Title: A queueing model with balking, server vacation and working breakdown

Authors: Kamlesh Kumar; Madhu Jain

Addresses: Department of Mathematics, Central University of Jammu, 181143, India ' Department of Mathematics, IIT Roorkee, Roorkee, 247667, India

Abstract: This paper focuses on a single server queueing model that includes customer's balking, server vacation, and working breakdown. When there is no customer in the system or the system becomes empty, the server goes on a vacation and returns back when one or more customer available in the system. The server resumes service to the customers accumulated during its vacation period. There is always the possibility of a server breakdown while providing services to the customers, which may result in slower service rate. Slower service rate is considered as working breakdown state of the server or a defective mode of service. If the server is providing normal or defective service, customers may balk. For the system states, some practicable performance measures such as average number of customers in the system, average total cost function, and system throughput have been established for the various system states.

Keywords: Markovian queue; balking; server vacation; working breakdown; probability generating function; PGF; cost function.

DOI: 10.1504/IJMOR.2025.146358

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.1, pp.41 - 59

Received: 23 Apr 2023
Accepted: 07 May 2023
Published online: 27 May 2025 *

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