Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System

Kathirvel Jeganathan, Thanushkodi Harikrishnan, Kumarasankaralingam Lakshmanan, Agassi Melikov and Janos Sztrik ()
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Kathirvel Jeganathan: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India
Thanushkodi Harikrishnan: Guru Nanak College (Autonomous), University of Madras, Chennai 600042, India
Kumarasankaralingam Lakshmanan: Department of Mathematics, St. Joseph University, Chümoukedima 797115, India
Agassi Melikov: Institute of Control Systems, National Academy of Science, Baku, AZ 1141, Azerbaijan
Janos Sztrik: Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2023, vol. 11, issue 22, 1-31

Abstract: This article deals with the queuing-inventory system, composed of c junior servers, a senior server, two finite waiting halls, and an infinite orbit. On occasion, junior servers encounter challenges during customer service. In these instances, they approach the senior server for guidance in resolving the issue. Suppose the senior server is engaged with another junior server. The approaching junior servers await their turn in a finite waiting area with a capacity of c for consultation. Concerning this, we study the performance of junior servers approaching the senior server in the retrial queuing-inventory model with the two finite waiting halls dedicated to the primary customers and the junior servers for consultation. We formulate a level-dependent QBD process and solve its steady-state probability vector using Neuts and Rao’s truncation method. The stability condition of the system is derived and the R matrix is computed. The optimum total cost has been obtained, and the sensitivity analyses, which include the expected total cost, the waiting time of customers in the waiting hall and orbit, the number of busy servers, and a fraction of the successful retrial rate of the model, are computed numerically.

Keywords: multi-server; classical retrial facility; ( s , Q ) ordering policy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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