Efficient scheduling in redundancy systems with general service times

TL;DR

This paper analyzes how different scheduling policies affect mean response time in redundancy systems with general service times, identifying optimal policies under various service time distributions and demonstrating significant improvements over oblivious policies.

Contribution

It characterizes the impact of redundancy-aware scheduling policies on response time, providing theoretical results and simulations for various service time distributions.

Findings

LRF policies outperform others with exponential service times

MRF-FCFS outperforms LRF-FCFS with high variability in New-Worse-than-Used times

Redundancy-aware policies significantly improve response time over oblivious policies

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 $\Pi$ 1 -- $\Pi$ 2 , where $\Pi$ 1 discriminates among job classes (e.g., least-redundant-first (LRF), most-redundantfirst (MRF)) and $\Pi$ 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.