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On the Markov property of the GI/G/∞ Gaussian limit

Published online by Cambridge University Press:  01 July 2016

Peter W. Glynn
Peter W. Glynn*
Affiliation:
Stanford University
*
∗Postal address: Department of Operations Research, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

It is shown that the heavy-traffic Gaussian limit for GI/G/∞ queues is Markovian if and only if the service-time distribution H(t) is of the form 1-H(t) = pe–αt for α > 0 and 0 < p ≦ 1.

Keywords

GI/G/s QUEUELIMIT THEOREM: GAUSSIAN PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 1 , March 1982 , pp. 191 - 194
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

This research was supported under National Science Foundation Grant MCS 79-09139, Office of Naval Research Contract N00014-76-C-0578 (NR 042-343), and a Natural Sciences and Engineering Research Council of Canada Postgraduate Scholarship.

References

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Iglehart, D. L. (1965) Limit diffusion approximations for the many server queue and the repairman problem. J. Appl. Prob. 2, 429–441.Google Scholar
Whitt, W. (1981) On the heavy-traffic limit theorem for GI/G/∞ queues. Adv. Appl. Prob. 14, 171–190.Google Scholar