Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints

Ellen Cardinaels (), Sem Borst () and Johan S. H. van Leeuwaarden ()
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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

Operations Research, 2024, vol. 72, issue 4, 1539-1555

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.

Keywords: Stochastic Models; assignment constraints; heterogeneity; parallel-server systems; load balancing; redundancy scheduling; heavy-traffic limit; state space collapse; resource pooling (search for similar items in EconPapers)
Date: 2024
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