Andrew S. Miner

Efficient Reachability Set Generation and Storage Using Decision Diagrams

We present a new technique for the generation and storage of the reachability set of a Petri net. Our approach is inspired by previous work on Binary and Multi-valued Decision Diagrams but exploits a concept of locality for the effect of a transitions firing to vastly improve algorithmic performance. The result is a data structure and a set of manipulation routines that can be used to generate and store enormous sets extremely efficiently in terms of both memory and execution time.

A data structure for the efficient Kronecker solution of GSPNs

Kronecker-based approaches have been proposed for the solution of structured GSPNs with extremely large state spaces. Representing the transition rate matrix using Kronecker sums and products of smaller matrices virtually eliminates its storage requirements, but introduces various sources of overhead. We show how, by using a new data structure which we call matrix diagrams, we are able to greatly reduce or eliminate many of these overheads, resulting in a very efficient overall solution process.

Logic and stochastic modeling with SMART

We describe the main features of SMART, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. SMART can combine different formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL model-checking algorithms, are available. For the study of stochastic and timing behavior, both sparse-storage and Kronecker-based numerical solution approaches are available when the underlying process is a Markov chain, while discrete-event simulation is always applicable regardless of the stochastic nature of the process, and certain classes of non-Markov models can also be solved numerically. Finally, since SMART targets both the classroom and realistic industrial settings as a learning, research, and application tool, it is written in a modular way that allows for easy integration of new formalisms and solution algorithms.

Storage Alternatives for Large Structured State Spaces

We consider the problem of storing and searching a large state space obtained from a high-level model such as a queueing network or a Petri net. After reviewing the traditional technique based on a single search tree, we demonstrate how an approach based on multiple levels of search trees offers advantages in both memory and execution complexity. Further execution time improvements are obtained by exploiting the concept of “event locality”. We apply our technique to three large parametric models, and give detailed experimental results.

SMART: simulation and Markovian analyzer for reliability and timing

SMART is a new tool for performance, reliability, availability, and performability modeling. Numerical solution algorithms are available for both continuous- and discrete-time Markov chains. Mixed-time non-Markovian models can be studied using simulation. Multiple interacting models and fixed-point iterative techniques for the decomposition and solution of complex models can be easily specified. To assist in the model specification and help in avoiding common mistakes, the input language is strongly typed.

Anomaly intrusion detection using one class SVM

Kernel methods are widely used in statistical learning for many fields, such as protein classification and image processing. We recently extend kernel methods to intrusion detection domain by introducing a new family of kernels suitable for intrusion detection. These kernels, combined with an unsupervised learning method - one-class support vector machine, are used for anomaly detection. Our experiments show that the new anomaly detection methods are able to achieve better accuracy rates than the conventional anomaly detectors.

Efficient solution of GSPNs using canonical matrix diagrams

The solution of a generalized stochastic Petri net (GSPN) is severely restricted by the size of its underlying continuous-time Markov chain. In recent work (G. Ciardo and A.S. Miner, 1999), matrix diagrams built from a Kronecker expression for the transition rate matrix of certain types of GSPNs were shown to allow for more efficient solution; however, the GSPN model requires a special form, so that the transition rate matrix has a Kronecker expression. In this paper, we extend the earlier results to GSPN models with partitioned sets of places. Specifically, we give a more restrictive definition for matrix diagrams and show that the new form is canonical. We then present an algorithm that builds a canonical matrix diagram representation for an arbitrary non-negative matrix, given encodings for the sets of rows and columns. Using this algorithm, a Kronecker expression is not required to construct the matrix diagram. The efficient matrix diagram algorithms for numerical solution presented earlier are still applicable. We apply our technique to several example GSPNs.

Using the exact state space of a Markov model to compute approximate stationary measures

We present a new approximation algorithm based on an exact representation of the state space S, using decision diagrams, and of the transition rate matrix R, using Kronecker algebra, for a Markov model with K submodels. Our algorithm builds and solves K Markov chains, each corresponding to a different aggregation of the exact process, guided by the structure of the decision diagram, and iterates on their solution until their entries are stable. We prove that exact results are obtained if the overall model has a product-form solution. Advantages of our method include good accuracy, low memory requirements, fast execution times, and a high degree of automation, since the only additional information required to apply it is a partition of the model into the K submodels. As far as we know, this is the first time an approximation algorithm has been proposed where knowledge of the exact state space is explicitly used.

Symbolic representations and analysis of large probabilistic systems

This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting high-level structure and regularity in the models to which they are applied, increasing the size of the state spaces which can be tackled. In general, this is done by using data structures which provide compact storage but which are still efficient to manipulate, usually based on binary decision diagrams (BDDs) or their extensions. In this paper we focus on BDDs, multi-valued decision diagrams (MDDs), multi-terminal binary decision diagrams (MTBDDs) and matrix diagrams.

Logical and Stochastic Modeling with Smart

We describe the main features of Smart, a software package providing a seamless environment for the logic and probabilistic analysis of complex systems. Smart can combine different formalisms in the same modeling study. For the analysis of logical behavior, both explicit and symbolic state-space generation techniques, as well as symbolic CTL model-checking algorithms, are available. For the study of stochastic and timing behavior, both sparse-storage and Kronecker numerical solution approaches are available when the underlying process is a Markov chain. In addition, discrete-event simulation is always applicable regardless of the stochastic nature of the process, but certain classes of non-Markov models can still be solved numerically. Finally, since Smart targets both the classroom and realistic industrial settings as a learning, research, and application tool, it is written in a modular way that allows for easy integration of new formalisms and solution algorithms.