The BMAP/GI/l Queue with Server Set-UpTimes and Server Vacations

PALM-MARTINGALE CALCULUS, QUEUES WITH VACATIONS, BATCH MARKOVIAN ARRIVAL PROCESSES,SERVER SET-UP Using Palm-martingale calculus, we derive the workload characteristic function and queue length moment generating function for the BMAP IGl/1 . queue with server vacations. In the queueing system under study, the server may start a vacation at the completion of a service or at the arrival of a customer finding an empty system. In the latter case we will talk of a server set-up time. The distribution of a set-up time or of a vacation period after a departure leaving a non-empty system behind is conditionally independent of the queue length and workload. Furthermore, the distribution of the server set-up times may~be different from the distribution of vacations at service completion times. The results are particularized to the M/Gl/1 queue and to the BMAPIGl/1 queue (without vacations).