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

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