A mathematical model for the double orbital queue with recurrent customers under working vacation and its optimal control analysis

Year 2025, Volume: 54 Issue: 5, 2139 - 2167, 29.10.2025

Joseph Sathiyavathy Micheal Mathavavisakan N

https://doi.org/10.15672/hujms.1638670

Abstract

This article analyzes the performance modeling and optimization of a double orbital queue system, focusing on recurring customers during working vacation periods. A unique aspect of this study is the consideration of customers willing to pay for improved service quality, addressing both efficiency and satisfaction. Using advanced techniques such as probability generating functions and the supplementary variable technique, the study rigorously models customer behavior and server performance under reduced service rates. Key performance measures, including system size and service delays, are evaluated using graphs and tables for clarity. A major contribution is the introduction of a cost function, optimized using the whale optimization algorithm to minimize resource allocation inefficiencies. The study further examines the convergence and optimality of the cost functions, demonstrating practical strategies to improve service efficiency. By integrating queueing theory with optimization techniques, this research provides valuable insight into managing double orbital queues with working vacations while considering customer preferences.

Keywords

Double orbital queue , working vacation , recurrent customer , supplementary variable technique , cost optimization

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