Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions

O.J. Boxma, J.W. Cohen

Research output: Contribution to journalArticleAcademicpeer-review

37 Citations (Scopus)

Abstract

We consider a GI/G/1 queue in which the service time distribution and/or the interarrival time distribution has a heavy tail, i.e., a tail behaviour like t -¿ with 1 <¿ ¿ 2 , so that the mean is finite but the variance is infinite. We prove a heavy-traffic limit theorem for the distribution of the stationary actual waiting time W. If the tail of the service time distribution is heavier than that of the interarrival time distribution, and the traffic load a ¿ 1, then W, multiplied by an appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the Kovalenko distribution. If the tail of the interarrival time distribution is heavier than that of the service time distribution, and the traffic load a ¿ 1, then W, multiplied by another appropriate ‘coefficient of contraction’ that is a function of a, converges in distribution to the negative exponential distribution.
Original languageEnglish
Pages (from-to)177-204
Number of pages28
JournalQueueing Systems: Theory and Applications
Volume33
Issue number1-3
DOIs
Publication statusPublished - 1999

Fingerprint

Dive into the research topics of 'Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions'. Together they form a unique fingerprint.

Cite this