Transient solution for queue-size distribution in a certain finite-buffer model with server working vacations

Abstract

A finite-buffer queueing model with Poisson arrivals and exponential processing times is investigated. Every time when the system empties, the server begins a generally distributed single working vacation period, during which the service is provided with another (slower) rate. After the completion of the vacation period the processing is being continued normally, with original speed. The next working vacation period is being initialized at the next time at which the system becomes empty, and so on. The system of Volterra-type integral equations for transient queue-size distribution, conditioned by the initial level of buffer saturation, is built. The solution of the corresponding system written for Laplace transforms is given in a compact-form using the linear algebraic approach and the corresponding result obtained for the ordinary model (without working vacation regime). Numerical examples are attached as well.