On the benefits of using functional transitions and Kronecker algebra

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.