Modelling, performance evaluation and optimisation of (&lt;i&gt;s&lt;/i&gt;, &lt;i&gt;Q&lt;/i&gt;) retrial inventory system with partial backlogging demands: a GSPN approach

Bazizi, Lydia; Rahmoune, Fazia; Lekadir, Ouiza; Labadi, Karim

doi:10.1504/ejie.2023.131778

Cited by 2 publications

(1 citation statement)

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“…Jeganatahan et al [36] studied the classical retrial queuing model with scrap items where the server takes a vacation once the storage becomes full or there are no customers in the queue. Bazizi et al [37] explored the optimization of an (s, Q) retrial inventory system with partial backlogging demands using a generalized stochastic Petri net approach. Very recently, Jeganathan et al [38] studied the asynchronous vacation policy in the retrial QIS with the (s, Q) ordering policy.…”

Section: Literature Reviewmentioning

confidence: 99%

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

Jeganathan,

Harikrishnan,

Lakshmanan

et al. 2023

Mathematics

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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.

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Section: Literature Reviewmentioning

confidence: 99%

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

Jeganathan,

Harikrishnan,

Lakshmanan

et al. 2023

Mathematics

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

Kathirvel,

Thanushkodi,

Kumarasankaralingam

et al. 2023

Preprint

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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.

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Modelling, performance evaluation and optimisation of (<i>s</i>, <i>Q</i>) retrial inventory system with partial backlogging demands: a GSPN approach

Cited by 2 publications

References 0 publications

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

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

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

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