Limiting distribution for infinite-server batch service queues

Bara Kim; Jeongsim Kim

doi:10.1016/j.spl.2024.110327

Limiting distribution for infinite-server batch service queues

Bara Kim, Jeongsim Kim

Department of Mathematics

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

Abstract

Nakamura and Phung-Duc (2023) conjectured that, for an infinite-server batch service queue with Poisson arrivals, the central limit theorem for the number of busy servers, conditioned on the number of waiting customers and the size of the batch to be served, holds as the arrival rate goes to infinity. In this paper, we resolve this conjecture using the theory of Markov regenerative processes and further extend the result to renewal arrival models.

Original language	English
Article number	110327
Journal	Statistics and Probability Letters
Volume	219
DOIs	https://doi.org/10.1016/j.spl.2024.110327
Publication status	Published - 2025 Apr

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Keywords

Central limit theorem
Infinite server queue
Law of large numbers
Markov regenerative processes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2024.110327

Cite this

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abstract = "Nakamura and Phung-Duc (2023) conjectured that, for an infinite-server batch service queue with Poisson arrivals, the central limit theorem for the number of busy servers, conditioned on the number of waiting customers and the size of the batch to be served, holds as the arrival rate goes to infinity. In this paper, we resolve this conjecture using the theory of Markov regenerative processes and further extend the result to renewal arrival models.",

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AB - Nakamura and Phung-Duc (2023) conjectured that, for an infinite-server batch service queue with Poisson arrivals, the central limit theorem for the number of busy servers, conditioned on the number of waiting customers and the size of the batch to be served, holds as the arrival rate goes to infinity. In this paper, we resolve this conjecture using the theory of Markov regenerative processes and further extend the result to renewal arrival models.

KW - Central limit theorem

KW - Infinite server queue

KW - Law of large numbers

KW - Markov regenerative processes

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Limiting distribution for infinite-server batch service queues

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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