Limiting distribution for infinite-server batch service queues

Bara Kim and Jeongsim Kim

Statistics & Probability Letters, 2025, vol. 219, issue C

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.

Keywords: Infinite server queue; Central limit theorem; Law of large numbers; Markov regenerative processes (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110327

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