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Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints

Author

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  • Ellen Cardinaels

    (Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands)

  • Sem Borst

    (Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands)

  • Johan S. H. van Leeuwaarden

    (Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, Netherlands)

Abstract

Service systems often face task-server assignment constraints because of skill-based routing or geographical conditions. Redundancy scheduling responds to this limited flexibility by replicating tasks to specific servers in agreement with these assignment constraints. We gain insight from product-form stationary distributions and weak local stability conditions to establish a state space collapse in heavy traffic. In this limiting regime, the parallel-server system with redundancy scheduling operates as a multiclass single-server system, achieving full resource pooling and exhibiting strong insensitivity to the underlying assignment constraints. In particular, the performance of a fully flexible (unconstrained) system can be matched even with rather strict assignment constraints.

Suggested Citation

  • Ellen Cardinaels & Sem Borst & Johan S. H. van Leeuwaarden, 2024. "Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints," Operations Research, INFORMS, vol. 72(4), pages 1539-1555, July.
    • Handle: RePEc:inm:oropre:v:72:y:2024:i:4:p:1539-1555
    DOI: 10.1287/opre.2022.2385
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