Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models

@article{Braverman2015SteinsMF,
  title={Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models},
  author={Anton Braverman and J. Dai and Jiekun Feng},
  journal={arXiv: Probability},
  year={2015}
}
  • Anton Braverman, J. Dai, Jiekun Feng
  • Published 2015
  • Mathematics
  • arXiv: Probability
  • This paper provides an introduction to the Stein method framework in the context of steady-state diffusion approximations. The framework consists of three components: the Poisson equation and gradient bounds, generator coupling, and moment bounds. Working in the setting of the Erlang-A and Erlang-C models, we prove that both Wasserstein and Kolmogorov distances between the stationary distribution of a normalized customer count process, and that of an appropriately defined diffusion process… CONTINUE READING
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    References

    SHOWING 1-10 OF 70 REFERENCES
    Stein's method for steady-state diffusion approximations of $M/Ph/n+M$ systems
    • 56
    Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State
    • 35
    • Highly Influential
    • PDF
    Diffusion models and steady-state approximations for exponentially ergodic Markovian queues.
    • 52
    • PDF
    Validity of heavy traffic steady-state approximations in generalized Jackson networks
    • 148
    • PDF
    Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic
    • 83
    • PDF
    Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime
    • 26
    • PDF
    Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines
    • I. Gurvich
    • Mathematics, Computer Science
    • Math. Oper. Res.
    • 2014
    • 27
    • PDF
    The diffusion approximation for tandem queues in heavy traffic
    • 106
    The G/GI/N queue in the Halfin–Whitt regime
    • 131
    • PDF
    State-space collapse in stationarity and its application to a multiclass single-server queue in heavy traffic
    • 21