On one nonstationary service model with catastrophes and heavy tails

The paper considers the nonstationary queuing system with catastrophes, one server, and special group arrivals of requests. The intensities of increasing groups of requests can decrease rather slowly. The process $X(t)$, which describes the number of requirements in such system, is considered, the existence of a limiting regime of the probability distribution of states and a limiting average for $X(t)$ is proved, and estimates of the rate of convergence to the limiting regime and the limiting average are obtained. Approximation estimates are obtained using truncations by finite processes. As an example, the authors consider a simple model of a nonstationary system with a rather slow rate of decrease in the arrival rates of customer groups when the group size grows.