On the large deviations behavior of acyclic networks of G/G/1 queues

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 char acterize the large deviations behavior of all the processes resulting from various operations in the network. For the network model that we are consid ering, these operations are passing-through-a-single-server-queue (the proc ess resulting from this operation being the departure process), superpositi on 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 app ly 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 re sults indicate how these large deviations occur, by concretely characterizi ng the most likely path that leads to them.