Before revision:  Furthermore, we analyze exponential convergence of the current location of the retrial supermarket model to the fixed point, and apply the Kurtz Theorem to study density-dependent jump Markov process given in the retrial supermarket model, which leads to a Lipschitz condition under which the fraction measure of the retrial supermarket model weakly converges to the system of differential equations . This paper arrives at a new understanding of how the workload probing can help in load balancing jobs in retrial supermarket models .
After revision:  Furthermore, we analyze exponential convergence of the current location of the retrial supermarket model . Specifically, some simple and basic conditions for the mean-field limit as well as for the Lipschitz condition are established through the first two moments of the queue length in any orbit. Finally, we show that the fixed point satisfies a system of nonlinear equations which is an interesting networking generalization of the tail equations given in the M/M/1 retrial queue, and also use the fixed point to give performance analysis of this retrial supermarket model through numerical computation .