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SOJOURN TIME TAILS IN THE M/D/1 PROCESSOR SHARING QUEUE

Published online by Cambridge University Press:  01 June 2006

Regina Egorova ,
Bert Zwart  and
Onno Boxma
Regina Egorova
Affiliation:
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
Bert Zwart
Affiliation:
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
Onno Boxma
Affiliation:
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
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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−γx 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−γx is excellent even for moderate values of x.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 3 , July 2006 , pp. 429 - 446
Copyright
© 2006 Cambridge University Press

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