In the study of large-scale stochastic networks, the mean-field theory is a useful mathematical tool. Li [2016] provided an excellent overview for the mean-field theory and the nonlinear Markov processes of large-scale stochastic networks. Li et al. [2014] developed a probabilistically computational method for setting up the system of mean-field equations in a supermarket model with server vacations, while  Li et al. [2016] gave a probabilistically computational method for setting up the system of mean-field equations in a supermarket model with Markovian arrival processes (non-Poisson inputs) and  phase-type service times (non-exponential service). Using the mean-field theory, Li et al. [2016] discussed a healthacre system, Li and Fan [2021] discussed a bike-sharing system under Markov enviornment.