Analysis of Bulk Arrival Recurrent Queue with Active and Passive Breakdowns

This study investigates the \(M^X/G/1\) queue with retrials and an optional service facility for the one who opts for it. Here the service provider may follow Bernoulli vacation schedule. If the server is occupied, the clients are forced to join the virtual orbit from where they retry for their primary essential service or secondary optional service . The service provider is subjected to either active breakdown when occupied or passive breakdown when unoccupied. Depending on their types of breakdown, they are subjected to either immediate or delayed repair, respectively. After each service, depending on the server’s choice, it may either go on a Bernoulli vacation or may serve the next client. Implementing the embedded Markov chain technique, the system’s ergodic condition is established. Also, the steady state solution for various queueing parameters is obtained using the generating functions defined for the queue length distribution. The consequences of different parameters on the performance measures have been illustrated numerically. Further to develop a low cost model, formulation of the cost function is done and the impact of sensitive parameters on the overall cost of the system is studied. The optimization of the cost function using a soft computing technique, Artificial Bee Colony is also discussed which makes the system cost effective.