Transient Analysis of Queueing-Based Congestion with Differentiated Vacations and Customer’s Impatience Attributes

The article delves into the transient analysis of queueing-based congestion management, focusing on systems with differentiated vacations and customer impatience attributes like balking and reneging. It introduces a systematic approach to managing customer congestion and optimizing service system performance. The research presents a detailed investigation of various vacation policies, including multi-vacation, single-vacation, and working vacation, and their impact on system dynamics. The study employs mathematical tools such as the modified Bessel function and Laplace transform to derive transient probabilities and performance measures. The article highlights the importance of understanding customer behavior in congestion scenarios and provides valuable insights into designing efficient and cost-effective service systems. The numerical results and qualitative insights offer a practical application of the theoretical findings, making the article a valuable resource for professionals in the field.