The MacLaurin series for the GI/G/1 queue

The MacLaurin series for the GI/G/1 queue

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Article ID: iaor19932434
Country: Israel
Volume: 29
Issue: 1
Start Page Number: 176
End Page Number: 184
Publication Date: Mar 1992
Journal: Journal of Applied Probability
Authors: ,
Abstract:

The authors derive the MacLaurin series for the moments of the system time and the delay with respect to the parameters in the service time or interarrival time distributions in the GI/G/1 queue. The coefficients in these series are expressed in terms of the derivatives of the interarrival time density function evaluated at zero and the moments of the service time distribution, which can be easily calculated through a simple recursive procedure. The light traffic derivatives can be obtained from these series. For the M/G/1 queue, the authors are able to recover the formulas for the moments of the system time and the delay, including the Pollaczek-Khinchin mean-value formula.

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