The tightness in the ergodic analysis of regenerative queueing processes

The tightness of some queueing stochastic processes is proved and its role in an ergodic analysis is considered. It is proved that the residual service time process in an open Jackson-type network is tight. The same problem is solved for a closed network, where the basic discrete time process is embedded at the service completion epochs. An extension of Kiefer and Wolfowitz's ‘key’ lemma to a nonhomogeneous multiserver queue with an arbitrary initial state is obtained. These results are applied to get the ergodic theorems for the basic regenerative network processes.