Hybrid process algebra

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Hybrid performance modelling of opportunistic networks

We demonstrate the modelling of opportunistic networks using the process algebra stochastic HYPE. Network traffic is modelled as continuous flows, contact between nodes in the network is modelled stochastically, and instantaneous decisions are modelled as discrete events. Our model describes a network of stationary video sensors with a mobile ferry which collects data from the sensors and delivers it to the base station. We consider different mobility models and different buffer sizes for the ferries. This case study illustrates the flexibility and expressive power of stochastic HYPE. We also discuss the software that enables us to describe stochastic HYPE models and simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055

Discrete Simulation of Behavioural Hybrid Process Calculus

Hybrid systems combine continuous-time and discrete behaviours. Simulation is one of the tools to obtain insight in dynamical systems behaviour. Simulation results provide information on performance of system and are helpful in detecting potential weaknesses and errors. Moreover, the results are handy in choosing adequate control strategies and parameters. In our contribution we report a work in progress, a technique for simulation of Behavioural Hybrid Process Calculus, an extension of process algebra that is suitable for the modelling and analysis of hybrid systems

Viewpoint Development of Stochastic Hybrid Systems

Nowadays, due to the explosive spreading of networked and highly distributed systems, mastering system complexity becomes a critical issue. Two development and verification paradigms have become more popular: viewpoints and randomisation. The viewpoints offer large freedom and introduce concurrency and compositionality in the development process. Randomisation is now a traditional method for reducing complexity (comparing with deterministic models) and it offers finer analytical analysis tools (quantification over non-determinism, multi-valued logics, etc). In this paper, we propose a combination of these two paradigms introducing a viewpoint methodology for systems with stochastic behaviours

Constitutive hybrid processes

Introduction When modeling a physical system, it is common practice to describe the components that constitute the system, using so-called constitutive relations on the physical variables that play a role in the system. The intersection of all these relations then forms a model of the system as a whole. The behavior of physical systems is usually assumed to be continuous and, therefore, the constitutive relations are often stated as differential algebraic equations. When part of the continuous behavior occurs very fast, however, as is for example the case when studying impact phenomena, it may be convenient to describe this behavior as being discontinuous. The constitutive relations that are used to describe the system, should in that case not only contain algebraic differential equations (for the large time-scale behavior), but using also equations that describe the discontinuous behavior (for the behavior during impact). In this report, we describe the constitutive relations of many more-or-less standard components in physical modeling, using the hybrid process algebra HyPA [4]. This algebra allows us to describe combinations of continuous and discontinuous behavior as one, hybrid, process (hence, the title of this report). As a vehicle for our thoughts, we use a graphical language named bond graphs [11] to formalize our physical models, before engaging in the construction of constitutive relations for them. Bond graphs generalize all domains of physics, such as electronics, hydraulics, and mechanics, in one framework. Recently, they have been extended with elements that are suitable for describing discontinuous behavior [10, 9, 1, 12]. This report, can therefore also be considered an attempt to give a formal semantics to hybrid bond graphs. Our expectation is, that after we have explained how to derive hybrid constitutive processes using hybrid bond graphs, it will also be easier to derive these processes directly, without using bond graphs as an intermediate step. Nevertheless, the construction of a bond graph sometimes gives additional insight in the workings of a system, and can facilitate analysis in many ways (see for example [8, 14, 3, 2]). In general, different model representations have strengths in different kinds of analysis. In the next section, we give a short discussion on the modeling of physical systems through constitutive relations, using an example from mechanical engineering. Then, we briefly explain the traditional bond graph modeling method and discuss the need for abstraction from small timescale behavior. In section 3 we briefly discuss the syntax and semantics of hybrid process algebra [4]. In section 4, we turn back to the bond graph modeling formalism, to see how the constitutive relations of the bond graph elements can be extended to include discontinuous behavior. In the last section, we give modeling examples that show how hybrid bond graph models can be made of several physical systems, and how these bond graph models can be turned into constitutive hybrid processes describing the systems algebraically

Constitutive hybrid processes

Introduction When modeling a physical system, it is common practice to describe the components that constitute the system, using so-called constitutive relations on the physical variables that play a role in the system. The intersection of all these relations then forms a model of the system as a whole. The behavior of physical systems is usually assumed to be continuous and, therefore, the constitutive relations are often stated as differential algebraic equations. When part of the continuous behavior occurs very fast, however, as is for example the case when studying impact phenomena, it may be convenient to describe this behavior as being discontinuous. The constitutive relations that are used to describe the system, should in that case not only contain algebraic differential equations (for the large time-scale behavior), but using also equations that describe the discontinuous behavior (for the behavior during impact). In this report, we describe the constitutive relations of many more-or-less standard components in physical modeling, using the hybrid process algebra HyPA [4]. This algebra allows us to describe combinations of continuous and discontinuous behavior as one, hybrid, process (hence, the title of this report). As a vehicle for our thoughts, we use a graphical language named bond graphs [11] to formalize our physical models, before engaging in the construction of constitutive relations for them. Bond graphs generalize all domains of physics, such as electronics, hydraulics, and mechanics, in one framework. Recently, they have been extended with elements that are suitable for describing discontinuous behavior [10, 9, 1, 12]. This report, can therefore also be considered an attempt to give a formal semantics to hybrid bond graphs. Our expectation is, that after we have explained how to derive hybrid constitutive processes using hybrid bond graphs, it will also be easier to derive these processes directly, without using bond graphs as an intermediate step. Nevertheless, the construction of a bond graph sometimes gives additional insight in the workings of a system, and can facilitate analysis in many ways (see for example [8, 14, 3, 2]). In general, different model representations have strengths in different kinds of analysis. In the next section, we give a short discussion on the modeling of physical systems through constitutive relations, using an example from mechanical engineering. Then, we briefly explain the traditional bond graph modeling method and discuss the need for abstraction from small timescale behavior. In section 3 we briefly discuss the syntax and semantics of hybrid process algebra [4]. In section 4, we turn back to the bond graph modeling formalism, to see how the constitutive relations of the bond graph elements can be extended to include discontinuous behavior. In the last section, we give modeling examples that show how hybrid bond graph models can be made of several physical systems, and how these bond graph models can be turned into constitutive hybrid processes describing the systems algebraically