Exact analysis of asymmetric polling systems with single buffers

A unified approach to general asymmetric polling systems with a single buffer at each station is presented. Two variations of single-buffer polling system are considered: the conventional system and the buffer-relaxation system. In the conventional system, a new massage is not allowed to queue until the previous message has been completely transmitted, while in the buffer-relaxation system, a newly arriving message can be stored in the buffer once the previous message´s transmission has started. For each system, the Laplace-Stieltjies transform (LST) of the joint probability-distribution function (PDF) of station times is derived, from which the LST of the PDF of message delay is straightforwardly obtained