  The performance of distributed storage systems deployed on wide-area networks
can be improved using weighted (majority) quorum systems instead of their
regular variants due to the heterogeneous performance of the nodes. A
significant limitation of weighted majority quorum systems lies in their
dependence on static weights, which are inappropriate for systems subject to
the dynamic nature of networked environments. To overcome this limitation, such
quorum systems require mechanisms for reassigning weights over time according
to the performance variations. We study the problem of node weight reassignment
in asynchronous systems with a static set of servers and static fault
threshold. We prove that solving such a problem is as hard as solving
consensus, i.e., it cannot be implemented in asynchronous failure-prone
distributed systems. This result is somewhat counter-intuitive, given the
recent results showing that two related problems -- replica set reconfiguration
and asset transfer -- can be solved in asynchronous systems. Inspired by these
problems, we present two versions of the problem that contain restrictions on
the weights of servers and the way they are reassigned. We propose a protocol
to implement one of the restricted problems in asynchronous systems. As a case
study, we construct a dynamic-weighted atomic storage based on such a protocol.
We also discuss the relationship between weight reassignment and asset transfer
problems and compare our dynamic-weighted atomic storage with reconfigurable
atomic storage.
