Transient Virtual Waiting Time Distribution in M / M / 1 / N System with Working Vacations

A queueing model with finite buffer, Poisson arrivals, and exponential processing times is considered. When system empties, the single server working vacation mode is initialized. During this period, the system offers another, slower rate of service. After completion of the vacation period, which duration is a generally distributed random variable, the service is continued with original speed. The system of integral equations for conditional transient virtual waiting time distribution is built, and solved in terms of Laplace transforms in an explicit form, using linear algebraic approach, and some results for the corresponding system without working vacation discipline.