On Distributed Storage Allocations for Memory-Limited Systems

In this paper we consider distributed allocation problems with memory constraint limits. Firstly, we propose a tractable relaxation to the problem of optimal symmetric allocations, considered by Leong et al. The approximated problem is based on the Q-error function, and its solution approaches the solution of the initial problem, as the number of storage nodes in the network grows. Secondly, exploiting this relaxation, we are able to formulate and to solve the problem for storage allocations for a memory-limited distributed storage system (DSS), with an arbitrary memory profile. Finally, we discuss the extension to the case of storing multiple data objects in one DSS.