Abstract
The present study deals with the stock-dependent Markovian demand of a retrial queueing system with a single server and multiple server vacation. The items are restocked under a continuous review (s,Q) ordering policy. When there is no item in the system, the server goes on vacation. Further, any arrival demand permits entry into an infinite orbit whenever the server is on vacation. In the Matrix geometric approach with the Neuts-Rao truncation technique, the steady-state joint distribution of the number of customers in orbit, the server status, and the inventory level is obtained. Under the steady-state conditions, some significant system performance measures, including the long-run total cost rate, are derived, and the Laplace-Stieltjes transform is also used to investigate the waiting time distribution. According to various considerations of uncontrollable parameters and costs, the merits of the proposed model, especially the important characteristics of the system with stock dependency over non-stock dependency, are explored. Ultimately, the important facts and ideas behind this model are given in conclusion.
Highlights
Accepted: 12 January 2022Normally, allowing a vacation for a server helps to maintain the working efficiency and increase the life span of the server
In such a period, an arriving primary customer enters into an infinite orbit with an intensity α
Using the Laplace-Stieltjes transform (LST), we look at the Waiting time (WT) of demand in orbit (LST)
Summary
Allowing a vacation for a server helps to maintain the working efficiency and increase the life span of the server (machine). Jeganathan et al [13], investigated a M | M |1 retrial inventory system connected to a finite capacity waiting hall, where the service rate is queue dependent and a classical retrial policy is used for orbital customers. Jeganathan et al [31] analyzed the comparative study in their queueing-inventory system in which they assumed that the arrival process of a customer was dependent on the current stock level of the system. Many authors applied a positive service time in their respective models, whereas Paul Manual et al [10], Sivakumar [33], Sivakumar [34], and Jeganathan et al [31] assumed that the inventory in the system was depleted at the instant of the arrival of a customer These observations strongly motivated us to do further research on an inventory system with stock-dependent arrivals.
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