Redundancy with Processor Sharing servers

Abstract

The main motivation to investigate redundancy models comes from empirical evidence suggesting that redundancy can help improve the performance of real-world applications. Under redundancy, a job that arrives to this system is dispatched to d servers uniformly chosen at random in order to benefit from the variability of the length of these queues. As soon as one of the copies finishes service, the job (and its copies) is removed from the system, and as a consequence, a job's delay is given by the minimum delay among the servers its copies are sent to. Most of the literature on performance evaluation of redundancy systems has been carried out when First Come First Served (FCFS) is implemented in the servers. In particular, for exponential service time distributions, Gardner et al. [4, 5] and Bonald and Comte [2] show that the stability region is not reduced due to adding redundant copies. In this extended abstract, we focus instead on Processor Sharing (PS) service policy and study how redundancy impacts the stability condition. In particular, we aim to study the impact that the correlation structure of the copies has on the performance of the redundancy-d model. In a recent paper, Gardner et al. [3] showed that the assumption of independent and identically distributed (i.i.d.) copies, can be unrealistic, and that it might lead to theoretical results that do not reflect the results of replication schemes in real-life computer systems. We consider the two extreme cases of correlation; (i) the copies are i.i.d. (ii) the copies of a job are exact replicas (identical copies). We observe that the stability condition strongly depends on the correlation structure, as well as on the number of redundant copies.