The power-series algorithm for Markovian queueing networks

A newversion of the Power-Series Algorithm is developed to compute the steady-state distribution of a rich class of Markovian queueing networks. The arrival process is a Multi-queue Markovian Arrival Process, which is a multi-queue generalization of the BMAP. It includes Poisson, fork and round-robin arrivals. At each queue the service process is a Markovian Service Process, which includes sequences of phase-type distributions, setup times and multi-server queues. The routing is Markovian. The resulting queueing network model is extremely general, which makes the Power-Series Algorithm a useful tool to study load-balancing, capacity-assignment and sequencing problems.Queueing Network;operations research

The power-series algorithm:A numerical approach to Markov processes

Abstract: The development of computer and communication networks and flexible manufacturing systems has led to new and interesting multidimensional queueing models. The Power-Series Algorithm is a numerical method to analyze and optimize the performance of such models. In this thesis, the applicability of the algorithm is extended. This is illustrated by introducing and analyzing a wide class of queueing networks with very general dependencies between the different queues. The theoretical basis of the algorithm is strengthened by proving analyticity of the steady-state distribution in light traffic and finding remedies for previous imperfections of the method. Applying similar ideas to the transient distribution renders new analyticity results. Various aspects of Markov processes, analytic functions and extrapolation methods are reviewed, necessary for a thorough understanding and efficient implementation of the Power-Series Algorithm.

Aluminium sheet forming simulations: influence of the yield surface

The accuracy of simulations of the plastic deformation of sheet metal depend to a large extend on\ud the description of the yield surface, the hardening and the friction. In this paper simulations of deep drawing of\ud an AlMg alloy with a shell model are presented. The yield surface is described by a Von Mises, a Hill ’48 and a\ud Vegter yield function. The parameters for the model are based on biaxial experiments. It is concluded that the\ud shape of the yield locus has a minor influence on the prediction of the punch force–displacement diagram and a\ud large influence on the prediction of the thickness strains. The Vegter model performs much better than the Hill\ud ’48 model, based on the same R-values