# Groups of Repairmen and Repair-based Load Balancing in Supermarket Models with Repairable Servers

## TL;DR

This paper applies mean-field theory to analyze supermarket queueing models with repairable servers, revealing how different repair groups impact system performance and providing a new approach for complex system analysis.

## Contribution

It introduces a novel mean-field approach to analyze repairable server supermarket models, including fixed point analysis and numerical performance evaluation.

## Key findings

- Impact of repair groups on system performance
- Asymptotic independence of models established
- Fixed points satisfy nonlinear equations

## Abstract

Supermarket models are a class of interesting parallel queueing networks with dynamic randomized load balancing and real-time resource management. When the parallel servers are subject to breakdowns and repairs, analysis of such a supermarket model becomes more difficult and challenging. In this paper, we apply the mean-field theory to studying four interrelated supermarket models with repairable servers, and numerically indicate impact of the different repairman groups on performance of the systems. First, we set up the systems of mean-field equations for the supermarket models with repairable servers. Then we prove the asymptotic independence of the supermarket models through the operator semi-group and the mean-field limit. Furthermore, we show that the fixed points of the supermarket models satisfy the systems of nonlinear equations. Finally, we use the fixed points to give numerical computation for performer analysis, and provide valuable observations on model improvement. Therefore, this paper provides a new and effective method in the study of complex supermarket models.