Title: Survey on queuing models with discouragement, policies and vacation

Authors: C.K. Anjali; Sreekanth Kolledath

Addresses: Department of Mathematics, Amrita School of Physical Sciences, Kochi, Amrita Vishwa Vidyapeetham, India ' Department of Mathematics, Amrita School of Physical Sciences, Kochi, Amrita Vishwa Vidyapeetham, India

Abstract: Queuing models with discouragement, policies, and vacation have been extensively investigated due to its wide range of applications in real-life scenarios. The effectiveness of a queuing system is questioned when customers balk or renege. However, the loss of customers can be prevented up to some extent by using customer retention strategies. Also, implementing vacation and threshold policies appropriately in the system improves the servers' capacity for providing service effectively. Based on these concepts many surveys have been made on finite and infinite population queuing models. But we have observed from the queuing theory literature that surveys have not been done by combining both the finite and infinite population models. The main objective of this survey is to provide an overview of the relevant research works done on finite and infinite population models with impatience, policies and vacation. By taking into account the models and methodologies used in various research articles, we also attempt to provide an outline of the works discussed in tabular format.

Keywords: machine repair problem; discouragement; balking; reneging; N-policy; F-policy; vacation; working vacation.

DOI: 10.1504/IJMOR.2024.138532

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.1, pp.105 - 145

Received: 05 Dec 2022
Accepted: 19 Mar 2023
Published online: 09 May 2024 *

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