NWU speed-variation load conjecture for redundancy systems

Let $N$ be the number of servers, let $d$ satisfy $1<d<N$, and suppose that job types are unknown. For each server $i=1,\dots,N$, let $\gamma_i$ denote its load in the system with one replica and let $\bar{\gamma}_i$ denote its load in the system with $d$ replicas. The speed variations are called NWU when they have the stated new-worse-than-used property.

NWU load conjecture. For NWU distributed speed variations, the loads satisfy

$$\bar{\gamma}_i\geq \gamma_i,\qquad i=1,\dots,N,$$

and for strictly NWU distributed speed variations the inequalities are strict:

$$\bar{\gamma}_i>\gamma_i,\qquad i=1,\dots,N.$$

The conjecture concerns whether starting multiple replicas creates at least as much load at every server as the single-replica system for unknown job types. The supplied text gives no evidence that this conjecture has been proved or refuted.