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Diffusion approximation of an infinite-server queue under Markovian environment with rapid switching

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  • Sen, Ankita
  • Selvaraju, N.

Abstract

We consider an infinite-server queue with Markov-modulated non-homogeneous arrival and service processes. We adopt the martingale central limit theorem to derive the diffusion approximation of the centered and normalized queue length processes of the queueing system under suitable scaling. In particular, the diffusion approximation results in an Ornstein–Uhlenbeck process with time-varying coefficients and the associated covariance captures the stochastic and predictable variabilities simultaneously.

Suggested Citation

  • Sen, Ankita & Selvaraju, N., 2023. "Diffusion approximation of an infinite-server queue under Markovian environment with rapid switching," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715223000020
    DOI: 10.1016/j.spl.2023.109778
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    References listed on IDEAS

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    1. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    2. D. Anderson & J. Blom & M. Mandjes & H. Thorsdottir & K. Turck, 2016. "A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 153-168, March.
    3. Pang, Guodong & Zheng, Yi, 2017. "On the functional and local limit theorems for Markov modulated compound Poisson processes," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 131-140.
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