Sojourn time tails in the M/D/1 processor sharing queue

R.R. Egorova, B. Zwart, O.J. Boxma

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)
2 Downloads (Pure)

Abstract

We consider the sojourn time V in the M/D/1 processor sharing (PS) queue and show that P(V > x) is of the form Ce-[gamma]x as x becomes large. The proof involves a geometric random sum representation of V and a connection with Yule processes, which also enables us to simplify Ott's [21] derivation of the Laplace transform of V. Numerical experiments show that the approximation P(V > x) [approximate] Ce-[gamma]x is excellent even for moderate values of x.
Original languageEnglish
Pages (from-to)429-446
JournalProbability in the Engineering and Informational Sciences
Volume20
Issue number3
DOIs
Publication statusPublished - 2006

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