The need for speed : Maximizing random walks speed on fixed environments

We study nearest neighbor random walks on fixed environments of $\mathbb{Z}$ composed of two point types : $(1\mathrm{/}2,1\mathrm{/}2)$ and $(p,1-p)$ for $p>1\mathrm{/}2$. We show that for every environment with density of $p$ drifts bounded by $\lambda$ we have ${\mathrm{lim\hspace{0.17em}sup}}_{n\to \mathrm{\infty }}\frac{X_n}{n}\le (2p-1)\lambda$, where $X_n$ is a random walk on the environment. In addition up to some integer effect the environment which gives the best speed is given by equally spaced drifts.