In this paper we quantify the efficiency of parallelism in systems that are prone to failures and exhibit power law processing delays. We characterize the performance of two prototype schemes of parallelism, redundant and split, in terms of both the power law exponent and exact asymptotics of the delay distribution tail. We also develop the optimal splitting scheme which ensures that split always outperforms redundant.
Bo Jiang. Jian Tan. Wei Wei. Ness Shroff. Don Towsley. "Heavy tails in queueing systems: impact of parallelism on tail performance." J. Appl. Probab. 50 (1) 127 - 150, March 2013. https://doi.org/10.1239/jap/1363784429