  Define a $\gamma$-reflected process
$W_\gamma(t)=Y_H(t)-\gamma\inf_{s\in[0,t]}Y_H(s)$, $t\ge0$ with input process
$\{Y_H(t), t\ge 0\}$ which is a fractional Brownian motion with Hurst index
$H\in (0,1)$ and a negative linear trend. In risk theory
$R_\gamma(t)=u-W_\gamma(t), t\ge0$ is referred to as the risk process with tax
of a loss-carry-forward type, whereas in queueing theory $W_1$ is referred to
as the queue length process. In this paper, we investigate the ruin probability
and the ruin time of the risk process $R_\gamma, \gamma \in [0,1]$ over a
surplus dependent time interval $[0, T_u]$.
