Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations

Jeganathan, K.; Reiyas, M. Abdul

doi:10.1016/j.matcom.2019.12.002

Cited by 14 publications

(6 citation statements)

References 15 publications

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“…In the second model, any waiting customers would be lost when the inventory reached zero. Jeganathan and Reiyas [14] analyzed delayed and modified working vacations in the QIS with two distinct servers in which the first server is capable of executing a modified working vacation and the second server can engage in a delayed working vacation.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Since each row in the final block of the T 0,1 matrix contains at least one non-zero element, all of the rows in the final block of the R-matrix should be regarded as non-zero rows. These presumptions lead to the structure of the unknown R-matrix being as shown in (14). The following set of non-linear homogeneous equations is derived by using each block matrix in Equation (13).…”

Section: Computation Of R Matrixmentioning

confidence: 99%

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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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Section: Literature Reviewmentioning

confidence: 99%

Section: Computation Of R Matrixmentioning

confidence: 99%

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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“…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. Melikov et al [21] investigated a perishable queueing-inventory system (QIS) involving fluctuating and fixed order quantities.…”

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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“…The server goes on vacation if the delayed vacation time expires and there are still no customers. Jeganathan and Reiyas [15] developed a Markovian inventory system with two parallel heterogeneous servers. In this study, the authors considered two different server vacation strategies.…”

Section: Introductionmentioning

confidence: 99%

A queueing system with Erlang-distributed replenishment time, multiple vacations and continuous-type inventory

Li,

Liu,

2023

Preprint

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In this paper, we consider a continuous-type inventory system with positive service time, Erlang distributed leading time, and multiple vacations. The inventory policy is (r, Q). Once the inventory level is less than r, the manager sends a replenishment request to the external supplier. After a replenishment time obeying the Erlang distribution, a fixed replenishment quantity Q arrives in the system. If, during this period, the inventory is depleted, the server takes multiple vacations. We assume that the lost sale occurs while the server is on vacation. Normal service begins once the server returns from a vacation and sees that the system inventory is Q. We introduce a continuous-type inventory model with zero service time. We also prove that the steady-state probability distribution of the original model can be decomposed into the product of the distribution of the queue length of the classical M/M/1 queueing model and the inventory distribution of the continuous-type inventory model with zero service time. Numerica examples display the effects of parameters on the performance measures and the optimal system cost.

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Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations

Cited by 14 publications

References 15 publications

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

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

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

A queueing system with Erlang-distributed replenishment time, multiple vacations and continuous-type inventory

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