  Redundancy scheduling has emerged as a powerful strategy for improving
response times in parallel-server systems. The key feature in redundancy
scheduling is replication of a job upon arrival by dispatching replicas to
different servers. Redundant copies are abandoned as soon as the first of these
replicas finishes service. By creating multiple service opportunities,
redundancy scheduling increases the chance of a fast response from a server
that is quick to provide service, and mitigates the risk of a long delay
incurred when a single selected server turns out to be slow.
  The diversity enabled by redundant requests has been found to strongly
improve the response time performance, especially in case of highly variable
service requirements. Analytical results for redundancy scheduling are
unfortunately scarce however, and even the stability condition has largely
remained elusive so far, except for exponentially distributed service
requirements. In order to gain further insight in the role of the service
requirement distribution, we explore the behavior of redundancy scheduling for
scaled Bernoulli service requirements. We establish a sufficient stability
condition for generally distributed service requirements and we show that, for
scaled Bernoulli service requirements, this condition is also asymptotically
nearly necessary. This stability condition differs drastically from the
exponential case, indicating that the stability condition depends on the
service requirements in a sensitive and intricate manner.
