  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.
