A revisit to queueing-inventory system with positive service time

Krishnamoorthy, A.; Manikandan, R.; Lakshmy, B.

doi:10.1007/s10479-013-1437-x

Cited by 55 publications

(16 citation statements)

References 17 publications

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“…Krishnamoorthy et al [22] analyzed an inventory systems with lost sales with generally distributed service times. At the end of the service, customers receive the requested item from inventory only with probability γ .…”

Section: Examplementioning

confidence: 99%

Loss systems in a random environment: steady state analysis

Krenzler

Daduna

2014

Queueing Syst

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We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove a product-form steady state distribution of the joint queueingenvironment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, for example, from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, for example, of queueing-inventory processes. We investigate further classical loss systems, where, due to finite waiting room, loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise.Keywords Queueing systems · Random environment · Product form steady state · Loss systems · M/M/1/∞ · M/M/m/∞ · M/M/m/N · Inventory systems · Availability · Lost sales Mathematics Subject Classification Primary 60K · 60J10 · 60F05 · 60K20 · 90B22 · 90B05

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Section: Examplementioning

confidence: 99%

Loss systems in a random environment: steady state analysis

Krenzler

Daduna

2014

Queueing Syst

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“…The considered model is very close to the models in which some additional resource is required to provide service to a customer. These models include, in particular, so-called queueing/inventory models (see, e.g., [4]), queueing systems with energy harvesting (see, e.g., [5]), queueing models with paired customers (see [6]), assembly-like queue (see [7]), passenger-taxi or double-ended queues (see [8]), coupled queues (see [9]), etc. In our model, the role of the additional resource is played by the lag between the critical and current value of the server's temperature.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Queueing Model with Server Heating and Cooling

Dudina

Dudin

2019

Mathematics

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The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.

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“…The served customers may or may not purchase the inventory item system after the service completion. The models with such customers were first considered in [7] and [14] and later applied in [15]. We use threedimensional Markov chain to describe the mathematical model of the system.…”

Section: Introductionmentioning

confidence: 99%

Simulation Model of Infinite Perishable Queueing Inventory System with Feedback

Shahmaliyev¹

2018

Upr. sist. maš.

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Perishable Queuing Inventory system with positive service time and customer feedback is considered. The system applies Variable Size Order policy for the inventory replenishment. Stochastic simulation method is used to calculate the system performance measures and find its stationary distribution. The dependence of performance measures on the reorder level is illustrated and analyzed using the numerical experiments.

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A revisit to queueing-inventory system with positive service time

Cited by 55 publications

References 17 publications

Loss systems in a random environment: steady state analysis

Loss systems in a random environment: steady state analysis

Optimization of Queueing Model with Server Heating and Cooling

Simulation Model of Infinite Perishable Queueing Inventory System with Feedback

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