Abstract
The paper discusses the problem of performance and timing parameters with respect to the validation of digital instrumentation and control systems (I&C). Statistical methods often implicitly assume that the probability distribution law of the estimated parameters is close to normal. Thus, the confidence intervals for the parameter are determined on the grounds of this assumption. However, we encountered cases when the delay distribution law in I&C is not normal. In these cases, we used the non-statistical network calculus method for time parameters estimation. The network calculus method is well elaborated for lossless digital system models with seamless processing algorithm depending only on data volume. We consider the extension of the method to the case of I&C systems with considerable changes in the data flow and content-dependent processing disciplines. The model is restricted to systems with cyclic processing algorithms and fast network connections. Network calculus describes the data flow and system parameters in terms of flow envelopes and service curves that are generally unknown in advance. In this paper, we define equations that allow the calculation of these characteristics from experimental data. The correspondence of the Network Calculus and classical statistical estimation methods is discussed. Additionally, we give an example of model application to a real I&C system.
Highlights
Modern instrumental and control systems (I&C) for industrial facilities are implemented in most cases as a distributed digital environment
Incomparing network calculus computed delays with delays obtained bymodel the statisthis paper,the having analyzed these drawbacks, we develop a mathematical of tical methods; the digital I&C system
The flow envelope and service curve will have pend on the probability distribution law of processing time and on the sam sections composed of data close in value, sorted in descending order for the flow envelope andand thethe number and amplitude individual outliers inservice the data
Summary
Modern instrumental and control systems (I&C) for industrial facilities are implemented in most cases as a distributed digital environment. The distinctive feature of the network calculus method is the use of specific functions to calculate delay and buffering parameters (service curves and envelopes of input and output data flow). Mathematics 2021, 9, 1732 parallel processing of multiple tasks on same computing resource; significant change in the amount of information at the input and output of a component (for example, when a component compresses information); С heterogeneity of data in a digital control system, in contrast to the information in streaming systems; it means that each element of data (bit) has its own value and can be processed according to a proper algorithm. A simple correlation with other characteristics (input investigated two subproblems that are of separate interest: data rate, burstiness, computational power of the component) becomes awkward. Where h is the maximal horizontal distance between two curves
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