On a Functional Equation Arising from a Queueing Model

摘要

Functional equations play an important role in many applications. They offer a powerful tool for narrowing the models used to describe many phenomena. In particular, a certain challenging class of functional equations arises recently from many applications like e.g. networks and databases. Usually, such class of equations stems when obtaining the generating functions of queueing systems distributions. To date, such class is still unsupervised because there is no general solution theory available to it. In this paper on one hand, we introduce a solution of a functional equation arising from a queueing model. The solution is obtained using boundary value problem approach. On the other hand, we use the idea of the resultant of two polynomials to compute the potential singularities of the unknowns of the functional equation.