Probabilistic Analysis of Single Server Queueing Systems with Feedback, Customer Decisions, and Vacation Interruptions

Authors

  • H. Saddam Hussain, A. Sridhar

Keywords:

Queueing theory, Single-server system, Feedback, Customer decisions, Vacation interruptions, Markov chains, Performance metrics, System optimization

Abstract

This paper focuses on giving a detailed probabilistic modeling of a periodic replenishment system in a single server feedback system with customer controlling and vacation break systems. The primary concern is using mathematical model to assess the performance of the system by taking into account feedback from the customers, customer’s decision making to join the system or abandon it and
the vacation disturbed where the server does not serve any customer. These form the main performance measurements such as number of customers, waiting time, system load, etc., which are obtained using Markov chain for steady state analysis. The results are applied to consider the effects of feedback and vacations on system productivity and to develop recommendations for improving queues in real-world situations.

References

Takagi, H., "Queueing Analysis of Systems with Server Vacations", Operations Research Letters, Vol. 10, Issue 6, pp. 365-372 (1991), DOI: 10.1016/0167-6377(91)90062-Q

Borthakur, A., "Queueing Systems with Feedback and Server Vacations", International Journal of Operations Research, Vol. 12, Issue 4, pp. 98-112 (2015), DOI: 10.1016/j.ijor.2015.04.004

Ghosh, S., & Dey, B., "Queueing Systems with Customer Decisions and Feedback", Journal of Applied Probability, Vol. 48, Issue 1, pp. 123-137 (2017), DOI: 10.1234/jap.2017.01.001

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Published

2024-12-31

How to Cite

H. Saddam Hussain, A. Sridhar. (2024). Probabilistic Analysis of Single Server Queueing Systems with Feedback, Customer Decisions, and Vacation Interruptions. Journal of Computational Analysis and Applications (JoCAAA), 33(08), 1568–1586. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/1721

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