Polling system with two markovian arrival proсesses, finite buffers and phase type distribution of service and switching times

A polling system with two queues with a limited number of places in buffers are considered. Each queue receives markovian flow of requests. The times of servicing the requests and switching between the queues have phase type distribution. The queuing discipline is gated. The formulas for finding the stationary probabilities of system states at an arbitrary moment in time, and the formulas for computing the main performance measures for the system are obtained. The expressions for the Laplace–Stieltjes transforms of waiting time distributions in buffers are found.