Mean Field Analysis of Join-Below-Threshold Load Balancing for Resource Sharing Servers

Abstract

Load balancing plays a crucial role in many large scale computer systems. Much prior work has focused on systems with First-Come- First-Served (FCFS) servers. However, servers in practical systems are more complicated. They serve multiple jobs at once, and their service rate can depend on the number of jobs in service. Motivated by this, we study load balancing for systems using Limited- Processor-Sharing (LPS). Our model has heterogeneous servers, meaning the service rate curve and multiprogramming level (limit on the number of jobs sharing the processor) differs between servers. We focus on a specific load balancing policy: Join-Below-Threshold (JBT), which associates a threshold with each server and, whenever possible, dispatches to a server which has fewer jobs than its threshold. Given this setup, we ask: how should we configure the system to optimize objectives such as mean response time? Configuring the system means choosing both a load balancing threshold and a multiprogramming level for each server. To make this question tractable, we study the many-server mean field regime.