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

This research article studies the critical issue of the single-server congestion problem with prominent customer impatience attributes and server strategic differentiated vacation. Despite their apparent practical relevance, the proposed congestion problem has yet to be studied from a service/production perspective with transient analysis. The queue-theoretic approach is used for mathematical modeling. The transient queue-size distribution has been derived using a modified Bessel function and generating function technique. A time-dependent solution is advantageous for queueing systems’ dynamic behavior over a planning phase and is predominantly valuable within the real-time design process for the state-of-the-art strategic system. The time-dependent explicit expression of variance and mean for the number of waiting customers in the system is also derived for quick statistical insights. Finally, numerical results are also exhibited to study the system’s behavior in depth.