  The paper studies closed queueing networks containing a server station and
$k$ client stations. The server station is an infinite server queueing system,
and client stations are single-server queueing systems with autonomous service,
i.e. every client station serves customers (units) only at random instants
generated by a strictly stationary and ergodic sequence of random variables.
The total number of units in the network is $N$. The expected times between
departures in client stations are $(N\mu_j)^{-1}$. After a service completion
in the server station, a unit is transmitted to the $j$th client station with
probability $p_{j}$ $(j=1,2,...,k)$, and being processed in the $j$th client
station, the unit returns to the server station. The network is assumed to be
in a semi-Markov environment. A semi-Markov environment is defined by a finite
or countable infinite Markov chain and by sequences of independent and
identically distributed random variables. Then the routing probabilities
$p_{j}$ $(j=1,2,...,k)$ and transmission rates (which are expressed via
parameters of the network) depend on a Markov state of the environment. The
paper studies the queue-length processes in client stations of this network and
is aimed to the analysis of performance measures associated with this network.
The questions risen in this paper have immediate relation to quality control of
complex telecommunication networks, and the obtained results are expected to
lead to the solutions to many practical problems of this area of research.
