On a queueing-inventory with reservation, cancellation, common life time and retrial

Krishnamoorthy, A.; Shajin, Dhanya; Lakshmy, B.

doi:10.1007/s10479-015-1849-x

Cited by 47 publications

(19 citation statements)

References 12 publications

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“…Among the related papers, we can mention the paper by Dudin and Klimenok (1996), where the additional item is interpreted as a passive server, and the papers of Kim et al (2009; where the additional item is interpreted as a token that is necessary to start service of a session in communication network. Similar queueing models arise in the analysis of so called queueing/inventory models, (see Krishnamoorthy et al, 2016c;2016b;2016a).…”

Section: Introductionmentioning

confidence: 91%

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Baek

Dudina

Kim

2017

International Journal of Applied Mathematics and Computer Science

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A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered. Type-1 customers have limited preemptive priority over type-2 customers. There is an infinite buffer for type-2 customers and no buffer for type-1 customers. There is also a finite buffer (stock) for consumable additional items (semi-products, half-stocks, etc.) which arrive according to the Markovian arrival process. Service of a customer requires a fixed number of consumable additional items depending on the type of the customer. The service time has a phase-type distribution depending on the type of the customer. Customers in the buffer are impatient and may leave the system without service after an exponentially distributed amount of waiting time. Aiming to minimize the loss probability of type-1 customers and maximize throughput of the system, a threshold strategy of admission to service of type-2 customers is offered. Service of type-2 customer can start only if the server is idle and the number of consumable additional items in the stock exceeds the fixed threshold. Stationary distributions of the system states and the waiting time are computed. In the numerical example, we show some interesting effects and illustrate a possibility of application of the presented results for solution of optimization problems.

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Section: Introductionmentioning

confidence: 91%

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Baek

Dudina

Kim

2017

International Journal of Applied Mathematics and Computer Science

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“…Concepts of reservation, cancellation, and common life time was first introduced in the queueing-inventory system by Krishnamoorthy et al [19] with a constant retrial rate. In their model, customers arrive according to a Poisson process and service time follows an exponentially distributed.…”

Section: Introductionmentioning

confidence: 99%

Analysis of an M/PH/1 Retrial Queueing-Inventory System with Level Dependent Retrial Rate

Liu

Luo

2020

Mathematical Problems in Engineering

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We analyze a queueing-inventory system which can model airline and railway reservation systems. An arriving customer to an idle server joins for service immediately with exactly one item from inventory at the moment of service completion if there are some on-hand inventory, or else he accesses to a buffer of varying size (the buffer capacity varies and equals to the number of the items in the inventory with maximum size S). When the buffer overflows, the customer joins an orbit of infinite capacity with probability p or is lost forever with probability 1−p. Arrivals form a Poisson process, and service time has phase type distribution. The time between any two successive retrials of the orbiting customer is exponentially distributed with parameter depending on the number of customers in the orbit. In addition, the items have a common life time with exponentially distributed. Cancellation of orders is possible before their expiry and intercancellation times are assumed to be exponentially distributed. The stability condition and steady-state probability vector have been studied by Neuts–Rao truncation method using the theory of Level Dependent Quasi-Birth-Death (LDQBD) processes. Several stationary performance measures are also computed. Furthermore, we provide numerical illustration of the system performance with variation in values of underlying parameters and analyze an optimization problem.

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“…The stationary system performance measures and the total expected cost rate were both calculated. Krishnamoorthy et al (2015b) analysed queueing-inventory model which combines reservation of inventory, its cancellation before the expiry of common life time and retrial of unsatised customers. In Krishnamoorthy et al (2015a) derived the steady-state distribution of the M /M /1 queueing-inventory system with positive service time.…”

Section: Introductionmentioning

confidence: 99%

A continuous review (<i>s</i>, <i>S</i>) inventory system with postponed demands at service facility

Jenifer¹

2019

EJIE

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In this article, we present a continuous review (s, S) inventory system with a service facility consisting of finite waiting hall (capacity N ) and a single server. The customers arrive according to a Poisson process. The individual customer's unit demand is satisfied after a random time of service, which is assumed to be exponential. An arriving customer, who finds the waiting hall is full, enters into the pool of infinite size or leaves the system which is according to a Bernolli trial. The joint probability distribution of the number of customers in the pool, number of customers in the waiting hall and the inventory level is obtained in the steady-state case. Various stationary system performance measures are computed and total expected cost rate is calculated. The results are illustrated numerically. [

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On a queueing-inventory with reservation, cancellation, common life time and retrial

Cited by 47 publications

References 12 publications

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Analysis of an M/PH/1 Retrial Queueing-Inventory System with Level Dependent Retrial Rate

A continuous review (<i>s</i>, <i>S</i>) inventory system with postponed demands at service facility

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