Heavy traffic approximations for busy period in an M/G/\(\infty\) queue
type: Item
instance of: scholarly article
title: Heavy traffic approximations for busy period in an M/G/\(\infty\) queue
zbMATH Open document ID: 0567.60088
DOI: 10.1016/0304-4149(85)90028-6
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: Let B denote a typical busy period in an M/G/\(\infty\) queue with arrival rate \(\lambda\) and service-time distribution H having mean 1. It is shown that a necessary and sufficient condition for B/EB to have an asymptotic exponential distribution as \(\lambda\) \(\to \infty\) is (log x)\(\int^{\infty}_{x}\{1-H(y)\}dy\to 0\) as \(x\to \infty.\) When (log x)\(\sup_{u\geq x}u\{1-H(u)\}\to 0\) as \(x\to \infty\), it is further shown that B/\(\nu\) (\(\lambda)\) has an asymptotic exponential distribution, where \(\nu\) (\(\lambda)\) is an appropriate norming different from EB.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 3905607
zbMATH Keywords: heavy traffic
zbMATH Keywords: busy period
zbMATH Keywords: asymptotic exponential distribution
reviewed by: D. P. Kennedy
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90028-6
OpenAlex ID: W1562578440
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author: Peter Hall
description: scientific article; zbMATH DE number 3905607