Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints

Ellen Cardinaels; Sem Borst; Johan S. H. van Leeuwaarden

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arXiv · 2005.14566

Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints

Ellen Cardinaels·Sem Borst·Johan S. H. van Leeuwaarden

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Abstract

Service systems often face task-server assignment-constraints due to 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 multi-class 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.

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BibTeX RIS

Ellen Cardinaels, Sem Borst, Johan S. H. van Leeuwaarden. 2020-05-29. Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints. https://arxiv.org/abs/2005.14566

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