmentation under different algorithms. Our
model also applies to dynamic linked-list storage allocation, and provides a
novel analysis in that domain. We prove that, interestingly, the 50% rule of
the classical (non-fragmented) allocation model carries over to our model.
Overall, the paper provides insights into the potential behavior of practical
fragmentation algorithms.
