Analysis of the Polling System with Two Markovian Arrival Flows, Finite Buffers, Gated Service and Phase-Type Distribution of Service and Switching Times

The polling system with two Markovian Arrival Flows, finite buffers, gated service discipline and Phase-Type (PH) distribution of service and switching times is considered. Stationary distribution of the continuous-time multi-dimensional Markov chain defining the current state of the server, number of customers in the buffers, the number of customers that should obtain service during the residual time of service of customers from various buffers and underlying processes of service or switching time and of arrival process is computed. Expressions for Laplace-Stieltjes transforms of distribution of waiting times of customers in both buffers are obtained. Numerical results giving some insight into performance of the system are presented. © 2022, Springer Nature Switzerland AG.