On some time non-homogeneous queueing systems with catastrophes

•Computations for non-homogeneous birth-and-death processes with catastrophes.•Applications to queueing and population dynamics problems.•Effect of the periodicity of the rates on the performance of systems with catastrophes.

Non-stationary queueing systems subject to catastrophes occurring with time varying intensity are considered. The effect of a catastrophe is to make the queue instantly empty. The transition probabilities, the related moments and the first visit time density to zero state are analyzed. Particular attention is dedicated to queueing systems in the presence of catastrophes with periodic intensity function. Various applications are provided, including the non-stationary birth–death process with immigration, the queueing systems M(t)/M(t)/1M(t)/M(t)/1 and M(t)/M(t)/∞M(t)/M(t)/∞.