Order Graphs and Cross-Layer Parametric Significance-Driven Modelling

Abstract

Traditional hierarchical modelling methods tend to have layers of abstraction corresponding to naturally existing layers of concern in multi-level systems. Although logically and functionally intuitive, this is not always optimal for analysis and design. For instance, parts of a system in the same logical layer may not contribute to the same degree on some metric, e.g. system power consumption. When focusing on a specific parameter or set of parameters, to moderate the analysis, design and runtime effort, less significant parts of the system should be modelled at higher levels of abstraction and more significant ones with more detail. This parametric significance-driven modelling approach focuses more on optimal parametric fidelity than on logical intuition. Using system power consumption as an example parameter, this paper presents Order Graphs (OGs), which have a clear hierarchical structure, and provide straightforward vertical zooming across multiple layers (orders) of model abstraction, resulting in the discovery of power-proportional cuts that run through different orders to be analysed together in a flat manner. Stochastic Activity Networks (SANs), a good flat modelling method, is suggested as an example of studying techniques for cuts discovered with OGs. A series of experiments on an Odroid development system consisting of an ARM big.LITTLE multicore structure provides initial validation for the approach.

Error-Based Metric for Cross-Layer Cut Determination

“…The workflow of the proposed method is illustrated in Figure 2. A hierarchical representation of the system resources in the form of an Order Graph (OG) [14] is derived from the system design knowledge. The behaviour of the system is captured in a detailed SAN model [16].…”

“…The distance from the root relates to the level of abstraction. The formal definition and properties can be found in [14].…”

“…Non-functional parameters like power also open up further ways to systematic model simplifications based on what may be called the "significance factor" [14]. During any particular operation of a heterogeneous system consisting of multiple parts, some parts of the system may consume more power than other parts.…”

On structuring holistic fault tolerance

“…One promising technique to ensure HFT scalability is Order Graphs [8], which support a rigorous selection of the level of detail at which models are reasoned about. In terms of energy consumption the efficient way is to focus only on the components that consume substantial amounts of energy (see our previous work on modelling many-core system fidelity [9]).…”

Architecting Holistic Fault Tolerance

“…At the moment we are applying Order Graphs [18] to support modelling and to make the HFT approach suitable for the general case. As part of our future work and further development of the HFT architecture we are planning to undertake the evaluation of the HFT architecture.…”