A Lévy input model with additional state-dependent services

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers {e(i) q } i =1,2,… according to a spectrally positive Lévy 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 (i) q)) at epoch e(i) 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