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The# language is a hybrid language for modeling, simulation and verification. As a result of the recently completed formal semantics, the language now consists of a number of orthogonal operators that operate on all process terms, including differential algebraic equations. The same # model can be used for simulation and verification. Verification is possible after a straightforward syntactical translation of the model. Simulation related information is clearly separated from the other statements. Copyright 2003 IFAC Keywords: Simulation, Simulation Languages, Formal Verification, Formal Languages.

Abstract. The verification formalism / modeling and simulation language hybrid Chi is defined. The semantics of hybrid Chi is formally specified using Structured Operational Semantics (SOS) and a number of associated functions. The χ syntax and semantics can also deal with local scoping of variables and/or channels, implicit differential algebraic equations, such as higher index systems, and they are very well suited for specification of pure discrete event systems. 1

this report. In practice, often the discrete part of a hybrid system is described and analysed using methods from computer science, while the continuous part is handled by control science. Because the analysis of the interaction between the discrete and continuous part is extremely difficult, the design of the complete system is usually such that this interaction is suppressed to a minimum. This is the main *This work was financed by Progress/STW Grant EES5173 reason for the development of a theory on hybrid systems. If we can obtain more insight in the interaction between discrete and continuous behaviour, we can get rid of the current restrictions on the design of a hybrid system. In the remainder of this report, system theory, automata theory and process theory, are referred to as classical theories, as opposed to combinations of those in hybrid theories. Our ultimate goal is a syntactical algebraic structure that can serve as a modeling framework for hybrid systems and in which we can do symbolic analysis. As will become clear in the next section, such an algebra should have an underlying mathematical structure that reflects the meaning of the algebraic operators. This underlying structure must be intuitive from both a control science and a computer science point of view

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Abstract. The language χ is a modeling and simulation language which is currently mainly used to analyse and optimize the performance of industrial systems. To be able to also verify functional properties of a system using a χ model, part of the language has been given a formal semantics. Rather than implementing a new model checker for χ, the philosophy is to provide automatic translations from χ into the specification languages of existing state-of-the-art model checkers such as, e.g., Spin and UPPAAL. In this paper, we propose for χ a notion of stuttering congruence, which is an adaptation of the notion of stuttering equivalence. We prove that our notion preserves the validity of CTL ∗ −X formulas, that it preserves deadlock, and that it is indeed a congruence with respect to the constructs of χ. We also indicate how our notion is to be used to establish confidence in the correctness of a translation from χ into Promela. 1

Abstract—We propose the model of discrete-time probabilistic reward graphs (DTPRGs) for performance analysis of systems exhibiting discrete deterministic time delays and probabilistic behavior, via their interpretation as discrete-time Markov reward chains. We build on the χ environment, a full-fledged platform for qualitative and quantitative analysis of timed systems based on the modeling language χ. The extension proposed in this paper is based on timed branching bisimulation reduction followed by a tailored inclusion of probabilities and rewards. The approach is applied in an industrial case study of a turntable drill. The resulting performance measures are shown to be comparable to those obtained by existent methods of the χ environment, viz. simulation and continuous-time Markovian analysis. I.

(met een samenvatting in het Nederlands)

Two different lines of research are presented in the study of an industrially relevant problem of impact control. One is focused on actual control of the process, while the other is focused on the development of a general language for modeling hybrid systems, of which the case study is an appropriate example.

The model used in this report focuses on the analysis of ship waiting statistics and stock fluctuations under different arrival processes. However, the basic outline is the same: central to both models are a jetty and accompanying tankfarm facilities belonging to a new chemical plant in the Port of Rotterdam. Both the supply of raw materials and the export of finished products occur through ships loading and unloading at the jetty. Since disruptions in the plants production process are very expensive, buffer stock is needed to allow for variations in ship arrivals and overseas exports through large ships. Ports provide jetty facilities for ships to load and unload their cargo. Since ship delays are costly, terminal operators attempt to minimize their number and duration. Here, simulation has proved to be a very suitable tool. However, in port simulation models, the impact of the arrival process of ships on the model outcomes tends to be underestimated. This article considers three arrival processes: stock-controlled, equidistant per ship type, and Poisson. We assess how their deployment in a port simulation model, based on data from a real case study, affects the efficiency of the loading and unloading process. Poisson, which is the chosen arrival process in many client-oriented simulations, actually performs worst in terms of both ship delays and required storage capacity. Stock-controlled arrivals perform best with regard to ship delays and required storage capacity. In the case study two types of arrival processes were considered. The first type are the so-called stock-controlled arrivals, i.e., ship arrivals are scheduled in such a way, that a base stock level is maintained in the tanks. Given a base stock level of a raw material or ...