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

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

doi:10.1017/S0269964806060268

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

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

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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-[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 language	English
Pages (from-to)	429-446
Journal	Probability in the Engineering and Informational Sciences
Volume	20
Issue number	3
DOIs	https://doi.org/10.1017/S0269964806060268
Publication status	Published - 2006

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title = "Sojourn time tails in the M/D/1 processor sharing queue",

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.",

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AU - Zwart, B.

AU - Boxma, O.J.

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AB - 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.

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DO - 10.1017/S0269964806060268

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EP - 446

JO - Probability in the Engineering and Informational Sciences

JF - Probability in the Engineering and Informational Sciences

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

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