When Do Redundant Requests Reduce Latency ? (1311.2851v1)

Abstract: Several systems possess the flexibility to serve requests in more than one way. For instance, a distributed storage system storing multiple replicas of the data can serve a request from any of the multiple servers that store the requested data, or a computational task may be performed in a compute-cluster by any one of multiple processors. In such systems, the latency of serving the requests may potentially be reduced by sending "redundant requests": a request may be sent to more servers than needed, and it is deemed served when the requisite number of servers complete service. Such a mechanism trades off the possibility of faster execution of at least one copy of the request with the increase in the delay due to an increased load on the system. Due to this tradeoff, it is unclear when redundant requests may actually help. Several recent works empirically evaluate the latency performance of redundant requests in diverse settings. This work aims at an analytical study of the latency performance of redundant requests, with the primary goals of characterizing under what scenarios sending redundant requests will help (and under what scenarios they will not help), as well as designing optimal redundant-requesting policies. We first present a model that captures the key features of such systems. We show that when service times are i.i.d. memoryless or "heavier", and when the additional copies of already-completed jobs can be removed instantly, redundant requests reduce the average latency. On the other hand, when service times are "lighter" or when service times are memoryless and removal of jobs is not instantaneous, then not having any redundancy in the requests is optimal under high loads. Our results hold for arbitrary arrival processes.

• The paper analytically characterizes when redundant requests reduce or increase latency in distributed systems based on service time distributions and load.
• Redundancy consistently reduces latency with memoryless service times but can be detrimental at high loads with light-everywhere distributions.
• Introducing redundancy does not improve and may degrade latency if removing completed requests incurs a latency cost.

Understanding the Impact of Redundant Requests on Latency Reduction

The paper, "When Do Redundant Requests Reduce Latency?" authored by Nihar B. Shah, Kangwook Lee, and Kannan Ramchandran, presents a comprehensive analytical paper on the latency performance of redundant requests in distributed systems. Redundancy, in this context, refers to sending identical requests to multiple servers, with the request being deemed completed upon successful service by a requisite number of these servers. This approach can potentially reduce latency but also increases system load, raising the question of when such redundancy is beneficial.

Key Contributions

The paper's primary contribution is a series of analytical results characterizing scenarios under which redundant requests are beneficial or detrimental. The authors present a model capturing crucial aspects of distributed systems with redundancy, analyzing the impact of varying service time distributions and system configurations. The findings are validated through rigorous proofs and supported by simulations, offering insight into optimal redundant requesting policies across different settings.

Analytical Insights

1. Memoryless Service Times: The paper identifies that in systems where service times are independently and identically distributed (i.i.d.) and memoryless (exponentially distributed), having a higher degree of redundancy consistently reduces latency. Specifically, when request-degree $r = n$ (requests sent to all servers), the system achieves minimal latency.
2. Heavy-everywhere and Light-everywhere Distributions: The authors categorize service time distributions into heavy-everywhere and light-everywhere classes. They establish:
   • For heavy-everywhere distributions, such as mixtures of exponential distributions, redundancy (where $r = n$) reduces latency, especially under high server utilization.
   • For light-everywhere distributions, like shifted exponential or uniform distributions, redundant requests become disadvantageous at high loads, thereby suggesting no redundancy (minimal request-degree) is optimal.
3. Impact of Removal Costs: In scenarios where completed requests can be removed with some latency cost, the paper demonstrates that introducing redundancy does not improve and may even degrade latency performance, aligning with observations for light-everywhere scenarios at high load.
4. Generalization to Distributed Buffers: Extending the analysis to systems with distributed buffers corroborates the centralized findings, offering insights applicable to more practical deployment environments.

Theoretical and Practical Implications

The theoretical implications are significant for designing and optimizing computer clusters, cloud storage, and communication networks. Practically, understanding optimal redundant-request strategies helps in resource management, ensuring efficient utilization while minimizing delay. The analysis informs system architects to tailor redundancy based on workload characteristics and operational conditions.

Future Directions

The paper opens several avenues for further exploration. These include extending the characterization to cover more complex service time distributions and network topologies, considering heterogeneous systems, or exploring adaptive policies that dynamically adjust redundancy levels based on real-time system states. Additionally, investigating the interplay between resource allocation and redundancy strategy under varying load conditions could further enhance system performance insights.

In conclusion, this paper offers an analytically validated framework that significantly advances our understanding of redundancy's role in latency reduction. Its results provide a foundation for future research and practical advancements in distributed system optimization.