Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

In this article, an unreliable single server bulk queueing model with overloading service, variant arrival rate, closedown under multiple vacations are considered. The arrival rates of the units are different and depends upon the server status. On service completion epoch, if the queue length is less than 'a' then the server perform closedown work. Following the closedown, the server leaves for multiple vacations of random length. We incorporated the overloading concept for the server which is assured in various practical applications. When the server is in working modes, breakdown may occur randomly at any instant during essential/overloading service. The repair job of broken down machine is done immediately and the server returns to render its remaining service. We derived the probability distribution of queue length at a departure and random epoch using supplementary variable technique. Various performance indices namely the expected length of the queue; the expected waiting time in the queue are obtained. Stability condition and steady-state probabilities are also established. In order to match our investigation with the earlier existing results, we discuss some particular cases. Finally, numerical illustration along with graphical studies are presented to visualise the effect of the parameters of the system.