Article: Recital facts of M X/G/1 queues with setup time, phases of service, and vacation Journal: International Journal of Mathematics in Operational Research (IJMOR) 2025 Vol.31 No.2 pp.241 - 262 Abstract: Researching group queueing systems that combine setup time and vacation work stages into a single server service is the aim of this MX/G/1 queueing study. In this queueing system, arrival time follows the Poisson distribution and service time follows a general distribution. The model is well equipped with setup time phases to do both a key maintenance task during the break and the necessary server pre-processing job. Additionally, the system is unavailable during the disruption because service disruptions are inevitable. The aforementioned mathematical queueing problem is solved using the supplemental variable technique, and the system's performance metrics are obtained. From the calculated probability generation function of queue size at a random time for the different system states, we extract performance measures such as the server's probability of idle time, the utilisation factor, the average queue length, and the average wait time. It is backed by methods for numerical portrayal, graphic representation, and real-world applications. This paradigm is entirely legal due to its practical use and algebraic demarcation mechanism. The graph provides precise readings of the implemented limitations. Inderscience Publishers - linking academia, business and industry through research

Title: Recital facts of M ^X/G/1 queues with setup time, phases of service, and vacation

Authors: S. Maragathasundari; K. Karthikeyan

Addresses: Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Thandalam, Chennai-602105, Tamilnadu, India ' Department of Mathematics, Velammal Institute of Technology, Chennai, India

Abstract: Researching group queueing systems that combine setup time and vacation work stages into a single server service is the aim of this M^X/G/1 queueing study. In this queueing system, arrival time follows the Poisson distribution and service time follows a general distribution. The model is well equipped with setup time phases to do both a key maintenance task during the break and the necessary server pre-processing job. Additionally, the system is unavailable during the disruption because service disruptions are inevitable. The aforementioned mathematical queueing problem is solved using the supplemental variable technique, and the system's performance metrics are obtained. From the calculated probability generation function of queue size at a random time for the different system states, we extract performance measures such as the server's probability of idle time, the utilisation factor, the average queue length, and the average wait time. It is backed by methods for numerical portrayal, graphic representation, and real-world applications. This paradigm is entirely legal due to its practical use and algebraic demarcation mechanism. The graph provides precise readings of the implemented limitations.

Keywords: non-Markovian queueing problem; batch arrival; supplementary variable technique; setup time stages; vacation; service interruption.

DOI: 10.1504/IJMOR.2025.147022

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.2, pp.241 - 262

Received: 01 Sep 2023
Accepted: 06 Sep 2023
Published online: 10 Jul 2025 *

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Title: Recital facts of M ^X/G/1 queues with setup time, phases of service, and vacation