Behaviour of the Imbedded Markov Chain of the General Bulk Service Queueing System

In this paper, the model of queueing system M/G/1 with group arrivals, batch service and more general control strategy is introduced; and several questions about the structure of the phase space of the imbedded Markov chain and its irreducibility and aperiodicity for this kind of queueing system are discussed completely, and the formula of the periodic value is also obtained.