Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility

K. Jeganathan, M. Abdul Reiyas, S. Selvakumar, N. Anbazhagan, S. Amutha, Gyanendra Prasad Joshi, Duckjoong Jeon and Changho Seo
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K. Jeganathan: Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chepauk, Chennai 600005, India
M. Abdul Reiyas: Department of Food Business Management, College of Food and Dairy Technology, The Tamil Nadu Veterinary and Animal Sciences University (TANUVAS), Chennai 600051, India
S. Selvakumar: Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chepauk, Chennai 600005, India
N. Anbazhagan: Department of Mathematics, Alagappa University, Karaikudi 630003, India
S. Amutha: Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630003, India
Gyanendra Prasad Joshi: Department of Computer Science and Engineering, Sejong University, Seoul 05006, Korea
Duckjoong Jeon: Department of Convergence Science, Kongju National University, Gongju 32588, Korea
Changho Seo: Department of Convergence Science, Kongju National University, Gongju 32588, Korea

Mathematics, 2022, vol. 10, issue 12, 1-22

Abstract: The use of a Markovian inventory system is a critical part of inventory management. The purpose of this study is to examine the demand for two commodities in a Markovian inventory system, one of which is designated as a major item (Commodity-I) and the other as a complimentary item (Commodity-II). Demand arrives according to a Poisson process, and service time is exponential at a queue-dependent rate. We investigate a strategy of ( s , Q ) type control for commodity-I with a random lead time but instantaneous replenishment for commodity-II. If the waiting hall reaches its maximum capacity of N , any arriving primary client may enter an infinite capacity orbit with a specified ratio. For orbiting consumers, the classical retrial policy is used. In a steady-state setting, the joint probability distributions for commodities and the number of demands in the queue and the orbit, are derived. From this, we derive a waiting time analysis and a variety of system performance metrics in the steady-state. Additionally, the physical properties of various performance measures are evaluated using various numerical assumptions associated with diverse stochastic behaviours.

Keywords: classical retrial policy; queue dependent service rate; waiting time analysis; infinite orbit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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