Abstract: The supermarket model is a dynamic randomized load balancing scheme for real-time dynamic control of large-scale parallel queuing network. It has many important practical applications in, for example, computer networks, cloud computing, manufacturing systems and transportation networks. In this paper, for the supermarket models we consider some important issues, such as, real-time dynamic control modes; efficiency comparison; mean-field black hole; Markov changing environment; stability; fixed point; system performance analysis. At the same time, we also study these important issues through some numerical examples, include performance comparison, and efficiency analysis for advantages and disadvantages among the supermarket models with either customers joining the shortest queue, or customers joining any queue randomly, or customers joining the longest queue. Further, we consider a more general supermarket model under an Markov changing environment, and provide performance evaluation for the supermarket model under an Markov changing environment.