  This work deals with the stationary analysis of two-dimensional partially
homogeneous nearest-neighbour random walks. Such type of random walks in the
quarter plane are characterized by the fact that the one-step transition
probabilities are functions of the state-space. We show that its stationary
behavior is investigated by solving a finite system of linear equations, and a
functional equation with the aid of the theory of Riemann(-Hilbert) boundary
value problems. This work is strongly motivated by emerging applications in
multiple access systems as well as in the study of a general class of queueing
systems with state dependent parameters. A simple numerical illustration
providing useful information about a queue-aware multiple access system is also
presented.
