We consider a single class, acyclic network of $G/G/1$ queues. We
impose some mild assumptions on the service and external arrival processes and
we characterize the large deviations behavior of all the processes resulting
from various operations in the network. For the network model that we are
considering, these operations are passing-through-a-single-server-queue (the
process resulting from this operation being the departure process),
superposition of independent processes and deterministic splitting of a process
into a number of processes. We also characterize the large deviations behavior
of the waiting time and the queue length observed by a typical customer in a
single server queue. We prove that the assumptions imposed on the external
arrival processes are preserved by these operations, and we show how to apply
inductively these results to obtain the large deviations behavior of the
waiting time and the queue length in all the queues of the network. Our results
indicate how these large deviations occur, by concretely characterizing the
most likely path that leads to them.