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Batch arrival and bulk service queueing systems are quite common in many real life situations such as the arrival of aircraft passengers, elevators, Manufacturing systems, communication network, giant wheel, tourism, etc. Bulk service queueing model was initially originated with Bailey [1]. Neuts [2] proposed the “General Bulk Service Rule” in which service initiates only when a certain number of customers in the queue is available. Some general bulk service results have discussed by Holman, Chaudhry, and Ghosal [3]. Chaudhry and Templeton [4] have worked on bulk service rule by using the supplementary variable technique. Banerjee et.al [5] has considered a queueing model with variable service capacity and batch-size-dependent service. Sikdar and Samanta [6] have analyzed a finite buffer queueing model with bulk service variable server capacity. Recently, bulk service queueing model with multiple working vacations have studied by Jeyakumar and Senthilnathan [7].

Analysis of Mx/G(a,b)/1 Queueing System with Two Phases of Service Subject to Server Breakdown and Extended Bernoulli Vacations