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State space collapse for multi-class queueing networks under SBP service policies

Author

Listed:
  • Chang Cao

    (Cornell University)

  • J. G. Dai

    (Cornell University
    The Chinese University of Hong)

  • Xiangyu Zhang

    (Cornell University)

Abstract

In Braverman et al. [3], the authors justify the steady-state diffusion approximation of a multiclass queueing network under static buffer priority policy in heavy traffic. A major assumption in [3] is the moment state space collapse (moment-SSC) property of the steady-state queue length. In this paper, we prove that moment-SSC holds under a corresponding state space collapse condition on the fluid model. Our approach is inspired by Dai and Meyn [8], which was later adopted by Budhiraja and Lee [4] to justify the diffusion approximation for generalized Jackson networks. We will verify that the fluid state space collapse holds for various networks.

Suggested Citation

  • Chang Cao & J. G. Dai & Xiangyu Zhang, 2022. "State space collapse for multi-class queueing networks under SBP service policies," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 87-122, October.
    • Handle: RePEc:spr:queues:v:102:y:2022:i:1:d:10.1007_s11134-022-09864-6
    DOI: 10.1007/s11134-022-09864-6
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    References listed on IDEAS

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    1. Hong Chen & Hanqin Zhang, 2000. "Diffusion Approximations for Some Multiclass Queueing Networks with FIFO Service Disciplines," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 679-707, November.
    2. Amarjit Budhiraja & Chihoon Lee, 2009. "Stationary Distribution Convergence for Generalized Jackson Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 45-56, February.
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