Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent service

Lumb, Vijay Rajan; Rani, Indra

doi:10.1007/s13198-021-01342-1

Cited by 5 publications

(2 citation statements)

References 62 publications

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“…Furthermore, the assessment of performance metrics is conducted through the utilization of probability vectors corresponding to diverse parameter values inherent to the queueing model. Within the queueing framework of Geo/Geo/1 design, encompassing catastrophes, balking, and service dependent on the system's state, handled by Lumb et al [27]. Seenivasan et al [28] explored a dual-server queueing model with heterogeneous characteristics involving distinct service rates and applied the MGM for restoration purposes.…”

Section: Literature Reviewmentioning

confidence: 99%

ANFIS-Enhanced M/M/2 Queueing Model Investigation in Heterogeneous Server Systems with Catastrophe and Restoration

2024

Contemp. Math.

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Section: Literature Reviewmentioning

confidence: 99%

ANFIS-Enhanced M/M/2 Queueing Model Investigation in Heterogeneous Server Systems with Catastrophe and Restoration

2024

Contemp. Math.

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“…Below this type of systems is called QISs with catastrophes in warehouse. It is necessary to distinguish between models of QIS with catastrophes in the warehouse and models of QIS with common lifetime (e.g., foods or medicines with the same expiry date), see [21][22][23][24][25][26][27]. In models of QISs with common lifetime, it is assumed that all items in the warehouse have the same age at any given time.…”

Section: Introductionmentioning

confidence: 99%

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Ozkar,

Melikov,

Sztrik

2023

Mathematics

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We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either (s,S) or (s,Q). If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity.

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Performance Evaluation of IoST–Mist–Fog–Cloud Framework for Geospatial Crime Data Visualization: A State Dependent Queueing Approach

Panigrahi,

Goswami,

Mund

et al. 2023

SN COMPUT. SCI.

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Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent service

Cited by 5 publications

References 62 publications

ANFIS-Enhanced <i>M</i>/<i>M</i>/2 Queueing Model Investigation in Heterogeneous Server Systems with Catastrophe and Restoration

ANFIS-Enhanced <i>M</i>/<i>M</i>/2 Queueing Model Investigation in Heterogeneous Server Systems with Catastrophe and Restoration

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Performance Evaluation of IoST–Mist–Fog–Cloud Framework for Geospatial Crime Data Visualization: A State Dependent Queueing Approach

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