Title: Finite population and finite capacity single server batch service queues with compulsory working vacation

Authors: R. Kalyanaraman; G. Janani

Addresses: Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India ' Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India

Abstract: A finite population Poisson queue with fixed batch service rule has been considered. After completion of each service the server takes vacation independent of the number of customers in the queue. During vacation, the server serves the customers in a slower rate. For this model, the system size probabilities are computed. Some system performance measures are derived. Also instead of finite population, infinite population model with finite waiting room capacity has been considered as a second model. The steady state results are obtained for this model. The two models are compared. Cost and profit structure are defined. Some numerical examples are given.

Keywords: finite population queue; batch service; steady state probability; performance measures; compulsory vacation.

DOI: 10.1504/IJMOR.2024.142117

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.2, pp.163 - 190

Received: 03 Feb 2023
Accepted: 26 Mar 2023
Published online: 08 Oct 2024 *

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