Investigation on inventory replenishment policy for a queueing system with catastrophic failure, negative arrival and discouragement customers

The single queues of inventory systems (IS) with warehouse catastrophes and negative arrivals (NA) occur in the service area were examined in this work. Arriving positive customers (PC) can queue up infinitely to make purchases. Customers in the system are still waiting for stock replenishment after catastrophes even when all of the system's commodities are destroyed. The positive customer that is now getting service from the server is disrupted and removed as a result of the negative arrival. The server is instantly impacted by the breakdown as a result of the negative customer's arrival. After examining queueing inventory system's stability conditions, busy period, and the transition probability vector was calculated using the matrix-analytic method. The results of numerical assessments have been presented together with formulas for performance measures.