Product form solution for some queueing-inventory supply chain problem

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

doi:10.1007/s12597-015-0215-8

Cited by 11 publications

(3 citation statements)

References 9 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: 90%

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: 90%

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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“…Saffari et al [4] researched an M/M/1 queueing system with inventory under (r, Q) policy and lost sales, in which lead times are random variables. Krishnamoorthy et al [5] considered a single server supply chain model with a (rQ, KQ) production inventory system. Rejitha and Jose [6] considered a stochastic inventory model with positive service time and retrial of customers.…”

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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“…Kim et al [16] and Kim et al [17] interpret additional items required for service as a token needed to start service. Similar queueing models arise in the analysis of so-called queueing/inventory models, see [20], [21], [22]. This paper is arranged as follows.…”

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confidence: 99%

A two-priority single server retrial queue with additional items

Shajin¹,

Dudin²,

Dudina³

et al. 2020

Journal of Industrial &Amp; Management Optimization

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In this paper, we study a priority queueing-inventory problem with two types of customers. Arrival of customers follows Marked Markovian arrival process and service times have phase-type distribution with parameters depending on the type of customer in service. For service of each type of customer, a certain number of additional items are needed. High priority customers do not have waiting space and so leave the system when on their arrival a priority 1 customer is in service or the number of available additional items is less than the required threshold. Preemptive priority is assumed. Type 2 customers, encountering a busy server or idle with the number of available additional items less than a threshold, go to an orbit of infinite capacity to retry for service. The customers in orbit are non-persistent: if on retrial the server is found to be busy/idle with the number of additional items less than the threshold, this customer abandons the system with certain probability. Such a system represents an accurate enough model of many real-world systems, including wireless sensor networks and system of cognitive radio with energy harvesting and healthcare systems. The probability distribution of the system states is computed, using which several of the characteristics are derived. A detailed numerical study of the system, including the analysis of the influence of the threshold, is performed.

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Product form solution for some queueing-inventory supply chain problem

Cited by 11 publications

References 9 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 two-priority single server retrial queue with additional items

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