Consensus protocols are used in a variety of reliable distributed systems, including both safety-critical and business-critical applications. The correctness of a consensus protocol is usually shown, by making assumptions about the environment in which it executes, and then proving properties about the protocol. But proofs about a protocol's behavior are only as good as the assumptions which were made to obtain them, and violation of these assumptions can lead to unpredicted and serious consequences. We present a new approach for the probabilistic verification of synchronous round based consensus protocols. In doing so, we make stochastic assumptions about the environment in which a protocol operates, and derive probabilities of proper and non proper behavior. We thus can account for the violation of assumptions made in traditional proof techniques. To obtain the desired probabilities, the approach enumerates possible states that can be reached during an execution of the protocol, and computes the probability of achieving the desired properties for a given fault and network environment. We illustrate the use of this approach via the evaluation of a simple consensus protocol operating under a realistic environment which includes performance, omission, and crash failures.

Probabilistic verification of a synchronous round-based consensus protocol

Probabilistic Evaluation for the Analytical Solution of Large Markov Models: Algorithms and Tool Support

Probabilistic validation is a new approach to deal with large state transitions systems. The user's need is to prove that, for a given period of operations, that a given assertion on the reached states is true with a sufficient level of probability. The system to be validated is modeled by a stochastic Petri net. The analysis relies on a partial exploration of the reachability set and tries to reach as quickly as possible critical states (states in which the assertion is not verified). An exact linear program solution allows to 'travel' through the graph. The main goal of the paper is to present the principles of this searching algorithm. >

Searching best paths to worst states

In a reliable computer system, correctly-functioning processors must be able to reach agreement despite the presence of malfunctioning components. This report discusses two such agreement problems. In the consensus problem, processors must reach a common decision despite failures. In the membership problem, agreement must be reached concerning the history of groups of correct processors that exist over time as well as on the membership of each group. A survey of some existing literature on consensus and membership protocols is carried out, pointing out the different assumptions about the properties of the system on which these protocols are based. Then, a unified validation framework is proposed in order to compare, in probabilistic terms, the properties of these different protocols, together with the problems involved with this validation.

Towards a Unified Comparison of Synchronous and Asynchronous Agreement Protocols

Probabilistic validation is an approach for the validation of highly dependable and complex systems. It relies on a partial analysis on a system model and tries to prove that the failed event occurrences has a sufficiently low probability. We define a probabilistic validation method using worst event driven and an importance sampling simulation. The system which must be validated is modeled by a stochastic Petri net. An efficient simulation of the net must be able to sample complex and improbable trajectories which eventually reach critical markings. Two problems have to be solved. The sequence of transition firings which may lead to critical markings must be characterized ad the Petri net level. The second problem is to sample these sequences and to build an accurate estimate of the incorrect behavior probability. We discuss several simulation algorithms in the Markovian and non-Markovian cases. We show the effectiveness of these techniques on the validation of several examples. >

Probabilistic validation using worst event driven and importance sampling simulation

This paper presents a new concept of validation of distributed or safety-critical systems. The main problem of existing methods is related to the exponential growth of the analysis complexity with the model size. Our method relies on a state transition model which includes a description of operation duration and frequency of events (stochastic Petri nets). The aim of our work is to develop a new approach based on a partial exploration of the reachability set. At the end of the partial exploration we can demonstrate, for a given period of operation, that assertions about the behaviour of the system are verified with an acceptable probability level.

C. Fraize

Papers

A New Approach of Formal Proof: Probabilistic Validation