Modeling of Stochastic Arrivals Depending on Base Stock Inventory System with a Retrial Queue

This paper mainly deals with the customers whose arrivals depend upon the existing stock level and base stock ordering policy in a stochastic queuing environment. The time between any successive primary as well as retrial arrivals and lead time are following independent exponential distributions. By applying Neuts Matrix Geometric Method, we present the time invariant joint distribution of number of customers in the orbit as well as stock level. Adequate numerical results are explored according to different characteristics of the system performance measures. Further we discuss the advantages between stock depending and non-depending arrivals about the expected total cost and parameter analysis. Also we explore the model with a different class of stock dependent arrivals under the various cost structure and replenishment time. Managerial insights of this model helps to make the decision for an appropriate base stock ordering policy under certain random conditions with a stock dependent demand rate and a limited holding capacity for ordered items.