Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

CBE-conveyor: a case-based reasoning system to assist engineers in designing conveyor systems

In this paper, we address the use of CBR in collaboration with numerical engineering models. This collaborative combination has a particular application in engineering domains where numerical models are used. We term this domain “Case Based Engineering” (CBE), and present the general architecture of a CBE system. We define and discuss the general characteristics of CBE and the special problems which arise. These are: the handling of engineering constraints of both continuous and nominal kind; interpolation over both continuous and nominal variables, and conformability for interpolation. In order to illustrate the utility of the method proposed, and to provide practical examples of the general theory, the paper describes a practical application of the CBE architecture, known as CBE-CONVEYOR, which has been implemented by the authors.Pneumatic conveying is an important transportation technology in the solid bulks conveying industry. One of the major industry concerns is the attrition of powders and granules during pneumatic conveying. To minimize the fraction of particles during pneumatic conveying, engineers want to know what design parameters they should use in building a conveyor system. To do this, engineers often run simulations in a repetitive manner to find appropriate input parameters. CBE-Conveyor is shown to speed up conventional methods for searching for solutions, and to solve problems directly that would otherwise require considerable intervention from the engineer.