S&X: Decoupling Server Slowdown (S) and Job Size (X) in Modeling Job Redundancy

Recent computer systems research has proposed using redundant requests to reduce latency. The idea is to replicate a request so that it joins the queue at multiple servers. The request is considered complete as soon as any one copy of the request completes. Redundancy is beneficial because it allows us to overcome server-side variability – the fact that the server we choose might be temporarily slow, due to factors such as background load, network interrupts, and garbage collection. When there is significant server-side variability, replicating requests can greatly reduce response times. In the past few years, queueing theorists have begun to study redundancy, first via approximations, and, more recently, via exact analysis. Unfortunately, for analytical tractability, most existing theoretical analysis has assumed models with independent service times. This is unrealistic because a job with large size should actually remain large at all servers, rather than getting a new independent size at each server. The unrealistic independence assumption has led to theoretical results which can be at odds with computer systems implementation results. This paper introduces a much more realistic model of redundancy. Our model allows us to decouple the inherent job size (X) from the server-side slowdown (S), where we track both S and X for each job. Analysis within the S&X model is, of course, much more difficult. Nevertheless, we design a policy, Redundant-on-Idle-Queue (RIQ) which is both analytically tractable within the S&X model and has provably excellent performance.