Replication of non-deterministic objects

EPFL, 1998
EPFL thesis

Abstract

This thesis discusses replication of non-deterministic objects in distributed systems to achieve fault tolerance against crash failures. The objects replicated are the virtual nodes of a distributed application. Replication is viewed as an issue that is to be dealt with only during the configuration of a distributed application and that should not affect the development of the application. Hence, replication of virtual nodes should be transparent to the application. Like all measures to achieve fault tolerance, replication introduces redundancy in the system. Not surprisingly, the main difficulty is guaranteeing the consistency of all replicas such that they behave in the same way as if the object was not replicated (replication transparency). This is further complicated if active objects (like virtual nodes) are replicated, and these objects themselves can be clients of still further objects in the distributed application. The problems of replication of active non-deterministic objects are analyzed in the context of distributed Ada 95 applications. The ISO standard for Ada 95 defines a model for distributed execution based on remote procedure calls (RPC). Virtual nodes in Ada 95 use this as their sole communication paradigm, but they may contain tasks to execute activities concurrently, thus making the execution potentially non-deterministic due to implicit timing dependencies. Such non-determinism cannot be avoided by choosing deterministic tasking policies. I present two different approaches to maintain replica consistency despite this non-determinism. In a first approach, I consider the run-time support of Ada 95 as a black box (except for the part handling remote communications). This corresponds to a non-deterministic computation model. I show that replication of non-deterministic virtual nodes requires that remote procedure calls are implemented as nested transactions. Unfortunately, effects of failures are not local to the replicas of a virtual node: when a failure occurs, nested remote calls made to other virtual nodes must be undone. Also, using transactional semantics for RPCs necessitates a compromise regarding transparency: the application must identify global state for it cannot be determined reliably in an automatic way. Further study reveals that this approach cannot be implemented in a transparent way at all because the consistency criterion of Ada 95 (linearizability) is much weaker than that of transactions (serializability). An execution of remote procedure calls as transactions may thus lead to incompatibilities with the semantics of the programming language. If remotely called subprograms on a replicated virtual node perform partial operations, i.e., entry calls on global protected objects, deadlocks that cannot be broken can occur in certain cases. Such deadlocks do not occur when the virtual node is not replicated. The transactional semantics of RPCs must therefore be exposed to the application. A second approach is based on a piecewise deterministic computation model, i.e., the execution of a virtual node is seen as a sequence of deterministic state intervals. Whenever a non-deterministic event occurs, a new state interval is started. I study replica organization under this computation model (semi-active replication). In this model, all non-deterministic decisions are made on one distinguished replica (the leader), while all other replicas (the followers) are forced to follow the same sequence of non-deterministic events. I show that it suffices to synchronize the followers with the leader upon each observable event, i.e., when the leader sends a message to some other virtual node. It is not necessary to synchronize upon each and every non-deterministic event — which would incur a prohibitively high overhead. Non-deterministic events occurring on the leader between observable events are logged and sent to the followers just before the leader executes an observable event. Consequently, it is guaranteed that the followers will reach the same state as the leader, and thus the effects of failures remain mostly local to the replicas. A prototype implementation called RAPIDS (Replicated Ada Partitions In Distributed Systems) serves as a proof of concept for this second approach, demonstrating its feasibility. RAPIDS is an Ada 95 implementation of a replication manager for semi-active replication for the GNAT development system for Ada 95. It is entirely contained within the run-time support and hence largely transparent for the application.

Official source

https://infoscience.epfl.ch/record/32380?ln=en

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EPFL, 1998
EPFL thesis

Abstract

Official source

https://infoscience.epfl.ch/record/32380?ln=en

About this result

Related concepts (12)

Related concepts

Related publications (2)

Related publications

Propagation Models for Biochemical Reaction Networks

Maria-Emanuela-Canini Mateescu

In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by describing the time evolution of probability distribution over the states of a Markov chain that represents a biological network, and thus its stochasticity is only implicit. The transient solution of a CME is the vector of probabilities over the states of the corresponding Markov chain at a certain time point t, and it has traditionally been obtained by applying methods that are general to continuous-time Markov chains: uniformization, Krylov subspace methods, and general ordinary differential equation (ODE) solvers such as the fourth order Runge-Kutta method. Even though biochemical reaction networks are the main application of our work, some of our results are presented in the more general framework of propagation models (PM), a computational formalism that we introduce in the first part of this thesis. Each propagation model N has two associated propagation processes, one in discrete-time and a second one in continuous-time. These propagation processes propagate a generic mass through a discrete state space. For example, in order to model a CME, N propagates probability mass. In the discrete-time case the propagation is done step-wise, while in the continuous-time case it is done in a continuous flow defined by a differential equation. Again, in the case of the chemical master equation, this differential equation is the equivalent of the chemical master equation itself where probability mass is propagated through a discrete state space. Discrete-time propagation processes can encode methods such as the uniformization method and the fourth order Runge-Kutta integration method that we have mentioned above, and thus by optimizing propagation algorithms we optimize both of these methods simultaneously. In the second part of our thesis, we define stochastic hybrid models that approximate the stochastic behaviour of biochemical reaction networks by treating some variables of the system deterministically. This deterministic approximation is done for species with large populations, for which stochasticity does not play an important role. We propose three such hybrid models, which we introduce from the coarsest to the most refined one: (i) the first one replaces some variables of the system with their overall expectations, (ii) the second one replaces some variables of the system with their expectations conditioned on the values of the stochastic variables, (iii) and finally, the third one, splits each variable into a stochastic part (for low valuations) and a deterministic part (for high valuations), while tracking the conditional expectation of the deterministic part. For each of these algorithms we give the corresponding propagation models that propagate not only probabilities but also the respective continuous approximations for the deterministic variables.

EPFL2011

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very appealing. It can be seen as a reduced basis method, thus solvable at a relatively low computational cost, in which the solution is expanded as a linear combination of a few deterministic functions with random coefficients. The distinctive feature of the DLRA is that both the deterministic functions and random coefficients are computed on the fly and are free to evolve in time, thus adjusting at each time to the current structure of the random solution. This is achieved by suitably projecting the dynamics onto the tangent space of a manifold consisting of all random functions with a fixed rank. In this thesis, we aim at further analysing and applying the DLR methods to time-dependent problems.Our first work considers the DLRA of random parabolic equations and proposes a class of fully discrete numerical schemes.Similarly to the continuous DLRA, our schemes are shown to satisfy a discrete variational formulation.By exploiting this property, we establish the stability of our schemes: we show that our explicit and semi-implicit versions are conditionally stable under a ``parabolic'' type CFL condition which does not depend on the smallest singular value of the DLR solution; whereas our implicit scheme is unconditionally stable. Moreover, we show that, in certain cases, the semi-implicit scheme can be unconditionally stable if the randomness in the system is sufficiently small. The analysis is supported by numerical results showing the sharpness of the obtained stability conditions. The discrete variational formulation is further applied in our second work, which derives a-priori and a-posteriori error estimates for the discrete DLRA of a random parabolic equation obtained by the three newly-proposed schemes. Under the assumption that the right-hand side of the dynamical system lies in the tangent space up to a small remainder, we show that the solution converges with standard convergence rates w.r.t. the time, spatial, and stochastic discretization parameters, with constants independent of singular values.We follow by presenting a residual-based a-posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The a-posteriori error estimate consists of four parts: the finite element method error, the time discretization error, the stochastic collocation error, and the rank truncation error. These estimators are then used to drive an adaptive choice of FE mesh, collocation points, time steps, and time-varying rank.The last part of the thesis examines the idea of applying the DLR method in data assimilation problems, in particular the filtering problem. We propose two new filtering algorithms. They both rely on complementing the DLRA with a Gaussian component. More precisely, the DLR portion captures the non-Gaussian features in an evolving low-dimensional subspace through interacting particles, whereas each particle carries a Gaussian distribution on the whole ambient space. We study the effectiveness of these algorithms on a filtering problem for the Lorenz-96 system.

EPFL2022

Propagation Models for Biochemical Reaction Networks

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