Kishor S. Trivedi

SPNP: stochastic Petri net package

SPNP, a powerful GSPN package that allows the modeling of complex system behaviors, is presented. Advanced constructs are available in SPNP such as marking-dependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; the full expressive power of the C programming language is also available to increase the flexibility of the net description. Sophisticated steady-state and transient solvers are available including cumulative and up-to-absorption measures. The user is not limited to a predefined set of measures; detailed expressions reflecting exactly the measures sought can be easily specified. The authors conclude by comparing SPNP with two other SPN-based packages, Great SPN and METASAN.<<ETX>>

Model-based evaluation: from dependability to security

The development of techniques for quantitative, model-based evaluation of computer system dependability has a long and rich history. A wide array of model-based evaluation techniques is now available, ranging from combinatorial methods, which are useful for quick, rough-cut analyses, to state-based methods, such as Markov reward models, and detailed, discrete-event simulation. The use of quantitative techniques for security evaluation is much less common, and has typically taken the form of formal analysis of small parts of an overall design, or experimental red team-based approaches. Alone, neither of these approaches is fully satisfactory, and we argue that there is much to be gained through the development of a sound model-based methodology for quantifying the security one can expect from a particular design. In this work, we survey existing model-based techniques for evaluating system dependability, and summarize how they are now being extended to evaluate system security. We find that many techniques from dependability evaluation can be applied in the security domain, but that significant challenges remain, largely due to fundamental differences between the accidental nature of the faults commonly assumed in dependability evaluation, and the intentional, human nature of cyber attacks.

Architecture-based approach to reliability assessment of software systems

Abstract With the growing emphasis on reuse, software development process moves toward component-based software design. As a result, there is a need for modeling approaches that are capable of considering the architecture of the software and estimating the reliability by taking into account the interactions between the components, the utilization of the components, and the reliabilities of the components and of their interfaces with other components. This paper details the state of the architecture-based approach to reliability assessment of component based software and describes how it can be used to examine software behavior right from the design stage to implementation and final deployment. First, the common requirements of the architecture-based models are identified and the classification is proposed. Then, the key models in each class are described in detail and the relation among them is discussed. A critical analysis of underlying assumptions, limitations and applicability of these models is provided which should be helpful in determining the directions for future research.

Performance and Reliability Analysis of Computer Systems

Table of

Numerical transient analysis of Markov models

Abstract We consider the numerical evaluation of Markov model transient behavior. Our research is motivated primarily by computer system dependability modeling. Other application areas include finitecapacity queueing models, closed queueing networks and inventory models. We focus our attention on the general problem of finding the state probability vector of a large, continuous-time, discrete-state Markov chain. Two computational approaches are examined in detail: uniformization and numerical linear multistep methods for ordinary differential equation solution. In general, uniformization provides greater accuracy but deals poorly with stiffness. A special stable ordinary differential equation solver deals well with stiffness, but it provides increased accuracy only at much greater cost. Examples are presented to illustrate the behavior of the techniques discussed as a function of model size, model stiffness, increased accuracy requirements and mission time.

Performability analysis: measures, an algorithm, and a case study

The behavior of the multiprocessor system is described as a continuous Markov chain, and a reward rate (performance measure) is associated with each state. The distribution of performability is evaluated for analytical models of a multiprocessor system using a polynomial-time algorithm that obtains the distribution of performability for repairable, as well as nonrepairable, systems with heterogeneous components with a substantial speedup over earlier work. Numerical results indicate that distributions of cumulative performance measures over finite intervals reveal behavior of multiprocessor systems not indicates by either steady-state or expected values alone. >

Reliability Modeling Using SHARPE

Combinatorial models such as fault trees and reliability block diagrams are efficient for model specification and often efficient in their evaluation. But it is difficult, if not impossible, to allow for dependencies (such as repair dependency and near-coincident-fault type dependency), transient and intermittent faults, standby systems with warm spares, and so on. Markov models can capture such important system behavior, but the size of a Markov model can grow exponentially with the number of components in this system. This paper presents an approach for avoiding the large state space problem. The approach uses a hierarchical modeling technique for analyzing complex reliability models. It allows the flexibility of Markov models where necessary and retains the efficiency of combinatorial solution where possible. Based on this approach a computer program called SHARPE (Symbolic Hierarchical Automated Reliability and Performance Evaluator) has been written. The hierarchical modeling technique provides a very flexible mechanism for using decomposition and aggregation to model large systems; it allows for both combinatorial and Markov or semi-Markov submodels, and can analyze each model to produce a distribution function. The choice of the number of levels of models and the model types at each level is left up to the modeler. Component distribution functions can be any exponential polynomial whose range is between zero and one. Examples show how combinations of models can be used to evaluate the reliability and availability of large systems using SHARPE.

Coverage modeling for dependability analysis of fault-tolerant systems

Several different models for predicting coverage in a fault-tolerant system, including models for permanent, intermittent, and transient errors, are discussed. Markov, semi-Markov, nonhomogeneous Markov, and extended stochastic Petri net models for computing coverage are developed. Two types of events that interfere with recovery are examined; and methods for modeling such events, whether they are deterministic or random, are given. The sensitivity of system reliability/availability to the coverage parameter and the sensitivity of the coverage parameter to various error-handling strategies are investigated. It is found that a policy of attempting transient recovery upon detection of an error (as opposed to automatically reconfiguring the affected component out of the system) can actually increase the unreliability of the system. >

A decomposition approach for stochastic reward net models

Abstract We present a decomposition approach for the solution of large stochastic reward nets (SRNs) based on the concept of near-independence. The overall model consists of a set of submodels whose interactions are described by an import graph. Each node of the graph corresponds to a parametric SRN submodel and an arc from submodel A to submodel B corresponds to a parameter value that B must receive from A. The quantities exchanged between submodels are based on only three primitives. The import graph normally contains cycles, so the solution method is based on fixed point iteration. Any SRN containing one or more of the nearly-independent structures we present, commonly encountered in practice, can be analyzed using our approach. No other restriction on the SRN is required. We apply our technique to the analysis of a flexible manufacturing system.

Markov regenerative stochastic Petri nets

Abstract Stochastic Petri nets of various types (SPN, GSPN, ESPN, DSPN etc.) are recognized as useful modeling tools for analyzing the performance and reliability of systems. The analysis of such Petri nets proceeds by utilizing the underlying continuous-time stochastic processes — continuous-time Markov chains for SPN and GSPN, semi-Markov processes for a subset of ESPNs and Markov regenerative processes for DSPN. In this paper, we introduce a new class of stochastic Petri nets, called Markov Regenerative Stochastic Petri Nets (MRSPNs), that can be analyzed by means of Markov regenerative processes and constitutes a true generalization of all the above classes. The MRSPNs allow immediate transitions, exponentially distributed timed transitions and generally distributed timed transitions. With a restriction that at most one generally distributed timed transition be enabled in each marking, the transient and steady state analysis of MRSPNs can be carried out analytically-numerically rather than by simulation. Equations for the solution of MRSPNs are developed in this paper, and are applied to an example.