Time to Buffer Overflow in a Queueing Model with Working Vacation Policy

A finite-buffer queueing model with Poisson arrivals and exponential processing times is investigated. Every time when the system becomes empty, the service station begins a generally distributed single working vacation period, during which the processing 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. Identifying Markov epochs in the evolution of the considered model, the system of Volterra-type integral equations for the time to buffer overflow tail distribution function, conditioned by the initial buffer state, is built. The solution of the corresponding system written for Laplace transforms is given in a compact-form using the linear algebraic approach. The considered queueing model can be used in modelling of the network node in which the typical processing rate changes periodically, due to e.g. introducing a priority traffic.