CONSTRUCTING ASYMPTOTIC SERIES FOR PROBABILITY-DISTRIBUTIONS OF MARKOV-CHAINS WITH WEAK AND STRONG-INTERACTIONS

Many applications arise in manufacturing systems, and queueing network problems involve Markov chains having slow and fast components. These components are coupled through weak and strong interactions. The main goal of this work is to study asymptotic properties for the probabili ty distribution of the aforementioned Markov chains. Explicit construc tion of series expansions, consisting of regular part and boundary lay er part or singular part, are developed by means of singular perturbat ion methods. The regular part is obtained by solving algebraic-differe ntial equations, and the singular part is derived via solution of diff erential equations. One of the key points in the constructions is to s elect appropriate initial conditions. This is done by taking into cons ideration the regular part and the singular part together with their i nteractions. It is shown that the singular part decays exponentially f ast. Analysis of residue is carried out, and the error bound for the r emainder terms is ascertained.