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Limiting distribution for infinite-server batch service queues

Author

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  • Kim, Bara
  • Kim, Jeongsim

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.

Suggested Citation

  • Kim, Bara & Kim, Jeongsim, 2025. "Limiting distribution for infinite-server batch service queues," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224002967
    DOI: 10.1016/j.spl.2024.110327
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