Connecting renewal age processes with M/D/1 and M/D/∞ queues through stick breaking

J.S.H. Leeuwaarden, van; A.H. Löpker; A.J.E.M. Janssen

doi:10.1080/15326340903517147

Connecting renewal age processes with M/D/1 and M/D/∞ queues through stick breaking

J.S.H. Leeuwaarden, van, A.H. Löpker, A.J.E.M. Janssen

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

2 Citations (Scopus)

Abstract

We consider the length of a busy period in the M/D/$\infty$ queue and show that it coincides with the sojourn time of the first customer in an M/D/1 processor-sharing queue. We further show that the busy period is intimately related with the stationary waiting time in the M/D/1 first-come-first-served queue. We present three characterizations for the distribution function of the busy period and an asymptotic expression for its tail distribution. The latter involves complex-valued branches of the Lambert W function. Keywords: Lambert W function; Processor sharing; Queues; Renewal age process; Stick breaking. Mathematics Subject Classification: 60K25; 97I80.

Original language	English
Pages (from-to)	141-163
Journal	Stochastic Models
Volume	26
Issue number	1
DOIs	https://doi.org/10.1080/15326340903517147
Publication status	Published - 2010

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title = "Connecting renewal age processes with M/D/1 and M/D/∞ queues through stick breaking",

abstract = "We consider the length of a busy period in the M/D/$\infty$ queue and show that it coincides with the sojourn time of the first customer in an M/D/1 processor-sharing queue. We further show that the busy period is intimately related with the stationary waiting time in the M/D/1 first-come-first-served queue. We present three characterizations for the distribution function of the busy period and an asymptotic expression for its tail distribution. The latter involves complex-valued branches of the Lambert W function. Keywords: Lambert W function; Processor sharing; Queues; Renewal age process; Stick breaking. Mathematics Subject Classification: 60K25; 97I80.",

author = "{Leeuwaarden, van}, J.S.H. and A.H. L{\"o}pker and A.J.E.M. Janssen",

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AU - Leeuwaarden, van, J.S.H.

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AU - Janssen, A.J.E.M.

PY - 2010

Y1 - 2010

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AB - We consider the length of a busy period in the M/D/$\infty$ queue and show that it coincides with the sojourn time of the first customer in an M/D/1 processor-sharing queue. We further show that the busy period is intimately related with the stationary waiting time in the M/D/1 first-come-first-served queue. We present three characterizations for the distribution function of the busy period and an asymptotic expression for its tail distribution. The latter involves complex-valued branches of the Lambert W function. Keywords: Lambert W function; Processor sharing; Queues; Renewal age process; Stick breaking. Mathematics Subject Classification: 60K25; 97I80.

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DO - 10.1080/15326340903517147

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EP - 163

JO - Stochastic Models

JF - Stochastic Models

IS - 1

ER -

Connecting renewal age processes with M/D/1 and M/D/∞ queues through stick breaking

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