Adjusting mean value of the beta distribution

Question

I'm reading a paper[1] that performs a simulation with task graphs. The paper uses beta distribution to assign weights for the nodes in the graph.

The graph is already known with certain weights in it, but before simulation happens weight of the graphs are modified in a certain way using Beta distribution.

Here what paper tells:

In the second phase of our experiments, once the deterministic graphs (and their schedules) have been produced, task durations are replaced by a random variable (RV) having as a mean the values described above. The distribution of these RV follows a Beta distribution with parameters $\alpha=2$ and $\beta=5$ (see [10] for a justification). In order to fully specify this, we also need to define the ratio between the maximum and the minimum bounds. We call this parameter the uncertainty level (UL) and set it to 1.1 on average with a very low dispersion (the UL is thus almost constant).

And original node weight is chosen using Poisson distribution.

Considering that mean of beta distribution equals $\frac{\alpha}{\alpha + \beta}$, and both $\alpha$ and $\beta$ are given. How can you adjust the mean value?

[1] Canon, Louis-Claude, et al. "Comparative evaluation of the robustness of dag scheduling heuristics." Grid Computing. Springer US, 2008.