Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers

Jeganathan, K.; Reiyas, M. Abdul; Lakshmi, K. Prasanna; Saravanan, S.

doi:10.1016/j.matcom.2018.03.001

Cited by 22 publications

(5 citation statements)

References 14 publications

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“…Hanukov et al [9] analyzed an inventory model denoted as M/M/2, where customer interest is piqued by observing the quantity of available stocks. Jeganathan et al [10] conducted a comparative study on a Markovian inventory model employing dual servers, examining both homogeneous and heterogeneous server configurations. Their numerical results underscored the superior efficiency of the heterogeneous system.…”

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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“…To obtain the sub matrices of ψ see [1]. From the well known structure of , that the CTMC, { z t ; t ≥0} with the finite state space is regular.…”

Section: Model Description and Notationsmentioning

confidence: 99%

“…Kalidass and Kasturi [2] discussed a slower rate of service with a queue, when the server is in breakdown condition. Further, with reference [1,3] interruption on various inventory problems are studied.…”

Section: Introductionmentioning

confidence: 99%

A Queueing Inventory System with Server Working Breakdown

Lakshmi¹,

Jeganathan*²,

Ahmed³

et al. 2019

IJITEE

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This paper considers a single server inventory queueing system with two types of server breakdowns, say Type 1(T1) breakdown and Type 2 (T2) breakdowns, and working breakdown. T1 breakdown occurs in regular service period whereas T2 breakdown occurs in the duration of working breakdown. The inter arrival time between any two customers and the times of occurrences of both types of breakdowns are all independent exponential distributions. The commencement of repairing process of T1 breakdown follows Bernoulli’s whereas the commencement of repairing process of T2 breakdown is instantaneous. By using matrix method, we obtain the steady state probability vector of the finite capacity queueing inventory system. Finally, the numerical examination of model sensitiveness is performed.

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“…Preliminary services are produced in advance, deteriorating over time, and used to reduce future customers' service and wait times. Jeganathan et al [19] studied comparing a perishable inventory system's two heterogeneous servers with homogeneous servers, leading to the identification of an optimized total cost in the heterogeneous system. In the perishable inventory models, Jeganathan and Reiyas [20] considered two servers exclusively for high and low-priority servers, respectively, with working vacation for the first server and delayed working vacation for the second one.…”

Section: Introductionmentioning

confidence: 99%

Replacement of failed items in a two commodity retrial queueing-inventory system with multi-component demand and vacation interruption

Jeganathan,

Anzen Koffer,

Lakshmanan

et al. 2024

Heliyon

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Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers

Cited by 22 publications

References 14 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

A Queueing Inventory System with Server Working Breakdown

Replacement of failed items in a two commodity retrial queueing-inventory system with multi-component demand and vacation interruption

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