Dominating tails in a tandem of queues with long range dependent arrival and service processes

We consider a tandem of queues fed by a superposition of on-off sources. The service process at each of the queues in the tandem are also independent on-off fluid processes. The off duration in the service process may be due to a server breakdown or due to the unavailability of the server because of the presence of higher priority cross-traffic. We obtain sufficient conditions for the tail of the stationary end-to-end backlog distribution to be dominated by one of the service processes or by one of the source processes