Existence of symmetric optimal allocations

An allocation distributes storage across $n$ nodes, and its recovery delay is denoted by $D$; the parameters are the node count $n$, request rate $\lambda$, and threshold $T$. An allocation is symmetric when it treats the nodes identically. Symmetric optimal allocation conjecture. A symmetric optimal allocation always exists for any $n$, $\lambda$, and $T$. This conjecture is motivated by numerical observations concerning the optimization of expected recovery delay. The supplied source does not state whether the conjecture has been resolved.