Title: Analysis of Markovian queueing model with two phase of services, single and multiple working vacations and customer balking

Authors: K. Baby Saroja; V. Suvitha

Addresses: Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur – 603203, Tamil Nadu, India ' Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur – 603203, Tamil Nadu, India

Abstract: We analyse a single server balking queueing model with featuring two phases of service in series. During the first phase, customers receive individual service, and in the second phase, they have the option to choose between two distinct services based on their specific needs and receive batch service. To optimise resource utilisation, the server enters a working vacation when there is no customer in the system. We apply the probability generating method to comprehensively analyse the system, considering both single and multiple working vacation. This research underscores the application's adaptability in addressing intricate data processing challenges within the queuing framework. Furthermore, we provide numerical results to demonstrate how the model performs under various conditions.

Keywords: two phases in series; working vacation; balking; batch service.

DOI: 10.1504/IJMOR.2025.149920

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.3, pp.277 - 293

Received: 28 Nov 2023
Accepted: 24 Dec 2023
Published online: 18 Nov 2025 *

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