  In this paper we consider a general L\'{e}vy process $X$ reflected at
downward periodic barrier $A_t$ and constant upper barrier $K$ giving a process
$V^K_t=X_t+L^A_t-L^K_t$. We find the expression for a loss rate defined by
$l^K=\mathbb{E} L^K_1$ and identify its asymptotics as $K\to\infty$ when $X$
has light-tailed jumps and $\mathbb{E}X_1<0$.
