A closed network consists of two 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 queue the number of customers in it, all
multiplied by 1/n.
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->\infty is currently studied by famous scientists K. Ramanan,
W. Whitt et al. In the last publications the arrival process is generalized to
time-dependent. We develop our previous asymptotics results for a network
also in this direction: instead of a simple time dependence a markov swithching
behavior of one multi-server is introduced. For the asymptotic process we in a
rough way nd equilibrium and prove convergence as n->\infty.
Motivation for studying such models: they represent call/contact centers, and
switching expresses the changes of the system environment.