We present SPNP, a powerful GSPN package developed at Duke University. SPNP allows the modeling of complex system behaviors. Advanced constructs are available, such as marking dependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; in addition, the full expressive power of the C programming language is available to increase the flexibility of the net description.

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 new and existing formalisms and solvers. This paper describes the method that a new modeling tool, cal led Mobius, uses to eliminate these limitations. Mobius provides an infrastructure to support multiple interacting formalisms and solvers, and is extensible in that new formalisms and 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.

Redundancy based on a parity encoding has been proposed for insuring that disk arrays provide highly reliable data. Parity-based redundancy will tolerate many independent and dependent disk failures (shared support hardware) without on-line spare disks and many more such failures with on-line spare disks. This paper explores the design of reliable, redundant disk arrays. In the context of a 70 disk strawman array, it presents and applies analytic and simulation models for the time until data is lost. It shows how to balance requirements for high data reliability against the overhead cost of redundant data, on-line spares, and on-site repair personnel in terms of an array’s architecture, its component reliabilities, and its repair policies.

Dependability evaluation is an important, but difficult, aspect of the design of fault-tolerant parallel and distributed computing systems. One possible technique is to use Markov models, but if applied directly to realistic designs, this often results in large and intractable models. Many authors have investigated methods to avoid this explosive state-space growth, but have typically either solved the problem for a specific system design, or required manipulation of the model at the state-space level. Stochastic activity networks (SANs), a stochastic extension of Petri nets, together with recently developed reduced base model construction techniques, have the potential to avoid this state space growth at the SAN level for many parallel and distributed systems. This paper investigates this claim, by considering their application to three different systems: a fault-tolerant parallel computing system, a distributed database architecture, and a multiprocessor-multimemory system. We show that this method does indeed result in tractable Markov models for these systems, and argue that it can be applied to the dependability evaluation of many parallel and distributed systems.

Distribution functions that can be expressed as exponential polynomials have useful computational properties in applied stochastic modeling and have gained widespread acceptance in recent years. Nevertheless, the implementation of ecient numerical procedures for estimating the distribution parameters remains an open problem that limits the use of this class of distributions in applications. The diculty of the tting problem is largely related to the non-linearity of the model and to the number of the parameters to be estimated. Many attempts have been presented in the literature. However, the lack of accepted and standardized test examples makes it dicult to establish a comparative merit among the various approaches. This paper proposes a benchmark based on the workshop on Fitting phase type distributions, organized by S. Asmussen in February 1991. It also presents the results obtained by applying the Maximum Likelihood (ML) estimation procedure to the canonical representation of Acyc...

... algorithm which incorporates coverage modeling into a BDD solution of a combinatorial model. BDDs, which do not use cutsets to generate system unreliability, may be used to nd exact solutions for extremely large systems. The DREDD algorithm takes advantage of the e ciency of the BDD solution approach and increases the accuracy of a combinatorial model by including consideration of (possibly) imperfect coverage. The usefulness of combinatorial models, long appreciated for their logical structure and concise representational form, is extended to include many fault tolerant systems previously thought to require more complicated analysis techniques in order to include coverage modeling. In this paper, the DREDD approach is presented and applied to the analysis of two sample systems, the F18 ight control system and a fault tolerant multistage interconnection network.

A common approach for the quantitative analysis of a generalized stochastic Petri net (GSPN) is to generate its entire state space and then solve the corresponding continuous-time Markov chain (CTMC) numerically. This analysis often suffers from two major problems: the state space explosion and the stiffness of the CTMC. In this paper we present parallel algorithms for shared-memory machines that attempt to alleviate both of these difficulties: the large main memory capacity of a multiprocessor can be utilized and long computation times are reduced by efficient parallelization. The algorithms comprise both CTMC construction and numerical steady--state solution. We give experimental results obtained with a Convex SPP16 shared-memory multiprocessor that show the behavior of the algorithms and the parallel speedups obtained.

Process algebras are one of the main tools for modeling and analyzing concurrent systems. However, they can be used to describe only the functional aspect of system behavior. Recently, the relevance of integrating performance evaluation within the process of specification, design and implementation of concurrent systems has been widely recognized. Hence, an effort has been made in order to handle also the temporal aspect of system behavior. In this paper the stochastic process algebra MPA (Markovian Process Algebra) is briefly introduced, together with its operational interleaving semantics, its markovian semantics and its operational net semantics. A concurrent system is described as a term of MPA. The operational interleaving semantics (defined by following Plotkin's structured operational semantics approach, augmented with two transformations) associates a labeled transition system with each MPA term. The markovian semantics is defined through an algorithm which transforms labeled t...

Over the last decade considerable effort has been put in the development of techniques to assess the performance and the dependability of computer and communication systems in an integrated way. This so-called performability modelling becomes especially useful when the system under study can operate partially, which is for instance the case for fault-tolerant computer systems and distributed systems. Modelling techniques are a fundamental prerequisite for actually doing performability analysis. A prerequisite of a more practical but not less important nature is the availability of software tools to support the modelling techniques and to allow system designers to incorporate the new techniques in the design process of systems. Since performability modelling requires many aspects of a system to be specified, high requirements should be posed on performability modelling tools. Moreover, these tools should be structured such that the models can be specified at a level that is easy to unde...

This paper presents a quantitative reliability analysis of a system designed to tolerate both hardware and software faults. The system being studied achieves integrated fault tolerance by implementing N-Version Programming (NVP) on redundant hardware. The analysis of the system considers independent software faults, related software faults, transient hardware faults, permanent hardware faults, and imperfect coverage. The overall model is a Markov reward model in which the states of the Markov chain represent the long-term evolution of the structure of the system. For each operational configuration, a fault tree model captures the effects of software faults and transient hardware faults on the task computation. The fault tree models define the reward structure for the overall model. The software fault model is parameterized using experimental data associated with a recent implementation of an NVP system using the current design paradigm, in which the predictions of software failures are...