A closed network consists of two multi-servers with $n$ customers. Service requirements of customers at a 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 queue the number of customers in it, all multiplied by $n^{-1}$.
Our objective: asymptotics of dynamics as $n\to \infty$. The asymptotics of dynamics of a single multi-server with an arrival process as the number of servers $n\to \infty$ 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 develop our previous asymptotics results for a network in discrete time: find equilibrium and prove convergence as $t\to \infty$.
Motivation for studying such models: they represent call/contact centers.