Sojourn Time Tails In The M/D/1 Processor Sharing Queue

Authors:
Regina Egorova;Bert Zwart;Onno Boxma
Affiliations:
CWI, 1090 GB Amsterdam, The Netherlands, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: r.egorova@tue.nl;CWI, 1090 GB Amsterdam, The Netherlands, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: a.p.zwart@tue.nl;CWI, 1090 GB Amsterdam, The Netherlands, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: o.j.boxma@tue.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2006

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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−&ggr;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) ≈ Ce−&ggr;x is excellent even for moderate values of x.