A matrix-analytic method for the steady state analysis of a Markovian queueing system with scrap items

Jeganathan, K.; Koffer, V. Anzen; Sugapriya, C.; Nagarajan, D.

doi:10.1016/j.dajour.2023.100244

Decision Analytics Journal

2023

DOI: 10.1016/j.dajour.2023.100244

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A matrix-analytic method for the steady state analysis of a Markovian queueing system with scrap items

K. Jeganathan,

V. Anzen Koffer,

C. Sugapriya

et al.

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2023

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

Jeganathan,

Harikrishnan,

Lakshmanan

et al. 2023

Mathematics

View full text Add to dashboard Cite

show abstract

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A matrix-analytic method for the steady state analysis of a Markovian queueing system with scrap items

Cited by 1 publication

References 40 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

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