 
Summary: Proceedings of the '26th Conference
on Decision and Control
Los Angeles, CA December 1987
HOW LARGE DELAYS BULD UP IN A GIiGil QUEUE
V. Anantharam
School of Electrical Engineering
Cornel1 University,Ithaca, NY 14853
FA9 = I t 3 0
ABSTRACT
Let It; denote the xaiting tim.: of customer k. k 2 0, in an initially empty
GI/G/l queue. Fix a > 0. \{'e prove ucak limittheoremsdescribing the
behavior of , 0 < k 5 nl; given I\',, > na. Let X have the distribution of the
dlffcrcnce betxecn the scrvicz ar.d interarrivaldistributions. \Ye consider
queuesfor which Cramertype conditions hold for X: and queuesfor which X
has regularly varying positive tail.
11,
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I. ISTRODECTIOS
In this paper we describe how largedcla)sbuild up in aGI/G/l q u a e .
Theengineeringmotivation for thls investigationcomes from the dcsir.: to
