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Redundancy-d (R(d)) is a load balancing method used to route incoming jobs toK servers, each with its own queue. Every arriving job is replicated into2<=d<=K tasks, which are then routed to d servers chosen uniformly at random.When the first task finishes service, the remaining d-1 tasks are cancelled andthe job departs the system.  Despite the fact that R(d) is known, under certain conditions, tosubstantially improve job completion times compared to not using redundancy atall, little is known on a more fundamental performance criterion: what is theset of arrival rates under which the R(d) queueing system with FIFO servicediscipline is stable? In this context, due to the complex dynamics of systemswith redundancy and cancellations, existing results are scarce and are limitedto very special cases with respect to the joint service time distribution oftasks.  In this paper we provide a non-trivial, closed form lower bound on thestability region of R(d) for a general joint service time distribution of taskswith finite first and second moments. We consider a discrete time system withBernoulli arrivals and assume that jobs are processed by their order ofarrival. We use the workload processes and a quadratic Lyapunov function tocharacterize the set of arrival rates for which the system is stable. Whilesimulation results indicate our bound is not tight, it provides aneasy-to-check performance guarantee.

A Lower Bound on the stability region of Redundancy-d with FIFO service discipline