This paper presents a matching procedure for generating an acyclic phase type distribution of order N given the first 2N − 1 moments, if they are feasible. The matching procedure uses an iterative approach and, theoretically, it can be applied to match an arbitrary number of moments. The first step of the iterative procedure contains the solution of an equation of order N and the order is decre...

In Part 1 of this paper, the properties of Discrete Phase Type (DPH) distributions have been investigated, which make the use of this class of distributions very convenient in the approximate analysis of discrete state stochastic systems. In particular, a minimal representation, called canonical form, has been derived for the subclass of the DPH distributions characterised by an acyclic transit...

We consider a discrete-time s S inventory model in which the stored items have a random common lifetime with a discrete phase-type distribution. Demands arrive in batches following a discrete phase-type renewal process. With zero lead time and allowing backlogs, we construct a multidimensional Markov chain to model the inventorylevel process. We obtain a closed-form expected cost function. Nume...