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Explicit M/G/1 waiting-time distributions for a class of long-tail service-time distributions by Joseph Abate; Ward Whitt is a Engineering article available to read on EtoBox.

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O.J. Boxma and J.W. Cohen recently obtained an explicit expression for the M/G/1 steady-state waiting-time distribution for a class of service-time distributions with power tails. We extend their explicit representation from a one-parameter family of service-time distributions to a two-parameter family. The complementary cumulative distribution function (ccdf 's) of the service times all have the asymptotic form F c (t) ∼ t -3=2 as t → ∞, so that the associated waiting-time ccdf 's have asymptotic form W c (t) ∼ ÿt -1=2 as t → ∞. Thus the second moment of the service time and the mean of the waiting time are inÿnite. Our result here also extends our own earlier explicit expression for the M/G/1 steady-state waiting-time distribution when the service-time distribution is an exponential mixture of inverse Gaussian distributions (EMIG). The EMIG distributions form a two-parameter family with ccdf having the asymptotic form F c (t) ∼ t -3=2 e -Át as t → ∞. We now show that a variant of our previous argument applies when the service-time ccdf is an undamped EMIG, i.e., with ccdf G c (t) = e Át F c (t) for F c (t) above, which has the power tail G c (t) ∼ t -3=2 as t → ∞. The Boxma-Cohen

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Author

Joseph Abate; Ward Whitt

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0167-6377)

Published

1999

Language

EN

Field

Engineering (Physical Sciences)