Algorithms for the design of finite-capacity service units

Finite-capacity queues arise naturally in many practical situations, notably in communications and manufacturing engineering. In this article, the matrix formalism of probability distributions of phase type is used to develop fast algorithms to compute various steady-state distributions for the finite-capacity PH/PH/1 queue. This algorithm is an important ingredient in solving nontraditional but significant design problems. Some of these are described as illustrative examples.