  To prevent service time bottlenecks in distributed storage systems, the
access balancing problem has been studied by designing almost supermagic edge
labelings of certain graphs to balance the access requests to different
servers. In this paper, we introduce the concept of robustness of edge
labelings under limited-magnitude swaps, which is important for studying the
dynamical access balancing problem with respect to changes in data popularity.
We provide upper and lower bounds on the robustness ratio for complete graphs
with $n$ vertices, and construct $O(n)$-almost supermagic labelings that are
asymptotically optimal in terms of the robustness ratio.
