A Lévy input model with additional state-dependent services

@inproceedings{Palmowski2009ALI,
title={A L{\'e}vy input model with additional state-dependent services},
author={Zbigniew Palmowski and Maria Vlasiou},
year={2009}
}

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers {e q }i=1,2,... according to a spectrally positive Lévy process Y (t) which is reflected at 0. When the exponential clock e q ends, the additional state-dependent service requirement modifies the workload so that the latter is equal to Fi(Y (e (i) q )) at epoch e (1) q + . . . + e (i) q for some random nonnegative i.i.d. functionals Fi. In particular, we focus on the case when Fi(y) = (Bi − y… CONTINUE READING