Scheduling with Explorable Uncertainty

We introduce a novel model for scheduling with explorable uncertainty. In this model, the processing time of a job can potentially be reduced (by an a priori unknown amount) by testing the job. Testing a job j takes one unit of time and may reduce its processing time from the given upper limit p\u27_j (which is the time taken to execute the job if it is not tested) to any value between 0 and p\u27_j. This setting is motivated e.g. by applications where a code optimizer can be run on a job before executing it. We consider the objective of minimizing the sum of completion times on a single machine. All jobs are available from the start, but the reduction in their processing times as a result of testing is unknown, making this an online problem that is amenable to competitive analysis. The need to balance the time spent on tests and the time spent on job executions adds a novel flavor to the problem. We give the first and nearly tight lower and upper bounds on the competitive ratio for deterministic and randomized algorithms. We also show that minimizing the makespan is a considerably easier problem for which we give optimal deterministic and randomized online algorithms

Exact Speedup Factors and Sub-Optimality for Non-Preemptive Scheduling

Fixed priority scheduling is used in many real-time systems; however, both preemptive and non-preemptive variants (FP-P and FP-NP) are known to be sub-optimal when compared to an optimal uniprocessor scheduling algorithm such as preemptive earliest deadline first (EDF-P). In this paper, we investigate the sub-optimality of fixed priority non-preemptive scheduling. Specifically, we derive the exact processor speed-up factor required to guarantee the feasibility under FP-NP (i.e. schedulability assuming an optimal priority assignment) of any task set that is feasible under EDF-P. As a consequence of this work, we also derive a lower bound on the sub-optimality of non-preemptive EDF (EDF-NP). As this lower bound matches a recently published upper bound for the same quantity, it closes the exact sub-optimality for EDF-NP. It is known that neither preemptive, nor non-preemptive fixed priority scheduling dominates the other, in other words, there are task sets that are feasible on a processor of unit speed under FP-P that are not feasible under FP-NP and vice-versa. Hence comparing these two algorithms, there are non-trivial speedup factors in both directions. We derive the exact speed-up factor required to guarantee the FP-NP feasibility of any FP-P feasible task set. Further, we derive the exact speed-up factor required to guarantee FP-P feasibility of any constrained-deadline FP-NP feasible task set

Development and certification of mixed-criticality embedded systems based on probabilistic timing analysis

An increasing variety of emerging systems relentlessly replaces or augments the functionality of mechanical subsystems with embedded electronics. For quantity, complexity, and use, the safety of such subsystems is an increasingly important matter. Accordingly, those systems are subject to safety certification to demonstrate system's safety by rigorous development processes and hardware/software constraints. The massive augment in embedded processors' complexity renders the arduous certification task significantly harder to achieve. The focus of this thesis is to address the certification challenges in multicore architectures: despite their potential to integrate several applications on a single platform, their inherent complexity imperils their timing predictability and certification. Recently, the Measurement-Based Probabilistic Timing Analysis (MBPTA) technique emerged as an alternative to deal with hardware/software complexity. The innovation that MBPTA brings about is, however, a major step from current certification procedures and standards. The particular contributions of this Thesis include: (i) the definition of certification arguments for mixed-criticality integration upon multicore processors. In particular we propose a set of safety mechanisms and procedures as required to comply with functional safety standards. For timing predictability, (ii) we present a quantitative approach to assess the likelihood of execution-time exceedance events with respect to the risk reduction requirements on safety standards. To this end, we build upon the MBPTA approach and we present the design of a safety-related source of randomization (SoR), that plays a key role in the platform-level randomization needed by MBPTA. And (iii) we evaluate current certification guidance with respect to emerging high performance design trends like caches. Overall, this Thesis pushes the certification limits in the use of multicore and MBPTA technology in Critical Real-Time Embedded Systems (CRTES) and paves the way towards their adoption in industry.Una creciente variedad de sistemas emergentes reemplazan o aumentan la funcionalidad de subsistemas mecánicos con componentes electrónicos embebidos. El aumento en la cantidad y complejidad de dichos subsistemas electrónicos así como su cometido, hacen de su seguridad una cuestión de creciente importancia. Tanto es así que la comercialización de estos sistemas críticos está sujeta a rigurosos procesos de certificación donde se garantiza la seguridad del sistema mediante estrictas restricciones en el proceso de desarrollo y diseño de su hardware y software. Esta tesis trata de abordar los nuevos retos y dificultades dadas por la introducción de procesadores multi-núcleo en dichos sistemas críticos: aunque su mayor rendimiento despierta el interés de la industria para integrar múltiples aplicaciones en una sola plataforma, suponen una mayor complejidad. Su arquitectura desafía su análisis temporal mediante los métodos tradicionales y, asimismo, su certificación es cada vez más compleja y costosa. Con el fin de lidiar con estas limitaciones, recientemente se ha desarrollado una novedosa técnica de análisis temporal probabilístico basado en medidas (MBPTA). La innovación de esta técnica, sin embargo, supone un gran cambio cultural respecto a los estándares y procedimientos tradicionales de certificación. En esta línea, las contribuciones de esta tesis están agrupadas en tres ejes principales: (i) definición de argumentos de seguridad para la certificación de aplicaciones de criticidad-mixta sobre plataformas multi-núcleo. Se definen, en particular, mecanismos de seguridad, técnicas de diagnóstico y reacción de faltas acorde con el estándar IEC 61508 sobre una arquitectura multi-núcleo de referencia. Respecto al análisis temporal, (ii) presentamos la cuantificación de la probabilidad de exceder un límite temporal y su relación con los requisitos de reducción de riesgos derivados de los estándares de seguridad funcional. Con este fin, nos basamos en la técnica MBPTA y presentamos el diseño de una fuente de números aleatorios segura; un componente clave para conseguir las propiedades aleatorias requeridas por MBPTA a nivel de plataforma. Por último, (iii) extrapolamos las guías actuales para la certificación de arquitecturas multi-núcleo a una solución comercial de 8 núcleos y las evaluamos con respecto a las tendencias emergentes de diseño de alto rendimiento (caches). Con estas contribuciones, esta tesis trata de abordar los retos que el uso de procesadores multi-núcleo y MBPTA implican en el proceso de certificación de sistemas críticos de tiempo real y facilita, de esta forma, su adopción por la industria.Postprint (published version

Scheduling (Dagstuhl Seminar 16081)

This report documents the program and the outcomes of Dagstuhl Seminar 16081 "Scheduling". The seminar was centered around recent new developments, discussion of open problems and exploring future research directions within the broader scheduling community