Stochastic analysis of a controlled bulk queueing system with continuously operating server: continuous time parameter queueing process

Stochastic processes in a bulk single-server queue with continuously operating server, semi-Markov modulated compound Poisson input process and general state dependent service process are studied. The authors treat the queueing process with continuous time parameter as a semi-regenerative process and obtain its stationary probability distribution. The authors also study the input and output processes and establish ergodic theorems for some functionals of these processes. The results obtained in the article are illustrated by various examples.