A Batch Arrival Queue System with Coxian-2 Server Vacations and Admissibility Restricted

The M/G/1 classic queueing system were extended by many authors in last two decades. The systems with server’s vacation are important models that extend the M/G/1 queueing system. Also another conditions such as admissibility restricted may occure in systems. From this motivation, in this system I consider a single server queue with batch arrival Poisson input. There is a restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. At each service completion epoch, the server may apt to take a vacation with probability θ or else with probability 1 − θ may continue to be available in the system for the next service. The vacation period of the server has two heterogenous phases. Phase one is compulsory, and phase two follows the phase one vacation in such a way that the server may take phase two with probability p or may return back to the system with probability 1 − p. The vacation times are assumed to be general. All stochastic processes involved in this system (service and vacation times) are independent of each other. We derive the PGF’s of the system and by using them the informance measures are obtained. Some numerical approaches are examined the validity of results.