This paper examines numerical issues in computing solutions to networks of stochastic automata. It is well-known that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrix-vector multiply, is given by ρ N = Π N i-1 n i × Σ N i=1 n i , where n i is the number of states in the i th automaton and N is the number of automata in the network. We introduce the concept of a generalized tensor product and prove a number of lemmas concerning this product. The result of these lemmas allows us to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions. Furthermore, we show how the automata should be ordered to achieve this.

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Much attention has been paid recently to the use of Kronecker or tensor product modelling techniques for evaluating the performance of parallel and distributed systems. While this approach facilitates the description of such systems and mimimizes memory requirements, it has suffered in the past from the fact that computation times have been excessively long. In this paper we propose a suite of modelling strategems and numerical procedures that go a long way to alleviating this drawback. Of particular note are the benefits obtained by using functional transitions that are implemented via a generalized tensor algebra. Examples are presented which illustrate the reduction in computation time as each suggested improvement is deployed.

The market for mobile applications has been growing dramatically, as has the complexity of the applications and the speed of the development process. These changes require a rethinking of the development process and of how developers are trained. In order to better prepare faculty and students for the emerging mobile application market, this study presents a new learning and software development framework that combines Agile methodologies with the ChallengeBased Learning (CBL) framework. CBL provides a studentcentered learning framework that mirrors the modern workplace. Agile methodologies address the changing landscape of mobile development environments. A combination of the CBL learning framework and Agile methodologies can better prepare students for the development market. This paper presents an empirical study applying CBL and Scrum in a mobile application development course evaluated through a series of post surveys. The results indicate that a teaching and learning environment based on practical experience combining the CBL framework with the Scrum process is an effective model to promptly teach undergraduates how to be successful mobile application developers.

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Many Markovian stochastic structured modeling formalisms like Petri nets, automata networks and process algebra represent the infinitesimal generator of the underlying Markov chain as a descriptor instead of a traditional sparse matrix. A descriptor is a compact and structured storage based on a sum of tensor (Kronecker) products of small matrices that can be handled by many algorithms allowing affordable stationary and transient solutions even for very large Markovian models. One of the most efficient algorithms used to compute iterative solutions of descriptors is the Shuffle algorithm which is used to perform the multiplication by a probability vector. In this paper we propose an alternative algorithm called Split, since it offers a flexible solution between the pure sparse matrix approach and the Shuffle algorithm using a hybrid solution. The Split algorithm puts the Shuffle approach in perspective by presenting a faster execution time for many cases and at least the same efficiency for the worst cases. The Split algorithm is applied to solve two SAN models based on real problems showing the practical contribution of this paper.

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