Jeganathan, K.; Harikrishnan, T.; Lakshmanan, K.; Melikov, A.; Sztrik, J. Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System. Mathematics2023, 11, 4581.
Jeganathan, K.; Harikrishnan, T.; Lakshmanan, K.; Melikov, A.; Sztrik, J. Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System. Mathematics 2023, 11, 4581.
Jeganathan, K.; Harikrishnan, T.; Lakshmanan, K.; Melikov, A.; Sztrik, J. Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System. Mathematics2023, 11, 4581.
Jeganathan, K.; Harikrishnan, T.; Lakshmanan, K.; Melikov, A.; Sztrik, J. Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System. Mathematics 2023, 11, 4581.
Abstract
This article deals with the queueing-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 queueing-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. Optimum total cost has been obtained, and sensitivity analyses, which include expected total cost, waiting time of customers in waiting hall and orbit, number of busy servers, and fraction of successful retrial rate of the model, are done numerically.
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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