A Markovian Agent Model (MAM) is a stochastic model that provides a flexible, powerful and scalab... more A Markovian Agent Model (MAM) is a stochastic model that provides a flexible, powerful and scalable way for analyzing complex systems of distributed interacting objects. The constituting bricks of a MAM are the Markovian Agents (MA) represented by a finite state continuous time Markov chain (CTMC) whose infinitesimal generator is composed by a fixed component (the local behaviour) and an induced component that depends on the interaction with the other MAs. An additional innovative aspect is that the single MA keeps track of its position so that the overall MAM model is spatial dependent. MAMs are expressed with analytical formulas suited for numerical solution. Extensive applications in different domains have shown the effectiveness of the approach. In the present paper, we propose an example that illustrates how the MAM technique can cope with extremely large state spaces.
The main goal of this paper is to derive properties about Discrete Phase Type (DPH) distributions... more The main goal of this paper is to derive properties about Discrete Phase Type (DPH) distributions and to provide results which make convenient their use in the approximate analysis of discrete state non-Markovian stochastic systems. To this end, similarities and di erences between DPH and Continuous Phase Type (CPH) distributions are investigated. An immediate di erence is that DPH distributions can represent in an exact way a number of distributions with nite support, like the deterministic. A minimal representation, called canonical form, for the subclass of Acyclic Discrete Phase Type distributions (ADPH) is provided. It is then shown that below a given order (that is a function of the expected value) the minimal coe cient of variation of the ADPH family is always less than the minimal coe cient of variation of the CPH family.
In this paper we address the issue of security of SCADA systems; a topic of paramount importance ... more In this paper we address the issue of security of SCADA systems; a topic of paramount importance because of the impact on physical security and very challenging because of the peculiarities that set SCADA systems aside from usual ICT networks. We apply the modeling technique based on structures called weighted Attack and Defense Trees (ADT) to a complex case study based on a typical SCADA architecture, in which the attack tree is enriched with the cost and the impact of the attack. We introduce a new analysis technique for weighted ADT based on the representation of the attack scenario by means of MultiTerminal Binary Decision Diagrams (MTBDD) that allow the modeler to identify the most probable attack scenarios, in term of probability cost and impact, and gives an indication on how to mitigate the located breaches by means of suitable countermeasures.
The paper discusses a class of stochastic models for evaluating the optimal calibration interval ... more The paper discusses a class of stochastic models for evaluating the optimal calibration interval in measuring instruments devoted to assess the quality levels of an industrial processes. The model is based on the assumption that the calibration condition of the instrument can be traced by monitoring the drift of an observable parameter. Various stochastic drift models are introduced and compared. A preliminary validation of the model is reported, based on experimental data collected on a class of instruments.
Quantitative modeling of software aging and rejuvenation has been the object of a vast literature... more Quantitative modeling of software aging and rejuvenation has been the object of a vast literature in the last decades. Due to the probabilistic nature of the phenomena to which these studies are devoted, the models rely on the theory of stochastic processes. The present Chapter is intended to provide an overview of the methods and analytical solution techniques related to the stochastic processes that are more often encountered in the literature on software aging and rejuvenation. The Chapter is particularly addressed to researchers who want to have an initial approach to these topics.
Markovian Agent Models are a rather new modeling technique to deal with complex systems composed ... more Markovian Agent Models are a rather new modeling technique to deal with complex systems composed by a multitude of interacting objects, whose spatial location is also relevant in determining their interaction. A preliminary example of application, which is a part of a larger project, is provided.
This paper provides a detailed study on discrete phase type (DPH) distributions and its acyclic s... more This paper provides a detailed study on discrete phase type (DPH) distributions and its acyclic subclass referred to as acyclic-DPH (ADPH). Previously not considered similarities and differences between DPH and continuous phase type (CPH) distributions are investigated and minimal representations, called canonical forms, for the subclass of ADPH distributions are provided. We investigate the consequences of the recent result about the minimal coefficient of variation of the DPH class [The minimal coefficient of variation of discrete phase type distributions, in: Proceedings of the Third International Conference on Matrix-analytic Methods in Stochastic Models, July 2000] and show that below a given order (that is a function of the expected value) the minimal coefficient of variation of the DPH class is always less than the minimal coefficient of variation of the CPH class. Since all the previously introduced Phase Type fitting methods were designed for fitting over the CPH class we p...
The paper presents the evaluation of a benchmark on dynamic reliability. Such system consists of ... more The paper presents the evaluation of a benchmark on dynamic reliability. Such system consists of a tank containing some liquid, two pumps and one valve to renew the liquid in the tank, a heat source warming the liquid, and a controller acting on the state of the components. Three failure conditions are possible: the dry out, the overflow or the high temperature of the liquid. Due to the presence of continuous variables, such as the liquid level and temperature, the system is modelled as a Fluid Stochastic Petri Net which is the object of simulation obtaining the unreliability evalua-
2016 46th Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshop (DSN-W), 2016
In this tutorial we will expose methods used in reliability, availability, performability and sur... more In this tutorial we will expose methods used in reliability, availability, performability and survivability modeling and analysis of systems in practice. Non-state-space solution methods are often used to solve reliability block diagrams, fault trees and reliability graphs [1,2,4]. Relatively efficient algorithms are known to handle systems with hundreds of components and have been implemented in many software packages. We will show the usage of these model types through practical examples and via the software package SHARPE [3].
A Markovian Agent Model (MAM) is a stochastic model that provides a flexible, powerful and scalab... more A Markovian Agent Model (MAM) is a stochastic model that provides a flexible, powerful and scalable way for analyzing complex systems of distributed interacting objects. The constituting bricks of a MAM are the Markovian Agents (MA) represented by a finite state continuous time Markov chain (CTMC) whose infinitesimal generator is composed by a fixed component (the local behaviour) and an induced component that depends on the interaction with the other MAs. An additional innovative aspect is that the single MA keeps track of its position so that the overall MAM model is spatial dependent. MAMs are expressed with analytical formulas suited for numerical solution. Extensive applications in different domains have shown the effectiveness of the approach. In the present paper, we propose an example that illustrates how the MAM technique can cope with extremely large state spaces.
The main goal of this paper is to derive properties about Discrete Phase Type (DPH) distributions... more The main goal of this paper is to derive properties about Discrete Phase Type (DPH) distributions and to provide results which make convenient their use in the approximate analysis of discrete state non-Markovian stochastic systems. To this end, similarities and di erences between DPH and Continuous Phase Type (CPH) distributions are investigated. An immediate di erence is that DPH distributions can represent in an exact way a number of distributions with nite support, like the deterministic. A minimal representation, called canonical form, for the subclass of Acyclic Discrete Phase Type distributions (ADPH) is provided. It is then shown that below a given order (that is a function of the expected value) the minimal coe cient of variation of the ADPH family is always less than the minimal coe cient of variation of the CPH family.
In this paper we address the issue of security of SCADA systems; a topic of paramount importance ... more In this paper we address the issue of security of SCADA systems; a topic of paramount importance because of the impact on physical security and very challenging because of the peculiarities that set SCADA systems aside from usual ICT networks. We apply the modeling technique based on structures called weighted Attack and Defense Trees (ADT) to a complex case study based on a typical SCADA architecture, in which the attack tree is enriched with the cost and the impact of the attack. We introduce a new analysis technique for weighted ADT based on the representation of the attack scenario by means of MultiTerminal Binary Decision Diagrams (MTBDD) that allow the modeler to identify the most probable attack scenarios, in term of probability cost and impact, and gives an indication on how to mitigate the located breaches by means of suitable countermeasures.
The paper discusses a class of stochastic models for evaluating the optimal calibration interval ... more The paper discusses a class of stochastic models for evaluating the optimal calibration interval in measuring instruments devoted to assess the quality levels of an industrial processes. The model is based on the assumption that the calibration condition of the instrument can be traced by monitoring the drift of an observable parameter. Various stochastic drift models are introduced and compared. A preliminary validation of the model is reported, based on experimental data collected on a class of instruments.
Quantitative modeling of software aging and rejuvenation has been the object of a vast literature... more Quantitative modeling of software aging and rejuvenation has been the object of a vast literature in the last decades. Due to the probabilistic nature of the phenomena to which these studies are devoted, the models rely on the theory of stochastic processes. The present Chapter is intended to provide an overview of the methods and analytical solution techniques related to the stochastic processes that are more often encountered in the literature on software aging and rejuvenation. The Chapter is particularly addressed to researchers who want to have an initial approach to these topics.
Markovian Agent Models are a rather new modeling technique to deal with complex systems composed ... more Markovian Agent Models are a rather new modeling technique to deal with complex systems composed by a multitude of interacting objects, whose spatial location is also relevant in determining their interaction. A preliminary example of application, which is a part of a larger project, is provided.
This paper provides a detailed study on discrete phase type (DPH) distributions and its acyclic s... more This paper provides a detailed study on discrete phase type (DPH) distributions and its acyclic subclass referred to as acyclic-DPH (ADPH). Previously not considered similarities and differences between DPH and continuous phase type (CPH) distributions are investigated and minimal representations, called canonical forms, for the subclass of ADPH distributions are provided. We investigate the consequences of the recent result about the minimal coefficient of variation of the DPH class [The minimal coefficient of variation of discrete phase type distributions, in: Proceedings of the Third International Conference on Matrix-analytic Methods in Stochastic Models, July 2000] and show that below a given order (that is a function of the expected value) the minimal coefficient of variation of the DPH class is always less than the minimal coefficient of variation of the CPH class. Since all the previously introduced Phase Type fitting methods were designed for fitting over the CPH class we p...
The paper presents the evaluation of a benchmark on dynamic reliability. Such system consists of ... more The paper presents the evaluation of a benchmark on dynamic reliability. Such system consists of a tank containing some liquid, two pumps and one valve to renew the liquid in the tank, a heat source warming the liquid, and a controller acting on the state of the components. Three failure conditions are possible: the dry out, the overflow or the high temperature of the liquid. Due to the presence of continuous variables, such as the liquid level and temperature, the system is modelled as a Fluid Stochastic Petri Net which is the object of simulation obtaining the unreliability evalua-
2016 46th Annual IEEE/IFIP International Conference on Dependable Systems and Networks Workshop (DSN-W), 2016
In this tutorial we will expose methods used in reliability, availability, performability and sur... more In this tutorial we will expose methods used in reliability, availability, performability and survivability modeling and analysis of systems in practice. Non-state-space solution methods are often used to solve reliability block diagrams, fault trees and reliability graphs [1,2,4]. Relatively efficient algorithms are known to handle systems with hundreds of components and have been implemented in many software packages. We will show the usage of these model types through practical examples and via the software package SHARPE [3].
Uploads
Papers by Andrea Bobbio