Presentation title

A New Model for Measuring the Performance Cost of Deadline Misses

Authors

Paolo Pazzaglia, Luigi Pannocchi, Alessandro Biondi and Marco Di Natale

Institution(s)

Scuola Superiore Sant'Anna, Pisa, Italy

Presentation type

Technical presentation

Abstract

Most works in schedulability analysis theory are based on the assumption that constraints on the performance of the application can be expressed by a very limited set of timing constraints (often simply hard deadlines) on a task model. This model is insufficient to represent a large number of systems in which deadlines can be missed, or in which late task responses affect the performance, but not the correctness of the application. For systems with a possible temporary overload, models like the m-K deadline have been proposed in the past. However, the m-K model has several limitations since it does not consider the state of the system and is largely unaware of the way in which the performance is affected by deadline misses (except for critical failures). In this work, we present a state-based representation of the evolution of a system with respect to each deadline hit or miss event. We consider a task actuation implemented using the LET paradigm, where the control output is updated at the task deadlines. When a job misses its deadline, the control output is not updated. The LET implementation imposes fixed delays of the control output, thus enabling a precise analysis of the control system. First, the freshness of the control output is extracted for each step of the possible sequences of hit and missed deadlines, considering different handling methods for the deadline miss event. Then, the corresponding sequence of update matrices for the state variables is constructed, and a performance value is assigned to the sequence. The sum of squared errors is chosen as a representative performance index. The proposed approach allows extracting useful information such as worst-case performance bounds and critical sequences of deadline hits/misses with respect to a target performance. Our representation is much more general (while hopefully concise enough) to represent the evolution in time of the performance of time-sensitive systems with possible time overloads. We provide the theoretical foundations for our model and also show an application to a simple system to give examples of the state representations and their use.

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Additional material

• Presentation slides: [pdf]

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