  Partial sharing allows providers to possibly pool a fraction of their
resources when full pooling is not beneficial to them. Recent work in systems
without sharing has shown that redundancy can improve performance considerably.
In this paper, we combine partial sharing and redundancy by developing partial
sharing models for providers operating multi-server systems with redundancy.
Two M/M/N queues with redundant service models are considered. Copies of an
arriving job are placed in the queues of servers that can serve the job.
Partial sharing models for cancel-on-complete and cancel-on-start redundancy
models are developed. For cancel-on-complete, it is shown that the Pareto
efficient region is the full pooling configuration. For a cancel-on-start
policy, we conjecture that the Pareto frontier is always non-empty and is such
that at least one of the two providers is sharing all of its resources. For
this system, using bargaining theory the sharing configuration that the
providers may use is determined. Mean response time and probability of waiting
are the performance metrics considered.
