Conjecture on the effect of coded file size on optimal allocation

Let $m$ be the coded file size ratio, and let $\alpha$ be the allocation parameter maximizing the average service rate $\mu_s(\alpha)$. The claim applies to both the fixed-size access model and the probabilistic access model. Redundancy conjecture. For both fixed-size access and probabilistic access models, when $m$ is increasing, the optimal $\alpha$ for $\mu_s(\alpha)$ is also increasing. The paper reports that this pattern appears in all displayed figures, but the supplied text does not provide a proof, so the monotonicity remains conjectural.