A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Baek, Jang Hyun; Dudina, Olga; Kim, Che Soong

doi:10.1515/amcs-2017-0026

Cited by 14 publications

(9 citation statements)

References 22 publications

(27 reference statements)

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“…Stationary distributions of the system states and the waiting time are computed. Dhanya et al [9] extended findings in Baek et al [2] to retrial of low priority customers.…”

mentioning

confidence: 72%

“…In Figure 2, we notice that as service rate µ is varied, keeping (s, S, λ, γ, θ) = (20, 45, 8,2,9), the probability of server being idle increases with increase in service rate. This could be attributed to the fact that, server becomes idle with faster rate of service.…”

Section: Effect Of the Service Rate µmentioning

confidence: 99%

“…A single-server queueing system with a marked Markovian arrival process of heterogeneous customers is considered in Baek et al [2]. Type-1 customers have limited preemptive priority over type-2 customers.…”

mentioning

confidence: 99%

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Stochastic decomposition in retrial queueing-inventory system

Shajin

Krishnamoorthy

2020

RAIRO-Oper. Res.

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The purpose of this paper is to obtain product form solution for retrial – queueing – inventory system. We study an M/M/1 retrial queue with a storage system driven by an (s,S) policy. When server is idle, external arrivals enter directly to an orbit. Inventory replenishment lead time is exponentially distributed. The interval between two successive retrials is exponentially distributed and only the customer at the head of the orbit is permitted to access the server. No customer is allowed to join the orbit when the storage system is empty and also when the serer is busy. We first derive the stationary joint distribution of the queue length and the on-hand inventory in explicit product form. Using the joint distribution, we investigate long-run performance measures such as distribution of number of customers served, number of arrivals, number of customers lost during an interval of random duration and a cost function. The optimal pair (s,S) is numerically investigated.

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“…Stationary distributions of the system states and the waiting time are computed. Dhanya et al [9] extended findings in Baek et al [2] to retrial of low priority customers.…”

mentioning

confidence: 72%

Section: Effect Of the Service Rate µmentioning

confidence: 99%

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Stochastic decomposition in retrial queueing-inventory system

Shajin

Krishnamoorthy

2020

RAIRO-Oper. Res.

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“…, K}. The arrival process is assumed to be defined by the MMAP (Marked Markovian Arrival Process), see [15,16]. The possible customer's arrival moments in the MMAP coincide with the moments of the jumps of an irreducible continuous-time Markov chain ν t , t ≥ 0, with a finite state space {1, 2, ..., W}.…”

Section: Mathematical Modelmentioning

confidence: 99%

Queueing Network with Moving Servers as a Model of Car Sharing Systems

2019

Self Cite

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We consider a queueing network with a finite number of nodes and servers moving between the nodes as a model of car sharing. The arrival process of customers to various nodes is defined by a marked Markovian arrival process. The customer that arrives at a certain node when there is no idle server (car) is lost. Otherwise, he/she is able to start the service. With known probability, which depends on the node and the number of available cars, this customer can balk the service and leave the system. The service time of a customer has an exponential distribution. Location of the server in the network after service completion is random with the known probability distribution. The behaviour of the network is described by a multi-dimensional continuous-time Markov chain. The generator of this chain is derived which allows us to compute the stationary distribution of the network states. The formulas for computing the key performance indicators of the system are given. Numerical results are presented. They characterize the dependence of some performance measures of the network and the nodes on the total number of cars (fleet size of the car sharing system) and correlation in the arrival process.

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“…In recent years, there has been gowning interest in the study of queueing systems with impatient customers (balking and reneging). For related literature, interested readers may refer to Shin and Choo [15], El-Paoumy and Nabwey [10], Kumar et al [12], Kumar and Sharma [13], Bouchentouf et al [7], Baek et al [6], Bouchentouf and Messabihi [8] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

Bouchentouf

Guendouzi

Kandouci

2018

Acta Universitatis Sapientiae, Mathematica

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This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

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A Queueing System with Heterogeneous Impatient Customers and Consumable Additional Items

Cited by 14 publications

References 22 publications

Stochastic decomposition in retrial queueing-inventory system

Stochastic decomposition in retrial queueing-inventory system

Queueing Network with Moving Servers as a Model of Car Sharing Systems

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

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