Investigations of various networks and systems of communications are very important nowadays. There is more than one approach in the literature to such study; namely, the experimental, numerical, simulation, and the analytical approaches. Each of them has its own advantages and disadvantages. The analytical approach describes such systems mathematically and end up in most cases with challenging two-place functional equations. They are mainly equations in which the unknowns are generating functions of systems distributions.
Various functional equations arise abundantly in models of widely diverse fields, such as population ethics, behavioral and social sciences, astronomy, networks, information theory, and economics. Specifically, each of these descriptions can be formulated so as to eventually lead to functional equations that can yield precise quantitative relationships. During the last six decades, a certain class of two-place functional equations arose from various models of networks and communication. The explicit closed-form solutions of those equations are very important because such functions will help computer scientists and engineers to find some performance measures of many engineering systems. This is a challenging task to find them and so far there are no such explicit solutions available except for some simple cases. The theory of boundary value problems has been extensively used in solving such interesting class of equations. This thesis is mainly devoted to the investigations of the analytical solutions of such a general class of equations that have many interesting applications in modern disciplines like wireless networks.