Abstract
This paper deals with an MX/G/1 Bernoulli vacation queue with two phases of service in which an unreliable server operates a randomised vacation policy with at most M consecutive vacations. If the system is empty by the end of the Mth vacation, the server becomes idle in the system until at least one customer arrives at the queue. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the joint distribution of state of the server and queue size, the pgf of the stationary queue size distribution at a departure epoch, LST of busy period distribution and waiting time distribution along with some important performance measures of the model. Finally, we develop a cost model to determine optimal randomised policy along with some numerical illustration.
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