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Moments Of the stationary waiting time in the Gi/Ph/1 queue

Published online by Cambridge University Press:  14 July 2016

V. Ramaswami  and
D. M. Lucantoni
V. Ramaswami*
Affiliation:
Bell Communications Research
D. M. Lucantoni*
Affiliation:
AT&T Bell Laboratories
*
∗ Postal address: Bell Communications Research Inc., Morris Township, NJ 07960, USA.
∗∗ Postal address: AT&T Bell Laboratories, Holmdel, NJ 07733, USA.
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Abstract

Recursive relations for computing the higher moments of the stationary waiting time distribution in a stable GI/PH/1 queue are derived. These provide an accurate and stable technique to compute these moments.

Keywords

SINGLE-SERVER QUEUESPHASE-TYPE SERVICE
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 636 - 641
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Lucantoni, D. M. and Ramaswami, V. (1985) Efficient algorithms for solving the nonlinear matrix equations arising in phase type queues. Stock. Models, 1, 29–52.Google Scholar
[2] Neuts, M. F. (1981) Matrix-geometric Solutions in Stochastic Models. The Johns Hopkins University Press, Baltimore, Md.Google Scholar
[3] Ramaswami, V. (1988) Nonlinear matrix equations in applied probability—solution techniques and open problems. SIAM Rev.Google Scholar
[4] Ramaswami, V. and Lucantoni, D. M. (1985) Stationary waiting time distribution in queues with phase type service and in quasi-birth-and-death processes. Stock. Models 1, 125–136.Google Scholar