Approximate performability and dependability analysis using generalized stochastic Petri Nets

Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task.\ud \ud To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described.\ud \ud In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness

Matrix-geometric solution of infinite stochastic Petri nets

We characterize a class of stochastic Petri nets that can be solved using matrix geometric techniques. Advantages of such on approach are that very efficient mathematical technique become available for practical usage, as well as that the problem of large state spaces can be circumvented. We first characterize the class of stochastic Petri nets of interest by formally defining a number of constraints that have to be fulfilled. We then discuss the matrix geometric solution technique that can be employed and present some boundary conditions on tool support. We illustrate the practical usage of the class of stochastic Petri nets with two examples: a queueing system with delayed service and a model of connection management in ATM network

Formal Dependability Engineering with MIOA

In this paper, we introduce MIOA, a stochastic process algebra-like specification language with datatypes, as well as a logic intSPDL, and its model checking algorithms. MIOA, which stands for Markovian input/output automata language, is an extension of Lynch's input/automata with Markovian timed transitions.MIOA can serve both as a fully fledged ``stand-alone'' specification language and the semantic model for the architectural dependability modelling and evaluation language Arcade. The logic intSPDL is an extension of the stochastic logic SPDL, to deal with the specialties of MIOA. intSPDL in the context of Arcade can be seen as the semantic model of abstract and complex dependability measures that can be defined in the Arcade framework. We define syntax and semantics of both MIOA and intSPDL, and show examples of applying MIOA and intSPDL in the realm of dependability modelling with Arcade

Computing lifetimes for battery-powered devices

The battery lifetime of mobile devices depends on the usage pattern of the battery, next to the discharge rate and the battery capacity. Therefore, it is important to include the usage pattern in battery lifetime computations. We do this by combining a stochastic workload, modeled as a continuous-time Markov model, with a well-known battery model. For this combined model, we provide new algorithms to efficiently compute the expected lifetime and the distribution and expected value of the delivered charge

GCSRL - A Logic for Stochastic Reward Models with Timed and Untimed Behaviour

In this paper we define the logic GCSRL (generalised continuous stochastic reward logic) that provides means to reason about systems that have states which sojourn times are either greater zero, in which case this sojourn time is exponentially distributed (tangible states), or zero (vanishing states).\ud In case of generalised stochastic Petri nets (GSPNs) and stochastic process algebras it turned out that these vanishing states can be very useful when it comes to define system behaviour. In the same way these states are useful for defining system properties using stochastic logics. We extend both the semantic model and the semantics of CSRL such that it allows to attach impulse rewards to transitions emanating from vanishing states. We show by means of a small example how model checking GCSRL formulae works

SPDL Model Checking via Property-Driven State Space Generation

In this report we describe how both, memory and time requirements for stochastic model checking of SPDL (stochastic propositional dynamic logic) formulae can significantly be reduced. SPDL is the stochastic extension of the multi-modal program logic PDL.\ud SPDL provides means to specify path-based properties with or without timing restrictions. Paths can be characterised by so-called programs, essentially regular expressions, where the executability can be made dependent on the validity of test formulae. For model-checking SPDL path formulae it is necessary to build a product transition system (PTS)\ud between the system model and the program automaton belonging to the path formula that is to be verified.\ud In many cases, this PTS can be drastically reduced during the model checking procedure, as the program restricts the number of potentially satisfying paths. Therefore, we propose an approach that directly generates the reduced PTS from a given SPA specification and an SPDL path formula.\ud The feasibility of this approach is shown through a selection of case studies, which show enormous state space reductions, at no increase in generation time.\u

Design and evaluation of a connection management mechanism for an ATM-based connectionless service

The Asynchronous Transfer Mode (ATM) has been developed as a connection-oriented technique for the transfer of fixed-size cells over high-speed networks. Many applications, however, require a connectionless network service. In order to provide such a technique, one can built a connectionless service on top of the connection-oriented service. In doing so, the issue of connection management comes into play. In this paper we propose a new connection management mechanism that provides for low bandwidth usage (as compared to a permanent connection) and low delays (as compared to a connection-per-packet approach). We model the new mechanism under two workload scenarios: an ordinary Poisson process and an interrupted Poisson process. We use Markovian techniques as well as matrix-geometric methods to evaluate the new connection management mechanism. From the evaluations it turns out that the proposed mechanism is superior to older approaches (which can be seen as limiting cases)

Beyond Model-Checking CSL for QBDs: Resets, Batches and Rewards

We propose and discuss a number of extensions to quasi-birth-death models (QBDs) for which CSL model checking is still possible, thus extending our recent work on CSL model checking of QBDs. We then equip the QBDs with rewards, and discuss algorithms and open research issues for model checking CSRL for QBDs with rewards

Extending the Logic IM-SPDL with Impulse and State Rewards

This report presents the logic SDRL (Stochastic Dynamic Reward Logic), an extension of the stochastic logic IM-SPDL, which supports the specication of complex performance and dependability requirements. SDRL extends IM-SPDL with the possibility to express impulse- and state reward measures.\ud The logic is interpreted over extended action-based Markov reward model (EMRM), i.e. transition systems containing both immediate and Markovian transitions, where additionally the states and transitions can be enriched with rewards.\ud We define ne the syntax and semantics of the new logic and show that SDRL provides powerful means to specify path-based properties with timing and reward-based restrictions.\ud In general, paths can be characterised by regular expressions, also called programs, where the executability of a program may depend on the validity of test formulae. For the model checking of SDRL time- and reward-bounded path formulae, a deterministic program automaton is constructed from the requirement. Afterwards the product transition\ud system between this automaton and the EMRM is built and subsequently transformed into a continuous time Markov reward model (MRM) on which numerical\ud analysis is performed.\u

CSL model checking of Deterministic and Stochastic Petri Nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described