  Trades, introduced by Hedayat, are two sets of blocks of elements which may
be exchanged (traded) without altering the counts of certain subcollections of
elements within their constituent blocks. They are of importance in
applications where certain combinations of elements dynamically become
prohibited from being placed in the same group of elements, since in this case
one can trade the offending blocks with allowed ones. This is particularly the
case in distributed storage systems, where due to privacy and other
constraints, data of some groups of users cannot be stored together on the same
server. We introduce a new class of balanced trades, important for access
balancing of servers, and perturbation resilient balanced trades, important for
studying the stability of server access frequencies with respect to changes in
data popularity. The constructions and bounds on our new trade schemes rely on
specialized selections of defining sets in minimal trades and number-theoretic
analyses.
