A Lévy input model with additional state-dependent services

Z.B. Palmowski, M. Vlasiou

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)


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 L\'evy process $Y(t)$ which is reflected at 0. When the exponential clock $e^{(i)}_q$ 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 $e^{(1)}_q + ... + e^{(i)}_q$ 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.
Original languageEnglish
Pages (from-to)1546-1564
JournalStochastic Processes and their Applications
Issue number7
Publication statusPublished - 2011


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