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.

In this paper we present a new modelling approach for dependability evaluation and sensitivity analysis of Scheduled Maintenance Systems, based on a Deterministic and Stochastic Petri Net approach. The DSPN approach offers significant advantages in terms of easiness and clearness of modelling with respect to the existing Markov chain based tools, drastically limiting the amount of user-assistance needed to define the model. At the same time, these improved modelling capabilities do not result in additional computational costs. Indeed, the evaluation of the DSPN model of SMS is supported by an efficient and fully automatable analytical solution technique for the time-dependent marking occupation probabilities.

In this study we focus on the specification and assessment of Stochastic Petri net (SPN) models to evaluate the design of an embedded system for reliability and availability. The system provides dynamic driving regulation (DDR) to improve vehicle derivability (antiskid,-slip and steering assist). A functional SPN abstraction was developed for each of three subsystems that incorporate mechanics, failure modes/effects and model parameters. The models are solved in terms of the subsystem and overall system reliability and availability. Four sets of models were developed. The first three sets include subsystem representations for the TC (Traction Control), AB (Antilock Braking) and ESA (Electronic Steering Assistance) systems. The last set combines these systems into one large model. We summarize the general approach and provide sample Petri net graphs and reliability charts that were used to evaluate the design of the DDR in parts and as a whole. 1.

Introduction The Stochastic Petri Net Package (SPNP) is a versatile modeling tool for the solution of Stochastic Petri Nets (SPN) models. The SPN models are described in the input language for SPNP called CSPL (C-based SPN Language). The CSPL is an extension of the ANSI C programming language [16] with additional constructs to facilitate the easy description of SPN models. The full power and generality of C is available, but a working knowledge of C is sufficient to use SPNP effectively. The SPN models specified to SPNP are actually "SPN Reward Models" or Stochastic Reward Nets (SRNs) [9, 10] which are based on the "Markov Reward Model" paradigm [18, 37]. This provides a powerful modeling environment for the analysis of: ffl Dependability (Reliability, Availability, Safety). ffl Performance. ffl Performability. Several important Petri net constructs like marking dependency, variable cardinality arc and enabling functions [9] facil

Contemporary approaches to software performance engineering suffer from weak integration with the design process and provide little feedback to developers. An approach to software performance modelling is presented, based on annotating design specifications with performance parameters and operational analysis of queueing networks representing the hardware. Analytical sensitivity analysis is provided to 1) point out where model refinement and parameter capture effort should be focused, and 2) suggest optimisations in the design specification. Sensitivities are obtained by differentiation of the combined software (workload) and hardware performance model. Only open queueing networks are considered at the hardware level. The results are validated, and it is pointed out that further work is particularly needed in the areas of dynamic software performance modelling and distributed systems.

A quasi-independence result holds for the go-back-n automatic repeat request #ARQ# protocol and the sliding window#ow control protocol if packet errors are independent. The result is independent of the magnitude of the packet error probability or the cost of an error. A parallel result for the selective repeat ARQ protocol, however, does not appear to hold. Keywords: Error Recovery Protocols, ARQ, Go-back-N, Window Flow Control. College of Computing Georgia Institute of Technology Atlanta, Georgia 30332#0280 # To be published in Computer Networks and ISDN Systems. This researchwas supported in part by the National Science Foundation under grant NCR91-16117. Parts of this paper were presented as evidence of quasi-independence in Sigmetrics 1990#7#. The proof of quasi-independence #Section 4# is new. 1 Introduction The objective of this paper is to show that under certain conditions, the performance of the go-back-n error recovery protocol and the sliding window#ow control protocol a...

In order to maximize system dependability improvements we need criteria for placement of component redundancy. One such criterion is based on quantitative measures provided by importance theory. Importance coefficients of components in mathematical models provide numerical ranks based on the contribution of the component to a system event occurrence (i.e., the one for which the model was constructed). If cost, size or weight are not objectives when maximizing system dependability, the importance ranks suggest components to which system upgrading effort should be directed first. Otherwise, the importance measures offer valid weighting factors to the optimization process. In this paper, we introduce novel techniques for computing importance measures in state space dependability models. Specifically, reward functions in a Markov reward model

We present the Stochastic Petri Net Package (SPNP), a versatile modeling tool for performance, dependability, and performability analysis of complex systems. Input models developed based on the theory of stochastic reward nets are solved by e cient and numerically stable algorithms. Steady-state, transient, cumulative transient, time-averaged, and \up-to-absorption " measures can be computed. Parametric sensitivity analysis of these measures is possible. Some degree of logical analysis capabilities are also available in the form of assertion checking and the number and types of markings in the reachability graph. Advanced constructs available- such as markingdependent arc multiplicities, guards, arrays of places and transitions, and subnets-reduce modeling complexity and enhance power of expressiveness of the package. The most powerful feature is the capability to assign reward rates at the net level and subsequently compute the desired measures of the system being modeled. The modeling description language is CSPL, a C-like language, although no previous knowledge of the C language is necessary to use SPNP.

Abstract—The increasing reliance on computer technology nowadays has resulted in a rapidly growing need to build reliable and fault resistant computer-based systems. Computer system reliabilities are conventionally modeled and analyzed using techniques such as fault tree analysis (FTA) and reliability block diagrams (RBD), which provide static representations of system reliabilities. A recent extension to RBD, called dynamic reliability block diagrams (DRBD), provides a framework for modeling dynamic reliability behaviors of computer-based systems. However, analyzing a DRBD model in order to locate and identify design errors, such as a deadlock error or a faulty state, is not trivial when done manually. A feasible approach to verifying a DRBD model is to develop a formal model of the DRBD, and analyze it using programmatic methods. In this paper, we first define a reliability markup language (RML) that can be used to formally describe DRBD models. Then we present an algorithm that automatically converts a DRBD model into a colored Petri net (CPN). We use a case study to illustrate the effectiveness of our approach and demonstrate how system properties of a DRBD model can be verified using an existing Petri net tool. Our approach is compositional and provides a potential solution to automated verification of DRBD models. Index Terms—System reliability, reliability block diagram (RBD), dynamic RBD (DRBD), extensible markup language (XML), colored Petri nets (CPN), formal modeling and analysis, automated verification, deadlock detection. 1

Abstract—Computer system reliability is conventionally modeled and analyzed using techniques such as fault tree analysis (FTA) and reliability block diagrams (RBD), which provide static representations of system reliability properties. A recent extension to RBD, called dynamic reliability block diagrams (DRBD), defines a framework for modeling dynamic reliability behavior of computer-based systems. However, analyzing a DRBD model in order to locate and identify design errors, such as a deadlock error or faulty state, is not trivial when done manually. A feasible approach to verifying it is to develop its formal model, and then analyze it using programmatic methods. In this paper, we first define a reliability markup language (RML) that can be used to formally describe DRBD models. Then we present an algorithm that automatically converts a DRBD model into a colored Petri net (CPN). We use a case study to illustrate the effectiveness of our approach and demonstrate how system properties of a DRBD model can be verified using an existing Petri net tool. Our formal modeling approach is compositional, thus it provides a potential solution to automated verification of DRBD models. Index Terms—System reliability, reliability block diagram (RBD), extensible markup language (XML), colored Petri net (CPN), time Petri net, formal modeling and analysis, automated verification, deadlock detection. API BNF