The Möbius State-Level Abstract Functional Interface

A key advantage of the Möbius modeling environment is the ease with which one can incorporate new modeling formalisms, model composition and connection methods, and model solution methods. In this paper, we describe a new state-level abstract functional interface (AFI) for Möbius that allows numerical solution methods to communicate with Möbius state-level models via the abstraction of a labeled transition system. This abstraction, and its corresponding implementation as a set of containers and iterators, yields an important separation of concerns: It is possible to treat separately the problem of representing large labeled transition systems, like generator matrices of continuoustime Markov chains, and the problem of analyzing these systems. For example, any numerical solver (e.g., Jacobi, SOR, or uniformization) that accesses a model through the Möbius state-level AFI can operate on a variety of state-space representations, including “on-the-fly,” disk-based, sparse-matrix, Kronecker, and matrix-diagram representations, without requiring that the implementation be changed to match the state-space representation. This abstraction thus avoids redundant implementations of solvers and state-generation techniques, eases research cooperation, and simplifies comparison of approaches as well as benchmarking. In addition to providing a formal definition of the Möbius state-level AFI, we illustrate its use on two state-space representations (a sparse matrix and a Kronecker representation) and two numerical solvers (Jacobi and SOR). With the help of this implementation and two example models, we demonstrate that the AFI provides the benefits of transparency while introducing only minor slowdowns in solution speed. ? This material is based upon work supported in part by the National Science Foundation under Grant No. 9975019, by the Motorola Center for High-Availability System Validation at the University of Illinois (under the umbrella of the Motorola Communications Center), and by the DFG, Collaborative Research Centre 559.