LAUSR

This paper studies the transient and the steady-state behaviour of an M[x]/G/1 queueing system with a randomised vacation policy at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair may be delayed, in which the repair time is a general random variable. Based on the supplementary variable technique, we developed the transient and the steady-state solutions for both queueing and reliability measures of the variant vacation system.