Spectral conditions for Phase-type representations

Current paper tries to find appropriate similarity transformation that could convert a given ME (Matrix Exponential) representation to a more favorable PH (Phase-type) representation. As the main result of this paper, we give necessary conditions for the existence of such a representation. We also give methods for the search and provide conjectures on necessary and sufficient conditions too. PH distribution is the distribution of the time until absorption into the absorbent state in a Markov chain. If the arrival and service time distributions are PH distributions in a queuing system, we can use simple linear algebraic methods to derive the most important features or to perform simulation. Robust methods exist that can approximate any distribution with a ME distribution (with respect to a given measure and matrix order), but the PH transformation have not been sufficiently examined yet. This transformation is the object of the current presentation

Representative queueing network models of computer systems in terms of time delay probability distributions

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Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems