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Singular control of (reflected) Brownian motion: a computational method suitable for queueing applications

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Listed:
  • Baris Ata

    (University of Chicago)

  • J. Michael Harrison

    (Stanford University)

  • Nian Si

    (IEDA, Hong Kong University of Science and Technology)

Abstract

Motivated by applications in queueing theory, we consider a class of singular stochastic control problems whose state space is the d-dimensional positive orthant. The original problem is approximated by a drift control problem, to which we apply a recently developed computational method that is feasible for dimensions up to $$d=30$$ d = 30 or more. To show that nearly optimal solutions are obtainable using this method, we present computational results for a variety of examples, including queueing network examples that have appeared previously in the literature.

Suggested Citation

  • Baris Ata & J. Michael Harrison & Nian Si, 2024. "Singular control of (reflected) Brownian motion: a computational method suitable for queueing applications," Queueing Systems: Theory and Applications, Springer, vol. 108(3), pages 215-251, December.
    • Handle: RePEc:spr:queues:v:108:y:2024:i:3:d:10.1007_s11134-024-09910-5
    DOI: 10.1007/s11134-024-09910-5
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    References listed on IDEAS

    as
    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Sunil Kumar & Kumar Muthuraman, 2004. "A Numerical Method for Solving Singular Stochastic Control Problems," Operations Research, INFORMS, vol. 52(4), pages 563-582, August.
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