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We consider a queuing model with the workload evolving between consecutivei.i.d. exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrallypositive L\'{e}vy process $Y(t)$ which is reflected at 0. When the exponentialclock $e_q^{(i)}$ ends, the additional state-dependent service requirementmodifies the workload so that the latter is equal to $F_i(Y(e_q^{(i)}))$ atepoch $e^{(1)}_q+...+e^{(i)}_q$ 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 thesteady-state workload distribution for this model.

A L\'{e}vy input model with additional state-dependent services