Practical Applications of Probabilistic Model Checking to Communication Protocols (original) (raw)
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Probabilistic Model Checking of the IEEE 802.11 Wireless Local Area Network Protocol
2002
The international standard IEEE 802.11 was developed recently in recognition of the increased demand for wireless local area networks. Its medium access control mechanism is described according to a variant of the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) scheme. Although collisions cannot always be prevented, randomised exponential backoff rules are used in the retransmission scheme to minimise the likelihood of repeated collisions. More precisely, the backoff procedure involves a uniform probabilistic choice of an integer-valued delay from an interval, where the size of the interval grows exponentially with regard to the number of retransmissions of the current data packet. We model the two-way handshake mechanism of the IEEE 802.11 standard with a fixed network topology using probabilistic timed automata, a formal description mechanism in which both nondeterministic choice and probabilistic choice can be represented. From our probabilistic timed automaton model, we obtain a finite-state Markov decision process via a property-preserving discrete-time semantics. The Markov decision process is then verified using Prism, a probabilistic model checking tool, against probabilistic, timed properties such as “at most 5,000 microseconds pass before a station sends its packet correctly.”
PRISM 4.0: Verification of probabilistic real-time systems
2011
This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and real-time characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is open-source, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite.
Symbolic Model Checking for Probabilistic Timed Automata
2004
Probabilistic timed automata are timed automata extended with discrete probability distributions, and can be used to model timed randomised protocols or faulttolerant systems. We present symbolic model-checking algorithms for probabilistic timed automata to verify both qualitative temporal logic properties, corresponding to satisfaction with probability 0 or 1, and quantitative properties, corresponding to satisfaction with arbitrary probability. The algorithms operate on zones, which represent sets of valuations of the probabilistic timed automaton's clocks. Our method considers only those system behaviours which guarantee the divergence of time with probability 1. The paper presents a symbolic framework for the verification of probabilistic timed automata against the probabilistic, timed temporal logic PTCTL. We also report on a prototype implementation of the algorithms using Difference Bound Matrices, and present the results of its application to the CSMA/CD and FireWire root contention protocol case studies.
Computer Science, 2022
Event-B is a formal method that is used in the development of safety-critical systems; however, these systems may introduce uncertainty and also need to meet real-time requirements, which make the modeling and analysis of such systems a challenging task. While some works exist that try to extend Event-B with probability and over time, they fail to address both in a single framework. Besides, these works mainly addressed extending the language itself, not integrating extended Event-B with verification. In this paper, we aim to represent both probability and time in the Event-B language, and we will show how such a representation can be automatically translated into the probabilistic timed automata (PTA) that are described in the language of the PRISM probabilistic model checker. This transformation approach would allow us to analyze the probabilistic and time-bounded probabilistic reachability properties of probabilistic real-time systems through probabilistic timed CTL (PTCTL) logic.
Modeling and Analysis of Probabilistic Timed Systems
2009
Abstract Probabilistic models are useful for analyzing systems which operate under the presence of uncertainty. In this paper, we present a technique for verifying safety and liveness properties for probabilistic timed automata. The proposed technique is an extension of a technique used to verify stochastic hybrid automata using an approximation with Markov Decision Processes. A case study for CSMA/CD protocol has been used to show case the methodology used in our technique.
Automated verification techniques for probabilistic systems
2011
This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to analyse a wide range of their properties, including specifications in the temporal logics PCTL and LTL, probabilistic safety properties and cost-or reward-based measures. We also discuss multiobjective probabilistic model checking, used to analyse trade-offs between several different quantitative properties. Applications of the techniques in this tutorial include performance and dependability analysis of networked systems, communication protocols and randomised distributed algorithms. Since such systems often comprise several components operating in parallel, we also cover techniques for compositional modelling and verification of multi-component probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial.
Automatic Verification of Real-Time Systems with Discrete Probability Distributions
1999
We consider the timed automata model of [3], which allows the analysis of real-time systems expressed in terms of quantitative timing constraints. Traditional approaches to real-time system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for real-time systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”
A framework for verification of software with time and probabilities
2010
Quantitative verification techniques are able to establish system properties such as "the probability of an airbag failing to deploy on demand" or "the expected time for a network protocol to successfully send a message packet". In this paper, we describe a framework for quantitative verification of software that exhibits both real-time and probabilistic behaviour. The complexity of real software, combined with the need to capture precise timing information, necessitates the use of abstraction techniques. We outline a quantitative abstraction refinement approach, which can be used to automatically construct and analyse abstractions of probabilistic, real-time programs. As a concrete example of the potential applicability of our framework, we discuss the challenges involved in applying it to the quantitative verification of SystemC, an increasingly popular system-level modelling language.
Probabilistic Model Checking of the CSMA/CD Protocol Using PRISM and APMC
Electronic Notes in Theoretical Computer Science, 2005
Carrier Sense Multiple Access/Collision Detection (CSMA/CD) is the protocol for carrier transmission access in Ethernet networks (international standard IEEE 802.3). On Ethernet, any Network Interface Card (NIC) can try to send a packet in a channel at any time. If another NIC tries to send a packet at the same time, a collision is said to occur and the packets are discarded. The CSMA/CD protocol was designed to avoid this problem, more precisely to allow a NIC to send its packet without collision. This is done by way of a randomized exponential backoff process. In this paper, we analyse the correctness of the CSMA/CD protocol, using techniques from probabilistic model checking and approximate probabilistic model checking. The tools that we use are PRISM and APMC. Moreover, we provide a quantitative analysis of some CSMA/CD properties.
Probabilistic Model Checking: One Step Forward in Wireless Sensor Networks Simulation
International Journal of Distributed Sensor Networks, 2015
A novel collision resolution algorithm for wireless sensor networks is formally analysed via probabilistic model checking. The algorithm called 2CS-WSN is specifically designed to be used during the contention phase of IEEE 802.15.4. Discrete time Markov chains (DTMCs) have been proposed as modelling formalism and the well-known probabilistic symbolic model checker PRISM is used to check some correctness properties and different operating modes and, furthermore, to collect some performance measures. Thus, all the benefits of formal verification and simulation are gathered. These correctness properties as well as practical and relevant scenarios for the real world have agreed with the algorithm designers.