How Hard is Asynchronous Weight Reassignment? (Extended Version)

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.