On the infimum attained by a reflected Lévy process

K.G. Debicki, K.M. Kosinski, M.R.H. Mandjes

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)


This paper considers a Lévy-driven queue (i.e., a Lévy process reflected at 0), and focuses on the distribution of M(t), that is, the minimal value attained in an interval of length t (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided Lévy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of P(M(T u )>u) (for different classes of functions T u and u large); here we have to distinguish between heavy-tailed and light-tailed scenarios.
Original languageEnglish
Pages (from-to)23-35
JournalQueueing Systems
Issue number1
Publication statusPublished - 2012


Dive into the research topics of 'On the infimum attained by a reflected Lévy process'. Together they form a unique fingerprint.

Cite this