Discrete-Time Geo/G/1 Queue with Single Working Vacation, Multiple Vacations, and State-Dependent Service

This paper considers a Geo/G/1 queueing system within a discrete-time framework. The model seamlessly integrates state-dependent policies, incorporating both single working vacation and multiple vacations, thereby reflecting the dynamic nature of telecommunication environments. The matrix analytic method is utilized to analyze essential system performance indices, such as long-run probabilities of the distinct server states and the expected queue size of the system, offering insights into the nuanced behavior of Geo/G/1 queueing systems within the discrete-time framework. The results are expected to offer valuable insights for enhancing the performance of telecommunication networks. These insights cover various aspects, including single working vacations, multiple vacations, and state-dependent policies. Consequently, they are poised to establish a solid foundation for improving system efficiency and adapting to dynamic operational conditions.