Heavy-Traffic Universality of Redundancy Systems with Assignment Constraints

TL;DR

This paper demonstrates that in heavy traffic, redundancy systems with assignment constraints behave like fully flexible systems, achieving resource pooling and insensitivity, despite limited flexibility in task-server matching.

Contribution

It establishes a universal heavy-traffic limit for constrained redundancy systems, showing they operate as a single pooled resource similar to unconstrained systems.

Findings

Heavy-traffic limit results show state space collapse.

Redundancy systems with constraints achieve resource pooling.

Performance matches fully flexible systems even with strict constraints.

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.