  As known, the commonly-utilized ways to determine mean first-passage time
$\overline{\mathcal{F}}$ for random walk on networks are mainly based on
Laplacian spectra. However, methods of this type can become prohibitively
complicated and even fail to work when the Laplacian matrix of network under
consideration is difficult to describe in the first place. In this paper, we
propose an effective approach to determining quantity $\overline{\mathcal{F}}$
on some widely-studied tree networks. To this end, we first build up a general
formula between Wiener index $\mathcal{W}$ and $\overline{\mathcal{F}}$ on a
tree. This enables us to convert issues to answer into calculation of
$\mathcal{W}$ on networks in question. As opposed to most of previous work
focusing on deterministic growth trees, our goal is to consider stochastic
case. Towards this end, we establish a principled framework where randomness is
introduced into the process of growing trees. As an immediate consequence, the
previously published results upon deterministic cases are thoroughly covered by
formulas established in this paper. Additionally, it is also straightforward to
obtain Kirchhoff index on our tree networks using the proposed approach. Most
importantly, our approach is more manageable than many other methods including
spectral technique in situations considered herein.
