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 n1.
Our objective: asymptotics of dynamics as n ! 1. The asymptotics of
dynamics of a single multi-server and its queue with an arrival process as the
number of servers n ! 1 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 ! 1.
Motivation for studying such models: they represent call/contact centers and
help to construct them effectively.