Abstract
A single server retrial queueing-inventory model is investigated in this study. In Bernoulli vacation, after providing service to the customer, the server may opt to avail vacation or start the service to subsequent customer. During the busy period, breakdown and balking may occur. The inventory is replenished to an (s, S) policy and the replenishing time is assumed to adopt an exponential distribution. Furthermore, assume that an emergency replenishment of one item with zero lead time takes place when the on-hand inventory level decreases to zero. We integrate the emergency replenishment into the system to ensure customer satisfaction. For our system, a stability criterion was developed and the stationary probability vector was evaluated by utilizing the matrix analytical approach. This model also examined the study of busy time and performance measures. Using two and three dimensional graphs, the numerical illustrations are shown.
Recommended Citation
Ayyappan, G. and Thilakavathy, M.
(2025).
(R2131) Analysis of MAP/PH/1 Retrial Inventory Queueing System with Constant Retrial Rate, Bernoulli Vacation, Breakdown, Delayed Repair, Balking, (s, S) Policy and Emergency Replenishment,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
2, Article 2.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss2/2