A closed network consists of several multi-servers with n customers. Service requirements of customers at a multi-server have a common cdf. State parameters of the network: for each multi-server empirical measure of the age of customers being serviced and for the queues the numbers of customers in them, all multiplied by n−1. Our objective: asymptotics of dynamics as n→∞. The asymptotics of dynamics of a single multi-server and its queue with an arrival process as the number of servers n→∞is currently studied by famous scientists K. Ramanan, W. Whitt et al. Presently there are no universal results for general distributions of service requirements — the results are either for continuous or for discrete time ones; the same for the arrival process. We establish the asymptotics for a network in discrete time, find its equilibrium and prove convergence as t→∞. Motivation for studying such models: they represent call/contact centers and help to construct them effectively.