Design diversity: an update from research on reliability modelling

Diversity between redundant subsystems is, in various forms, a common design approach for improving system dependability. Its value in the case of software-based systems is still controversial. This paper gives an overview of reliability modelling work we carried out in recent projects on design diversity, presented in the context of previous knowledge and practice. These results provide additional insight for decisions in applying diversity and in assessing diverseredundant systems. A general observation is that, just as diversity is a very general design approach, the models of diversity can help conceptual understanding of a range of different situations. We summarise results in the general modelling of common-mode failure, in inference from observed failure data, and in decision-making for diversity in development.

From K.A.M. Tori to Isospectral Invariants and Spectral Rigidity of Billiard Tables

This article is a part of a project investigating the relationship between the dynamics of completely integrable or close to completely integrable billiard tables, the integral geometry on them, and the spectrum of the corresponding Laplace-Beltrami operators. It is concerned with new isospectral invariants and with the spectral rigidity problem for families of Laplace-Beltrami operators with Dirichlet, Neumann or Robin boundary conditions, associated with C^1 families of billiard tables. We introduce a notion of weak isospectrality for such deformations. The main dynamical assumption on the initial billiard table is that the corresponding billiard ball map or an iterate of it has a Kronecker invariant torus with a Diophantine frequency and that the corresponding Birkhoff Normal Form is nondegenerate in Kolmogorov sense. Then we obtain C^1 families of Kronecker tori with Diophantine frequencies. If the family of the Laplace-Beltrami operators satisfies the weak isospectral condition, we prove that the average action on the tori and the Birkhoff Normal Form of the billiard ball maps remain the same along the perturbation. As an application we obtain infinitesimal spectral rigidity for Liouville billiard tables in dimensions two and three. Applications are obtained also for strictly convex billiard tables of dimension two as well as in the case when the initial billiard table admits an elliptic periodic billiard trajectory. Spectral rigidity of billard tables close elliptical billiard tables is obtained. The results are based on a construction of C^1 families of quasi-modes associated with the Kronecker tori and on suitable KAM theorems for C^1 families of Hamiltonians.Comment: 170 pages; new results about the spectral rigidity of elliptical billiard tables; new Modified Iterative Lemma in the proof of KAM theorem with parameter

Assessing Asymmetric Fault-Tolerant Software

The most popular forms of fault tolerance against design faults use "asymmetric" architectures in which a "primary" part performs the computation and a "secondary" part is in charge of detecting errors and performing some kind of error processing and recovery. In contrast, the most studied forms of software fault tolerance are "symmetric" ones, e.g. N-version programming. The latter are often controversial, the former are not. We discuss how to assess the dependability gains achieved by these methods. Substantial difficulties have been shown to exist for symmetric schemes, but we show that the same difficulties affect asymmetric schemes. Indeed, the latter present somewhat subtler problems. In both cases, to predict the dependability of the fault-tolerant system it is not enough to know the dependability of the individual components. We extend to asymmetric architectures the style of probabilistic modeling that has been useful for describing the dependability of "symmetric" architectures, to highlight factors that complicate the assessment. In the light of these models, we finally discuss fault injection approaches to estimating coverage factors. We highlight the limits of what can be predicted and some useful research directions towards clarifying and extending the range of situations in which estimates of coverage of fault tolerance mechanisms can be trusted

Improving DBMS performance through diverse redundancy

Database replication is widely used to improve both fault tolerance and DBMS performance. Non-diverse database replication has a significant limitation - it is effective against crash failures only. Diverse redundancy is an effective mechanism of tolerating a wider range of failures, including many non-crash failures. However it has not been adopted in practice because many see DBMS performance as the main concern. In this paper we show experimental evidence that diverse redundancy (diverse replication) can bring benefits in terms of DBMS performance, too. We report on experimental results with an optimistic architecture built with two diverse DBMSs under a load derived from TPC-C benchmark, which show that a diverse pair performs faster not only than non-diverse pairs but also than the individual copies of the DBMSs used. This result is important because it shows potential for DBMS performance better than anything achievable with the available off-the-shelf servers

Rephrasing rules for off-the-shelf SQL database servers

We have reported previously (Gashi et al., 2004) results of a study with a sample of bug reports from four off-the-shelf SQL servers. We checked whether these bugs caused failures in more than one server. We found that very few bugs caused failures in two servers and none caused failures in more than two. This would suggest a fault-tolerant server built with diverse off-the-shelf servers would be a prudent choice for improving failure detection. To study other aspects of fault tolerance, namely failure diagnosis and state recovery, we have studied the "data diversity" mechanism and we defined a number of SQL rephrasing rules. These rules transform a client sent statement to an additional logically equivalent statement, leading to more results being returned to an adjudicator. These rules therefore help to increase the probability of a correct response being returned to a client and maintain a correct state in the database

How to make a mature accreting magnetar

Several candidates for accreting magnetars have been proposed recently by different authors. Existence of such systems contradicts the standard magnetic field decay scenario where a large magnetic field of a neutron star reaches $\lesssim$ few$\times 10^{13}$G at ages $\gtrsim 1$ Myr. Among other sources, the high mass X-ray binary 4U0114+65 seems to have a strong magnetic field around $10^{14}$ G. We develop a new Bayesian estimate for the kinematic age and demonstrate that 4U0114+65 has kinematic age 2.4-5 Myr ($95\%$ credential interval) since the formation of the neutron star. We discuss which conditions are necessary to explain the potential existence of magnetars in accreting high-mass binaries with ages about few Myrs and larger. Three necessary ingredients are: the Hall attractor to prevent rapid decay of dipolar field, relatively rapid cooling of the crust in order to avoid Ohmic decay due to phonons, and finally, low values of the parameter $Q$ to obtain long Ohmic time scale due to impurities. If age and magnetic field estimates for proposed accreting magnetars are correct, then these systems set the strongest limit on the crust impurity for a selected sample of neutron stars and provide evidence in favour of the Hall attractor.Comment: 8 pages, 3 figures, accepted to MNRAS on September 2

Evolution of isolated neutron stars till accretion. The role of initial magnetic field

We study evolution of isolated neutron stars on long time scale and calculate distribution of these sources in the main evolutionary stages: Ejector, Propeller, Accretor, and Georotator. We compare different initial magnetic field distributions taking into account a possibility of magnetic field decay, and include in our calculations the stage of subsonic Propeller. It is shown that though the subsonic propeller stage can be relatively long, initially highly magnetized neutron stars (B_0\ga 10^{13} G) reach the accretion regime within the Galactic lifetime if their kick velocities are not too large. The fact that in previous studies made $>$10 years ago, such objects were not considered results in a slight increase of the Accretor fraction in comparison with earlier conclusions. Most of the neutron stars similar to the Magnificent seven are expected to become accreting from the interstellar medium after few billion years of their evolution. They are the main predecestors of accreting isolated neutron stars.Comment: 8 pages, 3 figures. Accepted to MNRAS, typos correcte