Distributions of unexpended services in a D-node Markov-renewal network distinguished by customer class
Customer units from any one of \(K\) distinct classes arrive at random but in a fixed, known order for processing in a \(D\)-node Markov-renewal network that contains at least one absorbing node and no proper closed subsets of nodes. The joint probability function of counts of units in nodes, distinguished by customer class, is derived for the transient case. A numerical method for routinely computing all possible marginal distribution is demonstrated for implementation on off-the-shell spreadsheets or database systems. The model permits explicit computation of counts by units, by class and node, for arrivals that are not Poisson distributed. Case study for a system consisting of Poisson distributed arrivals with constant arrival intensity and two node network is presented in detail.
scientific article; zbMATH DE number 96913