The asymptotic variance of departures in critically loaded queues

A. Al Hanbali; M. Mandjes; Y. Nazarathy; W. Whitt

doi:10.1239/aap/1300198521

The asymptotic variance of departures in critically loaded queues

A. Al Hanbali^*
, M. Mandjes
, Y. Nazarathy
, W. Whitt

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time /. We focus on the case where the system load q equals 1, and prove that the asymptotic variance rate satisfies lim_t→∞ var D(t)/t = Λ.(l

Original language	English
Pages (from-to)	243-263
Number of pages	21
Journal	Advances in Applied Probability
Volume	43
Issue number	1
DOIs	https://doi.org/10.1239/aap/1300198521
State	Published - Mar 2011
Externally published	Yes

Keywords

Brownian bridge
Critically loaded system
Departure process
GT/G/1 queue
Multiserver queue
Renewal theory
Uniform integrability

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics

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10.1239/aap/1300198521

Cite this

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AB - We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time /. We focus on the case where the system load q equals 1, and prove that the asymptotic variance rate satisfies limt→∞ var D(t)/t = Λ.(l

KW - Brownian bridge

KW - Critically loaded system

KW - Departure process

KW - GT/G/1 queue

KW - Multiserver queue

KW - Renewal theory

KW - Uniform integrability

UR - https://www.scopus.com/pages/publications/79953144281

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The asymptotic variance of departures in critically loaded queues

Abstract

Keywords

ASJC Scopus subject areas

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Cite this