(Revision) On an Unreliable Retrial Queue with General Repeated Attempts and J Optional Vacations

This paper considers a single-server retrial queue with constant retrial rate and batch arrivals, where an unreliable server may take an additional optional vacation after the first essential vacation. Customers arrive at the system according to a compound Poisson process, and they are served immediately if the server is available; otherwise, they will enter a retrial orbit and form a single waiting line. If the orbit becomes empty, the server leaves for the first essential vacation. At the end of first essential vacation, the server may either remain idle in the system or take one of J additional vacations. The server may break down at any instant while providing service. It is assumed that the service times and repair times of the server and the retrial times of customers are all arbitrarily distributed. By using the supplementary variable technique, we derive the probability generating functions of the system size at a random epoch and at a departure epoch. Various system performance measures and two reliability indices are developed. Finally, we deal with a cost optimization problem and provide numerical examples.