# Job Allocation in Large-Scale Service Systems with Affinity Relations

## TL;DR

This paper studies load balancing in large-scale service systems with affinity relations, proposing schemes that allocate jobs to primary or secondary servers, and analyzing stability and performance through coupling and fluid limit techniques.

## Contribution

It introduces load balancing schemes considering affinity relations and develops novel coupling methods for stability analysis and performance bounds.

## Key findings

- Stability conditions depend on affinity and load parameters.
- Fluid limit analysis reveals the impact of model parameters on performance.
- Coupling construction provides bounds for system stability.

## Abstract

We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be allocated to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job-server affinity relations can model network topologies based on geographical proximity, or data locality in cloud scenarios. We introduce load balancing schemes that allocate jobs to primary servers if available, and otherwise to secondary servers. A novel coupling construction is developed to obtain stability conditions and performance bounds using a coupling technique. We also conduct a fluid limit analysis for symmetric model instances, which reveals a delicate interplay between the model parameters and load balancing performance.