recurrence time for transient state

Question

I have the following transition matrix for a MC with state space $S = \{ 1,2,3,4,5,6,7,8 \}$ \begin{bmatrix} 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0.4 & 0 & 0 & 0 & 0.6 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0.2 & 0.7 & 0 & 0 & 0.1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0.2 & 0 & 0 & 0.8 & 0 \\ 0 & 0.4 & 0 & 0 & 0 & 0.6 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0.3 & 0.4 & 0 & 0.3\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix} It is straight forward to the see that there are two closed classes, $C_1 = \{1,3,8\}$ and $C_2 = \{2,6\}$ and a transient class $T = \{4, 5, 7 \}$. How do you determine the mean recurrence time for $C_1$ and $T$? I would have expected that since $T$ is transient, then (since these states are eventually left) the mean recurrence time wouldn't be defined?