  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.
