The M/M/1 queue with mass exodus and mass arrivals when empty

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate {αr; r≥ 1} when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Manufacturing knowledge verification in design support systems

This paper identifies the need for a verification methodology for manufacturing knowledge in design support systems; and proposes a suitable methodology based on the concept of ontological commitment and the PSL ontology (ISO/CD18629). The use of the verification procedures within an overall system development methodology is examined, and an understanding of how various categories of manufacturing knowledge (typical to design support systems) map onto the PSL ontology is developed. This work is also supported by case study material from industrial situations, including the casting and machining of metallic components. The PSL ontology was found to support the verification of most categories of manufacturing knowledge, and was shown to be particularly suited to process planning representations. Additional concepts and verification procedures were however needed to verify relationships between products and manufacturing processes. Suitable representational concepts and verification procedures were therefore developed, and integrated into the proposed knowledge verification methodology.