Salem Derisavi

The Mobius modeling tool

Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in the chosen formalism cannot be combined with models expressed in other formalisms. This monolithic approach both limits the usefulness of such tools to practitioners, and hampers modeling research, since it is difficult to compare new and existing formalisms and solvers. This paper describes the method that a new modeling tool, called Mobius, uses to eliminate these limitations. Mobius provides an infrastructure to support multiple interacting formalisms and solvers, and is extensible in that new formalisms anal solvers can, be added to the tool without changing those already implemented. Mobius provides this capability through the use of an abstract functional interface, which provides a formalism-independent interface to models. This allows models expressed in multiple formalisms to interact with each other, and with multiple solvers.

Optimal state-space lumping in Markov chains

We prove that the optimal lumping quotient of a finite Markov chain can be constructed in O(mlg n) time, where n is the number of states and m is the number of transitions. Our proof relies on the use of splay trees (designed by Sleator and Tarjan [J. ACM 32 (3) (1985) 652-686]) to sort transition weights.

The Möbius state-level abstract functional interface

A key advantage of the Mobius modeling environment is the ease with which one can incorporate new modeling formalisms, model composition and connection methods, and model solution methods. We present a new state-level abstract functional interface (AFI) for Mobius that allows numerical solution methods to communicate with Mobius state-level models via the abstraction of a labeled transition system (LTS). This abstraction and its corresponding implementation yield a useful separation of concerns. We illustrate use of the Mobius state-level AFI by implementing two state-space representations and several numerical solvers for steady-state and transient analysis.

On integrating the MOBIUS and MODEST modeling tools

frame-work components. This translation preserves the structureof the models, allowing efficient solutions. The frameworkis implementedin the toolby a well-definedAbstract Func-tional Interface (AFI). Models and solution techniques in-teract with one another through the use of the standardinterface, allowing them to interact with M

Lumping matrix diagram representations of Markov models

Continuous-time Markov chains (CTMCs) have been used successfully to model the dependability and performability of many systems. Matrix diagrams (MDs) are known to be a space-efficient, symbolic representation of large CTMCs. In this paper, we identify local conditions for exact and ordinary lumpings that allow us to lump MD representations of Markov models in a compositional manner. We propose a lumping algorithm for CTMCs that are represented as MDs that is based on partition refinement, is applied to each level of an MD directly, and results in an MD representation of the lumped CTMC. Our compositional lumping approach is complementary to other known model-level lumping approaches for matrix diagrams. The approach has been implemented, and we demonstrate its efficiency and benefits by evaluating an example model of a tandem multi-processor system with load balancing and failure and repair operations.

The Mobius Modeling Environment: Recent Extensions - 2005

The Mobius modeling environment is an extensible framework for discrete-event system analysis that allows multiple formalisms and solution techniques to easily intemperate, and new modules to be easily added. The basis of the framework is an abstract functional interface that defines the behavior and data to be shared among modules. New formalism and solver modules continue to be added to the tool. This paper describes recent additions to Mobius, including a fault tree model definition formalism, a model composition formalism based on action synchronization, improvements in reward model definition, and additional lumping capabilities in the symbolic state space generator

Overview: an integrated framework for performance engineering and resource-aware compilation

Design of next-generation computing and communication systems will be application-driven, and requires fundamental advances in 1) performance engineering frameworks, methods, and tools, and 2) adaptive compilation and runtime support techniques. Our work is taking a systematic and synergetic approach to developing both of these capabilities, and is demonstrating their use via application to several important distributed applications. In conducting the work, we are making fundamental advances in techniques for system and model composition, multi-level/formalism modeling and performance evaluation, adaptive compilation, and dynamic runtime support.