On the method of calculating the stationary distribution in the finite two-channel system with ordered input

This paper considers a queueing system with ordered input and two servers (labelled by numbers 1 and 2). Each server has a buffer of finite capacity in front of it. Queues capacities are different. Customers arrive according to a Poisson process with constant rate. Upon arrival, a new customer goes to the server with label 1 or, if it is busy, occupies a place in the queue in front of it. If upon arrival a customer sees the queue in front of the server 1 full, it goes to the server with label 2 or, if it is busy, enters the queue in front of it. If upon arrival of a new customer the system is full, the new customer is lost. Customers from both queues are served according to the FIFO (first in, first out) discipline and each server serves customers exponentially distributed times with the same parameter. A new method for recursive computation of the joint stationary distribution of queues is proposed.