Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience

This paper studies the time‐dependent behavior of a single server queueing model with slow service during single and multiple working vacations, and customers’ impatience due to slow service. The time‐dependent system size probabilities for the underlying model are obtained in closed form. Further, time‐dependent mean and variance are deduced. Finally, numerical illustrations are shown to visualize the system effect for various values of parameters.