Transient performance analysis of a single server queuing model with retention of reneging customers

Kumar, Rakesh; Sharma, Sapana

doi:10.2298/yjor170415007k

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…They have obtained the steady-state solution of the model. Kumar and Sharma [14] considered a single-server queuing model with reneging and retention of reneging customers. They have derived the transient solution of the model.…”

Section: Review Of Related Literaturementioning

confidence: 99%

A Multi-Server Queuing Model With Balking and Correlated Reneging With Application in Health Care Management

et al. 2020

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Queues or waiting lines are an integral part of health care facilities such as hospitals, outpatient clinics, medical laboratories, and many other health facilities. Health care management must have waiting lines control strategies for smooth functioning. Due to the lack of proper queuing control and management, patients may become dissatisfied and may leave (renege) the health care facilities without getting service. But, the reneging of patients at two consecutive time marks may be correlated in the sense that if a patient reneges at the current time mark, then there is a probability that a patient may or may not renege at the next time mark. This kind of reneging is referred to as correlated reneging. In this paper, we have introduced the concept of correlated reneging in a finite capacity multi-server queuing model with balking with its application in health care. The steady-state as well as the transient analyses of the model are carried out. We have also derived an expression for the correlation coefficient between the interreneging times and for the rate at which the health facility is losing patients (patient loss probability) due to insufficient capacity, reneging, and balking. We have provided numerical examples in order to demonstrate the effect of balking and correlated reneging on performance measures such as the mean number of patients waiting to be serviced, mean waiting time of patients, and the probability of patient rejection. Further, the effect of the number of servers on performance measures is investigated. Finally, the effect of the correlation coefficient between the inter-reneging times on performance measures is studied. The queuing model discussed in this paper could be useful to the health care firms facing the problem of patient impatience and capacity constraints.

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Section: Review Of Related Literaturementioning

confidence: 99%

A Multi-Server Queuing Model With Balking and Correlated Reneging With Application in Health Care Management

et al. 2020

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“…Models with customers impatience in queues like the process of reneging and balking have been studied by various authors in the past. Most recent results about systems having the impatience property can be found for example in [7,8,16].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

Sztrik

Tóth

Danilyuk

et al. 2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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In this paper, we consider a retrial queueing system of M/G/1 type with an unreliable server, collisions, and impatient customers. The novelty of our work is to carry out a sensitivity analysis applying different distributions of service time of customers on significant performance measures for example on the probability of abandonment, the mean waiting time of an arbitrary, successfully served, impatient customer, etc. A customer is able to depart from the system in the orbit if it does not get its appropriate service after a definite random waiting time so these will be the so-called impatient customers. In the case of server failure, requests are allowed to enter the system but these will be forwarded immediately towards the orbit. The service, retrial, impatience, operation, and repair times are supposed to be independent of each other. Several graphical illustrations demonstrate the comparisons of the investigated distributions and the interesting phenomena which are obtained by our self-developed simulation program. The achieved results are compared to the results of the [2] to check how the system characteristics changes if we use other distributions of service time and to present the advantages of performing simulations in certain scenarios.

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Transient analysis of a Markovian queuing model with multiple-heterogeneous servers, and customers’ impatience

Kumar

Sharma

2021

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Transient performance analysis of a single server queuing model with retention of reneging customers

Cited by 7 publications

References 21 publications

A Multi-Server Queuing Model With Balking and Correlated Reneging With Application in Health Care Management

A Multi-Server Queuing Model With Balking and Correlated Reneging With Application in Health Care Management

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

Transient analysis of a Markovian queuing model with multiple-heterogeneous servers, and customers’ impatience

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