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arXiv · 2206.10164

Efficient scheduling in redundancy systems with general service times

Elene Anton·Rhonda Righter·Ina Maria Maaike Verloop
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Abstract

We characterize the impact of scheduling policies on the mean response time in nested systems with cancel-on-complete redundancy. We consider not only redundancy-oblivious policies, such as FCFS and ROS, but also redundancy-aware policies of the form $Π$ 1 -- $Π$ 2 , where $Π$ 1 discriminates among job classes (e.g., least-redundant-first (LRF), most-redundantfirst (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, redundancy-aware policies can considerably improve the mean response time compared to redundancy-oblivious policies. We also explore the effect of redundancy on the stability region.

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Elene Anton, Rhonda Righter, Ina Maria Maaike Verloop. 2025-06-04. Efficient scheduling in redundancy systems with general service times. https://arxiv.org/abs/2206.10164

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