RETRACTED ARTICLE: Transient behavior of a Markovian queue with working vacation variant reneging and a waiting server

Azhagappan, A.

doi:10.1007/s11750-018-00495-w

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…Some of the works in this area have been done in this area are Kumar et al Also, returning to the orbit (feedback) is considered in many of the studied systems. For example, Kumar et al [ [19], modified vacation by Jain and Bhagat [20], Bernoulli vacation by Choudhury and Ke [21], working vacation by Azhagappan [22] and variant vacation by Ke [23].…”

Section: Introduction *mentioning

confidence: 99%

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Abdollahi

Rad

2020

IJRRS

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Queueing theory is a way for real-world problems modeling and analyzing. In many processes, the input is converted to the desired output after several successive steps. But usually limitations and conditions such as Lack of space, feedback, vacation, failure, repair, etc. have a great impact on process efficiency.This article deals with the modeling the steady-state behavior of a‫ܯ‬ Ȁ‫ܩ‬Ȁ ͳretrial queueing system with ݇ phases of service. The arriving batches join the system with dependent admission due to the server state.If the customers find the server busy, they join the orbit to repeat their request. Although, the first phase of service is essential for all customers, any customer has three options after the completion of the ݅ െ ‫݄ݐ‬phaseሺ݅ ൌ ͳǡʹǡ ǥ ǡ ሻ. They may take the ሺ݅ ͳሻ െ ‫݄ݐ‬ phase of service with probabilityɅ ୧ , otherwise return the orbit with probability ୧ or leave the system with probability ሺͳ െ ୧ െ Ʌ ୧ ሻ. Also, after each phase, the probabilistic failure, delay, repair and vacation are considered.In this article, after finding the steady-state distributions, the probability generating functions of the system and orbit size have been found. Then, some important performance measures of the system have been derived. Also, the system reliability has been defined. Eventually, to demonstrate the capability of the proposed model, the sensitivity analysis of performance measures via some model parameters (arrival/retrial/vacation rate) in different reliability levels have been investigated in a specific case of this model. Additionally, for optimizing the performance of system, some technical suggestions are presented.

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Section: Introduction *mentioning

confidence: 99%

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Abdollahi

Rad

2020

IJRRS

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Reliability and Sensitivity Analysis of Retrial Queue with Optional k-Phases Services, Vacation and Feedback

Abdollahi

Rad

Farsi

2021

Iran J Sci Technol Trans Sci

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Variant impatient behavior of a Markovian queue with balking reserved idle time and working vacation

Azhagappan

Deepa

2020

RAIRO-Oper. Res.

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The customers’ impatience and its effect plays a major role in the economy of a country. It directly affects the sales of products and profit of a trading company. So, it is very important to study various impatient behaviors of customers and to analyze different strategies to hold such impatient customers. This situation is modeled mathematically in this research work along with working vacation and reserved idle time of server, balking and re-service of customers. This paper studies the transient analysis of an M/M/1 queueing model with variant impatient behavior, balking, re-service, reserved idle time and working vacation. Whenever the system becomes empty, the server resumes working vacation. When he is coming back from the working vacation and finding the empty system, he stays idle for a fixed time period known as reserved idle time and waits for an arrival. If an arrival occurs before the completion of reserved idle time, the server starts a busy period. Otherwise, he resumes another working vacation after the completion of reserved idle time. During working vacation, the arriving customers may either join or balk the queue. The customers waiting in the queue for service, during working vacation period, become impatient. But, the customer who is receiving the service in the slow service rate, does not become impatient. After each service, the customer may demand for immediate re-service. The transient system size probabilities for the proposed model are derived using generating function and continued fraction. The time-dependent mean and variance of system size are also obtained. Finally, numerical illustrations are provided to visualize the impact of various system parameters.

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RETRACTED ARTICLE: Transient behavior of a Markovian queue with working vacation variant reneging and a waiting server

Cited by 3 publications

References 19 publications

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Reliability and Sensitivity Analysis of a Batch Arrival Retrial Queue with k-Phase Services, Feedback, Vacation, Delay, Repair and Admission

Reliability and Sensitivity Analysis of Retrial Queue with Optional k-Phases Services, Vacation and Feedback

Variant impatient behavior of a Markovian queue with balking reserved idle time and working vacation

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