Title: Cost analysis of a transient Markovian queueing model with provision of options between regular and working vacation

Authors: Mayank Singh; Madhu Jain; A. Azhagappan

Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India ' Department of Mathematics, St. Anne's College of Engineering and Technology, Anna University, Panruti, Cuddalore District, 607110, Tamil Nadu, India

Abstract: A transient Markov queue is investigated that provides options for two types of server vacations. When the server becomes idle after serving the last customer, he has the choice to take a complete vacation (CV) or a working vacation (WV). New arrivals can join the system in CV or WV mode with different arrival rates, which are dependent on the state of the system. During CV, the server remains idle, while during WV, he serves at a slower rate. After returning from the CV (or WV), the server immediately starts the service if some customers are waiting in the system; otherwise, he waits for the arrivals. The transient queue size distribution and other queueing indices are determined using continued fractions and probability generating function techniques. The stationary distribution is also derived from the transient distribution. Numerical analysis is conducted using a practical application to display the analytical results in real-life scenarios.

Keywords: transient analysis; vacation; working vacation; continued fractions; probability generating function; queue size.

DOI: 10.1504/IJMOR.2024.138906

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.2, pp.209 - 229

Received: 01 Feb 2023
Accepted: 09 Mar 2023
Published online: 03 Jun 2024 *

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