Analysis of a two-stage queueing system with a Markov arrival and service processes in discrete time

A two-stage queueing system with one server and a buffer of finite capacity in each stage and with a discrete Markov flow of customers is considered. If at the transition moment of a customer to the second stage, the server and all waiting places in the second stage are occupied, this customer is lost. The algorithm to calculate the stationary state probabilities of the number of customers in each stage at an arbitrary discrete time moment is derived. Expressions for loss probabilities are obtained