In this note, we identify a simple setup from which one may easily infer various decomposition results for queues with interruptions as well as càdlàg processes with certain secondary jump inputs. Special cases are processes with stationary or stationary and independent increments. In the Lévy process case, the decomposition holds not only in the limit but also at independent exponential times, due to the Wiener-Hopf decomposition. A similar statement holds regarding the GI/GI/1 setting with multiple vacations.
Bibliographical noteFunding Information:
Acknowledgments Jevgenijs Ivanovs study was supported by the Swiss National Science Foundation Project 200021-124635/1, and Offer Kella study was supported in part by Grant No. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics.
- G/G/1 queue
- Lévy process
- Random walk
- Secondary jump input
- Server vacations
- Wiener-Hopf factorization