Probabilistic Timed Automata Research Articles

Probabilistic performance evaluation of the class-A device in LoRaWAN protocol on the MAC layer

LoRaWAN is a network technology that provides a long-range wireless network while maintaining low energy consumption. It adopts the pure Aloha MAC protocol and the duty-cycle limitation at both uplink and downlink on the MAC layer to conserve energy. Additionally, LoRaWAN employs orthogonal parameters to mitigate collisions. However, synchronization in star-of-star topology networks and the complicated collision mechanism make it challenging to conduct a quantitative performance evaluation in LoRaWAN. Our previous work proposes a Probabilistic Timed Automata (PTA) model to represent the uplink transmission in LoRaWAN. It is a mathematical model that presents the nondeterministic and probabilistic choice with time passing. However, this model remains a work in progress. This study extends the PTA model to depict Class-A devices in the LoRaWAN protocol. The complete characteristics of LoRaWAN’s MAC layer, such as duty-cycle limits, bidirectional communication, and confirmed message transmission, are accurately modeled. Furthermore, a comprehensive collision model is integrated into the PTA. Various properties are verified using the probabilistic model checker PRISM, and quantitative properties are calculated under diverse scenarios. This quantitative analysis provides valuable insights into the performance and behavior of LoRaWAN networks under varying conditions.

Modeling and Analysis of Probabilistic Real-time Systems through Integrating Event-B and Probabilistic Model Checking

Event-B is a formal method used in the development of safety critical systems. However, these systems may introduce uncertainty, and need also to meet real-time requirements, which make their modeling and analysis a challenging task. Existing works on extending Event-B with probability and time did not address both probability and time in a single framework. Besides, they did focus the most on extending the language itself, not on integrating the 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 Probabilistic Timed Automata (PTA) described in the language of the probabilistic model checker PRISM. This translation would allow us to analyze probabilistic, as well as time-bounded probabilistic reachability properties of probabilistic real-time systems through the Probabilistic Timed CTL (PTCTL) logic.

Verifying Plans and Scripts for Robotics Tasks Using Performance Level Profiles

Performance-Level Profiles (PLPs) were introduced as a type of action representation language suitable for capturing the behavior of functional code for robotics. This paper addresses two issues that PLPs raise: (1) Their formal semantics. (2) How to verify a script or a plan that schedule the use of components that have been documented by PLPs. We provide a formal semantics for PLPs by mapping them to probabilistic timed automata (PTAs). We also show how, given a script that refers to components specified using PLPs, we derive a PTA specification of the entire system. This PTA can be used to verify the system’s properties and answers queries about its behavior. Finally, we empirically evaluate an implemented system based on these ideas, demonstrating its scalability. The result is a pragmatic approach for verifying component-based robotic systems.

Time dependent anomaly detection system for smart environment using probabilistic timed automaton

The wide-ranging implementation of the digital Internet of Things (IoT) system in recent years has contributed to the development of smart cities. In real-world time, smart cities are designed to encourage simplicity and quality of life in developed areas. A smart city’s network traffic from loT networks is increasingly growing and posing new cybersecurity problems, because these loT devices are linked to sensors that are directly connected to large cloud servers. The researchers need to refine new methods for identifying compromised loT machines to prevent such cyberattacks. In the smart networks, traditional protection strategies are cumbersome to implement because of complexity in communication systems, vendor regulations, requirements, technology and location-specific resources. To address these difficulties, we used a Probabilistic Timed Automaton (PTA) to model the operating actions of smart devices and introduced novel Time Dependent Anomaly Detection Systems (TDADS) utilizing the operational behaviour of smart home environment. Simulations to test our concept are performed in real time. It is clear from the simulation findings that our TDADS achieves effective usage of resources and robust packet transport.

Modelling Behavioural Dynamics for Asymmetric Application Layer DDoS Detection

Asymmetric application layer DDoS attacks using computationally intensive HTTP requests are an extremely dangerous class of attacks capable of taking down web servers with relatively few attacking connections. These attacks consume limited network bandwidth and are similar to legitimate traffic, which makes their detection difficult. Existing detection mechanisms for these attacks use indirect representations of actual user behaviour and complex modelling techniques, which leads to a higher false positive rate (FPR) and longer detection time, which makes them unsuitable for real time use. There is a need for simple, efficient and adaptable detection mechanisms for asymmetric DDoS attacks. In this work, an attempt is made to model the actual behavioural dynamics of legitimate users using a simple annotated Probabilistic Timed Automata (PTA) along with a suspicion scoring mechanism for differentiating between legitimate and malicious users. This allows the detection mechanism to be extremely fast and have a low FPR. In addition, the model can incrementally learn from run-time traces, which makes it adaptable and reduces the FPR further. Experiments on public datasets reveal that our proposed approach has a high detection rate and low FPR and adds negligible overhead to the web server, which makes it ideal for real time use.

Probabilistic timed graph transformation systems

Today, software has become an intrinsic part of complex distributed embedded real-time systems. The next generation of embedded real-time systems will interconnect the today unconnected systems via complex software parts and the service-oriented paradigm. Due to these interconnections, the architecture of systems can be subject to changes at run-time, e.g. when dynamic binding of service end-points is employed or complex collaborations are established dynamically. However, suitable formalisms and techniques that allow for modeling and analysis of timed and probabilistic behavior of such systems as well as of their structure dynamics do not exist so far.To fill the identified gap, we propose Probabilistic Timed Graph Transformation Systems (PTGTSs) as a high-level description language that supports all the necessary aspects of structure dynamics, timed behavior, and probabilistic behavior. We introduce the formal model of PTGTSs in this paper as well as present and formally verify a mapping of models with finite state spaces to probabilistic timed automata (PTA) that allows to use the PRISM model checker to analyze PTGTS models with respect to PTCTL properties.

New Insights Into Soft-Faults Induced Cardiac Pacemakers Malfunctions Analyzed at System-Level via Model Checking

Progressive shrinking of CMOS device sizes has permitted reductions in power consumption and miniaturization of electronic devices. In parallel, modern pacemakers implemented with advanced technologies have proved to be more sensitive than earlier models to soft errors induced notably by external radiations. Traditionally, the analysis of the impact of soft faults (SFs), such as those induced by single-event upsets, on the behavior of pacemaker devices, has been carried out by dynamic radiation ground testing and clinical observations . However, these techniques are expensive. They can only be done very late in the design cycle, after the design is manufactured and in part after it is implanted. This paper presents a new model-based analysis of the impact of SFs on the behavior of cardiac pacemakers at a system level. It is performed by: 1) introducing a new probabilistic timed automata (PTA) model; 2) verifying this model against a set of functional properties to ensure it meets its specifications under normal conditions; 3) applying a new methodology to inject SFs at a certain time in the PTA model of the pacemaker and to verify their impact on the pacemaker’s behavior is introduced; and 4) identifying different scenarios for SFs that may lead to malfunction, including oversensing, undersensing , and output failure . The reported formal modeling is done in PRISM and the analysis is done with the Storm model checker.

A New Improved and Extended Version of the Multicell Bacterial Simulator gro.

gro is a cell programming language developed in Klavins Lab for simulating colony growth and cell-cell communication. It is used as a synthetic biology prototyping tool for simulating multicellular biocircuits and microbial consortia. In this work, we present several extensions made to gro that improve the performance of the simulator, make it easier to use, and provide new functionalities. The new version of gro is between 1 and 2 orders of magnitude faster than the original version. It is able to grow microbial colonies with up to 105 cells in less than 10 min. A new library, CellEngine, accelerates the resolution of spatial physical interactions between growing and dividing cells by implementing a new shoving algorithm. A genetic library, CellPro, based on Probabilistic Timed Automata, simulates gene expression dynamics using simplified and easy to compute digital proteins. We also propose a more convenient language specification layer, ProSpec, based on the idea that proteins drive cell behavior. CellNutrient, another library, implements Monod-based growth and nutrient uptake functionalities. The intercellular signaling management was improved and extended in a library called CellSignals. Finally, bacterial conjugation, another local cell-cell communication process, was added to the simulator. To show the versatility and potential outreach of this version of gro, we provide studies and novel examples ranging from synthetic biology to evolutionary microbiology. We believe that the upgrades implemented for gro have made it into a powerful and fast prototyping tool capable of simulating a large variety of systems and synthetic biology designs.

Symbolic optimal expected time reachability computation and controller synthesis for probabilistic timed automata

In this paper we consider the problem of computing the optimal (minimum or maximum) expected time to reach a target and the synthesis of an optimal controller for a probabilistic timed automaton (PTA). Although this problem admits solutions that employ the digital clocks abstraction or statistical model checking, symbolic methods based on zones and priced zones fail due to the difficulty of incorporating probabilistic branching in the context of dense time. We work in a generalisation of the setting introduced by Asarin and Maler for the corresponding problem for timed automata, where simple and nice functions are introduced to ensure finiteness of the dense-time representation. We find restrictions sufficient for value iteration to converge to the optimal expected time on the uncountable Markov decision process representing the semantics of a PTA. We formulate Bellman operators on the backwards zone graph of a PTA and prove that value iteration using these operators equals that computed over the PTA's semantics. This enables us to extract an ε-optimal controller from value iteration in the standard way.

Verifying Collision Avoidance Behaviours for Unmanned Surface Vehicles using Probabilistic Model Checking

Abstract: Collision avoidance is an essential safety requirement for unmanned surface vehicles (USVs). Normally, its practical verification is non-trivial, due to the stochastic behaviours of both the USVs and the intruders. This paper presents the probabilistic timed automata (PTAs) based formalism for three collision avoidance behaviours of USVs in uncertain dynamic environments, which are associated with the crossing situation in COLREGs. Steering right, acceleration, and deceleration are considered potential evasive manoeuvres. The state-of-the-art prism model checker is applied to analyse the underlying models. This work provides a framework and practical application of the probabilistic model checking for decision making in collision avoidance for USVs.

Model checking for probabilistic timed automata

Probabilistic timed automata (PTAs) are a formalism for modelling systems whose behaviour incorporates both probabilistic and real-time characteristics. Applications include wireless communication protocols, automotive network protocols and randomised security protocols. This paper gives an introduction to PTAs and describes techniques for analysing a wide range of quantitative properties, such as maximum probability of the airbag failing to deploy within 0.02 seconds, maximum expected time for the protocol to terminate or minimum expected energy consumption required to complete all tasks. We present a temporal logic for specifying such properties and then give a survey of available model-checking techniques for formulae specified in this logic. We then describe two case studies in which PTAs are used for modelling and analysis: a probabilistic non-repudiation protocol and a task-graph scheduling problem.

Model Checking Probabilistic Real-Time Properties for Service-Oriented Systems with Service Level Agreements

The assurance of quality of service properties is an important aspect of service-oriented software engineering. Notations for so-called service level agreements (SLAs), such as the Web Service Level Agreement (WSLA) language, provide a formal syntax to specify such assurances in terms of (legally binding) contracts between a service provider and a customer. On the other hand, formal methods for verification of probabilistic real-time behavior have reached a level of expressiveness and efficiency which allows to apply them in real-world scenarios. In this paper, we suggest to employ the recently introduced model of Interval Probabilistic Timed Automata (IPTA) for formal verification of QoS properties of service-oriented systems. Specifically, we show that IPTA in contrast to Probabilistic Timed Automata (PTA) are able to capture the guarantees specified in SLAs directly. A particular challenge in the analysis of IPTA is the fact that their naive semantics usually yields an infinite set of states and infinitely-branching transitions. However, using symbolic representations, IPTA can be analyzed rather efficiently. We have developed the first implementation of an IPTA model checker by extending the PRISM tool and show that model checking IPTA is only slightly more expensive than model checking comparable PTA.

Time and Probability-Based Information Flow Analysis

In multilevel systems, it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely, the so-called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that systems that are proven to be secure in a possibilistic framework may turn out to be insecure when time or probability is considered. Recently, work has been done in order to consider also aspects either of time or of probability, but not both. In this paper, we propose a general framework based on Probabilistic Timed Automata, where both probabilistic and timing covert channels can be studied. We define a Noninterference security property and a Nondeducibility on Composition security property, which allow expressing information flow in a timed and probabilistic setting. We then compare these properties with analogous ones defined in contexts where either time or probability or neither of them are taken into account. This permits a classification of the properties depending on their discerning power. As an application, we study a system with covert channels that we are able to discover by applying our techniques.

A Classification of Time and/or Probability Dependent Security Properties

In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that systems that are considered to be secure may turn out to be insecure when time or probability are considered. Recently, work has been done in order to consider also aspects either of time or of probability, but not both. In this paper we propose a general framework, based on Probabilistic Timed Automata, where both probabilistic and timing covert channels can be studied. We define a Non-Interference security property that allows one to express information flow in a timed and probabilistic setting, and we compare the property with analogous properties defined in settings where either time or probability or none of them are taken into account. This allows to classify properties depending on their discerning power.

PROBABILISTIC HYBRID AUTOMATA WITH VARIABLE STEP WIDTH APPLIED TO THE ANAYLSIS OF NETWORKED AUTOMATION SYSTEMS

Probabilistic Timed Automata (PTA) have successfully been applied to discuss problems specific to the field of Networked Automation Systems (NAS). This paper shows the transition from PTA towards Probabilistic Hybrid Automata (PHA) by introducing an event triggered variable time version of PTAs. The main idea is to increase accuracy and decrease state space of the underlying Discrete Time Markov Chains (DTMC) which are input for those probabilistic model checking algorithms for which these models should be used. For a better illustration of the advancement, the approach is applied to a typical example from the field of NAS.