Efficient scheduling in redundancy systems with general service times

We characterize the impact of scheduling policies on the mean response time in nested systems with cancel-on-complete redundancy. We consider not only class- and state-oblivious policies such as FCFS and ROS, but also class-based, and, in particular, redundancy-aware policies of the form Π _1-Π _2 , where Π _1 discriminates among job classes based on their degree of redundancy (e.g., Least-Redundant-First (LRF), Most-Redundant-First (MRF)) and Π _2 discriminates among jobs of the same class. Assuming that jobs have independent and identically distributed (i.i.d.) copies we prove the following: (i) When jobs have exponential service times, LRF policies outperform any other policy. (ii) When service times are New-Worse-than-Used, MRF-FCFS outperforms LRF-FCFS as the variability of the service time grows infinitely large. (iii) When service times are New-Better-than-Used, LRF-ROS (resp. MRF-ROS) outperforms LRF-FCFS (resp. MRF-FCFS) in a two-server system. Statement (iii) also holds when job sizes follow a general distribution and have identical copies (all the copies of a job have the same size). Moreover, we show via simulation that, for a large class of redundancy systems, class-based (and, in particular, redundancy-aware) policies can considerably improve the mean response time compared to policies that ignore the class. We also explore the effect of redundancy on the stability region.