  We consider a queuing model with the workload evolving between consecutive
i.i.d. exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally
positive L\'{e}vy process $Y(t)$ which is reflected at 0. When the exponential
clock $e_q^{(i)}$ ends, the additional state-dependent service requirement
modifies the workload so that the latter is equal to $F_i(Y(e_q^{(i)}))$ at
epoch $e^{(1)}_q+...+e^{(i)}_q$ for some random nonnegative i.i.d. functionals
$F_i$. In particular, we focus on the case when $F_i(y)=(B_i-y)^+$, where
$\{B_i\}_{i=1,2,...}$ are i.i.d. nonnegative random variables. We analyse the
steady-state workload distribution for this model.
