Performance of Redundancy(d) with Identical/Independent Replicas

Abstract

Queueing systems with redundancy have received considerable attention recently. The idea of redundancy is to reduce latency by replicating each incoming job a number of times and to assign these replicas to a set of randomly selected servers. As soon as one replica completes service the remaining replicas are cancelled. Most prior work on queueing systems with redundancy assumes that the job durations of the different replicas are independent and identically distributed (i.i.d.), which yields insights that can be misleading for computer system design. In this article, we develop a differential equation, using the cavity method, to assess the workload and response time distribution in a large homogeneous system with redundancy without the need to rely on this independence assumption. More specifically, we assume that the duration of each replica of a single job is identical across the servers and follows a general service time distribution. Simulation results suggest that the differential equation yields exact results as the system size tends to infinity and can be used to study the stability of the system. We also compare our system to the one with i.i.d. replicas and show the similarity in the analysis used for independent, respectively, identical replicas.