  The paper studies a closed queueing network containing two types of node. The
first type (server station) is an infinite server queueing system, and the
second type (client station) is a single server queueing system with autonomous
service, i.e. every client station serves customers (units) only at random
instants generated by strictly stationary and ergodic sequence of random
variables. It is assumed that there are $r$ server stations. At the initial
time moment all units are distributed in the server stations, and the $i$th
server station contains $N_i$ units, $i=1,2,...,r$, where all the values $N_i$
are large numbers of the same order. The total number of client stations is
equal to $k$. The expected times between departures in the client stations are
small values of the order $O(N^{-1})$ ~ $(N=N_1+N_2+...+N_r)$. After service
completion in the $i$th server station a unit is transmitted to the $j$th
client station with probability $p_{i,j}$ ~ ($j=1,2,...,k$), and being served
in the $j$th client station the unit returns to the $i$th server station. Under
the assumption that only one of the client stations is a bottleneck node, i.e.
the expected number of arrivals per time unit to the node is greater than the
expected number of departures from that node, the paper derives the
representation for non-stationary queue-length distributions in non-bottleneck
client stations.
