Performance of Load Balancers with Bounded Maximum Queue Length in case of Non-Exponential Job Sizes

TL;DR

This paper analyzes how load balancing policies with bounded maximum queue lengths perform under non-exponential job size distributions, providing a unified framework and closed-form bounds for large-scale systems.

Contribution

It extends existing load balancing analysis to phase-type distributed job sizes, offering a unified approach and explicit bounds on queue length and response time.

Findings

Bounds on maximum queue length can be expressed in closed form.

The cavity process accurately predicts system behavior in large-scale limits.

Job size variability affects the bounds and performance metrics.

Abstract

In large-scale distributed systems, balancing the load in an efficient way is crucial in order to achieve low latency. Recently, some load balancing policies have been suggested which are able to achieve a bounded maximum queue length in the large-scale limit. However, these policies have thus far only been studied in case of exponential job sizes. As job sizes are more variable in real systems, we investigate how the performance of these policies (and in particular the value of these bounds) is impacted by the job size distribution. We present a unified analysis which can be used to compute the bound on the queue length in case of phase-type distributed job sizes for four load balancing policies. We find that in most cases, the bound on the maximum queue length can be expressed in closed form. In addition, we obtain job size (in)dependent bounds on the expected response time. Our methodology relies on the use of the cavity process. That is, we conjecture that the cavity process captures the behaviour of the real system as the system size grows large. For each policy, we illustrate the accuracy of the cavity process by means of simulation.