Before revision:  We describe the retrial supermarket model as a system of differential equations by means of density-dependent jump Markov processes, and obtain an iterative algorithm for computing the fixed point of the system of differential equations. Based on the fixed point, we analyze the expected sojourn time that a tagged arriving customer spends in this system, and use numerical examples to indicate different influence of the two probing-server numbers on system performance including the fixed point and the expected sojourn time. 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 .
After revision:  We describe the retrial supermarket model as a system of differential equations (or mean-field equations) satisfied by 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 .