Single server queues with a Batch Markovian Arrival Process and server vacations

Single server queues with a Batch Markovian Arrival Process and two types of server vacations are considered. For the steady state behaviour of the number of customers in the system first appropriate embedded Markov chains are analyzed using matrix analytic methods. Then computationally tractable results for the continuous time process are given using the theory of semi-regenerative processes. Finally a cost model is considered and the cost rate is derived.