Single server queueing system with dependent interarrival times

The paper studies a single server queueing system with an infinite number of positions in the queue and random distribution of the service time. The incoming flow of claims is a Poisson flow with a random intensity. The current intensity value is selected from a finite set with given probabilities at the start of the countdown to the next receipt of the claim. Sequential intensities form a Markov chain of a special kind. Particular cases of such flows are hyperexponential flows and flows arising in the study of Bayesian models of queueing systems with a discrete prior distribution. Considered flows describe well the work of queueing systems operating in a random environment with a finite set of different states and Markov relationship between them. Furthermore, such flows can accurately approximate real flows in data networks. The nonstationary behavior of the queue length is studied.