Analysis of queueing model with catastrophe and restoration

Seenivasan, M.; Kameswari, M.; Chakravarthy, V J; Indumathi, M.

doi:10.1063/5.0062890

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…Note that similar models of QS (but not QIS) with catastrophes are widely investigated in available literature. In lieu of reviewing work related to models of QS with catastrophes, we highlight representative papers [28][29][30][31][32][33][34] and refer readers to their reference lists. In QS, disaster events immediately destroy the system.…”

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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Section: Introductionmentioning

confidence: 99%

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Ozkar,

Melikov,

Sztrik

2023

Mathematics

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Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Ozkar,

Melikov,

Sztrik

2023

Preprint

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We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to Poisson process and upon arrival of a catastrophe all inventory in the system is instantly destroyed. But consumer customers in the system (in the server or in the buffer) continue still waiting for the replenishment of the stock. The arrivals of the consumer customers follow a Markovian Arrival Process (MAP) and they can be queued in an infinite buffer. Service time of a consumer customer follows a phase-type distribution. The system receives negative customers whose have Poisson flows to service facility and upon arrival of a negative customer one consumer customer is pushed out from the system, if any. One of two replenishment policies can be used in the system: either (s,S) or (s,Q). If upon arrival of the consumer customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or join the queue (backorder sale scheme). The system is formulated by a four-dimensional continuous-time Markov chain. Steady state distribution is obtained using the matrix-geometric method. A comprehensive numerical study is performed on the performance measures under various replenishment policies. Finally, an optimization study is presented.

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Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

Melikov,

Poladova,

Edayapurath

et al. 2023

Mathematics

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In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) in service facility. Consumer customers (c-customers) that arrived to buy inventory can be queued in an infinite buffer. Under catastrophes, all inventory of the system is destroyed but customers in the system (on server or in buffer) are still waiting for replenishment of stocks. Upon arrival of n-customer one c-customer is pushed out, if any. One of two replenishment policies (RP) can be used in the system: either (s,S) or randomized. In the investigated QISs, a hybrid service scheme was used: if upon arrival of the c-customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or joining the queue (backorder scheme). Mathematical models of the investigated QISs were constructed as two-dimensional Markov chains (2D MC). Ergodicity conditions of the investigated QISs were obtained, and the matrix-analytic method (MAM) was used to calculate the steady-state probabilities of the constructed 2D MCs. Formulas for performance measures were found and the results of numerical experiments are presented.

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Analysis of queueing model with catastrophe and restoration

Cited by 3 publications

References 12 publications

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

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