On functional limit theorems for the cumulative times in alternating renewal processes

Guodong Pang; Jiankui Yang; Yuhang Zhou

doi:10.1016/j.orl.2017.01.008

On functional limit theorems for the cumulative times in alternating renewal processes

Guodong Pang
, Jiankui Yang
, Yuhang Zhou

Harold and Inge Marcus Department of Industrial and Manufacturing Engineering

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

1 Scopus citations

Abstract

We provide new proofs for two functional central limit theorems, and prove strong approximations for the cumulative “on” times in alternating renewal processes. The proofs rely on a first-passage-time representation of the cumulative “on” time process. As an application, we establish strong approximations for the queueing process in a single-server fluid queue with “on–off” sources.

Original language	English (US)
Pages (from-to)	145-150
Number of pages	6
Journal	Operations Research Letters
Volume	45
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2017.01.008
State	Published - Mar 1 2017

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2017.01.008

Cite this

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title = "On functional limit theorems for the cumulative times in alternating renewal processes",

abstract = "We provide new proofs for two functional central limit theorems, and prove strong approximations for the cumulative “on” times in alternating renewal processes. The proofs rely on a first-passage-time representation of the cumulative “on” time process. As an application, we establish strong approximations for the queueing process in a single-server fluid queue with “on–off” sources.",

author = "Guodong Pang and Jiankui Yang and Yuhang Zhou",

note = "Funding Information: G. Pang and Y. Zhou are supported in part by NSF CMMI-1538149 and J. Yang is supported in part by NSFC 11541006. The authors thank the reviewer for helpful comments.",

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AU - Zhou, Yuhang

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Y1 - 2017/3/1

N2 - We provide new proofs for two functional central limit theorems, and prove strong approximations for the cumulative “on” times in alternating renewal processes. The proofs rely on a first-passage-time representation of the cumulative “on” time process. As an application, we establish strong approximations for the queueing process in a single-server fluid queue with “on–off” sources.

AB - We provide new proofs for two functional central limit theorems, and prove strong approximations for the cumulative “on” times in alternating renewal processes. The proofs rely on a first-passage-time representation of the cumulative “on” time process. As an application, we establish strong approximations for the queueing process in a single-server fluid queue with “on–off” sources.

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M3 - Article

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SP - 145

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JO - Operations Research Letters

JF - Operations Research Letters

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ER -

On functional limit theorems for the cumulative times in alternating renewal processes

Abstract

All Science Journal Classification (ASJC) codes

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