(R2141) Analysis of MAP^I_1 , PH^(OA)_2 / PH^I_1 , PH^O_2 / 1 Retrial Inventory Queue with Two Way Communication, (s, S) Replenishment Policy, Feedback, Bernoulli Vacation and Impatient Customers

Authors

G. Ayyappan, Puducherry Technological University Puducherry, India
V. Ganesan, Sri Venkateshwaraa College of Engineering and Technology Puducherry, India

Abstract

This work discusses about the topic as the two-way communication retrial inventory queue model, the (s, S) replenishment policy, immediate feedback, Bernoulli vacations, and impatient customers. The assumption we make is that arrivals follow a Markovian arrival process, and the server provides phase type services. When the server is idle and there is a positive inventory, an arriving customer immediately receives service. If not, arriving customers goes to orbit with infinite capacity. Only in the account of positive inventory the server renders rapid feedback for incoming call arrivals, otherwise customer departs. Outgoing calls will only be made by the server in the accordance with the PH distribution when idle with positive inventory, otherwise it remains idle. In this scenario, we use the (s, S) policy to replenish the items. The steady state probability vector can be determined using a matrix analytic method, and performance metrics such as busy periods, efficiency measures, cost analysis, and numerical examples are examined.

Recommended Citation

Ayyappan, G. and Ganesan, V. (2025). (R2141) Analysis of MAP^I_1 , PH^(OA)_2 / PH^I_1 , PH^O_2 / 1 Retrial Inventory Queue with Two Way Communication, (s, S) Replenishment Policy, Feedback, Bernoulli Vacation and Impatient Customers, Applications and Applied Mathematics: An International Journal (AAM), Vol. 20, Iss. 2, Article 4.
Available at: https://digitalcommons.pvamu.edu/aam/vol20/iss2/4