  Distributed computing systems implement redundancy to reduce the job
completion time and variability. Despite a large body of work about computing
redundancy, the analytical performance evaluation of redundancy techniques in
queuing systems is still an open problem. In this work, we take one step
forward to analyze the performance of scheduling policies in systems with
redundancy. In particular, we study the pattern of shared servers among
replicas of different jobs. To this end, we employ combinatorics and graph
theory and define and derive performance indicators using the statistics of the
overlaps. We consider two classical nonadaptive scheduling policies: random and
round-robin. We then propose a scheduling policy based on combinatorial block
designs. Compared with conventional scheduling, the proposed scheduling
improves the performance indicators. We study the expansion property of the
graphs associated with round-robin and block design-based policies. It turns
out the superior performance of the block design-based policy results from
better expansion properties of its associated graph. As indicated by the
performance indicators, the simulation results show that the block design-based
policy outperforms random and round-robin scheduling in different scenarios.
Specifically, it reduces the average waiting time in the queue to up to 25%
compared to the random policy and up to 100% compared to the round-robin
policy.
