Bulk service queue with server breakdown and repairs

Abstract

A single server Erlangian bulk service queue with certain concepts like vacation, break down and repair has been analysed. The units arrive to the service point according to Poisson process with various arrival rates which depend on the position of the server. The units are served in batches under general bulk service rule in k service phases. When the system becomes empty, the server leaves the system and takes vacation for a random period of time. The server may breakdown which leads to repairs. In this paper, the expressions for the state probabilities and the expected number of units in the system under different positions of the server are derived.